Model generation method and device of thin-wall structure, engineering machinery and medium

Abstract

The invention relates to a thin-wall structure model generation method and device, engineering machinery and a medium, and relates to the technical field of engineering machinery. The model generation method comprises the following steps: discretizing a thin-wall structure into a plurality of shell units by utilizing a finite element analysis method, wherein each shell unit in the plurality of shell units comprises a plurality of nodes; dividing the first mass value of the thin-wall structure into a second mass value corresponding to each node in the plurality of nodes, and determining the translational inertia force of each shell unit according to the second mass value and the position vector of each node in the global coordinate system; dividing the first rotational inertia value of the thin-wall structure into a second rotational inertia value corresponding to each node, and determining the rotational inertia force of each shell unit according to the second rotational inertia value and the angular velocity vector and the angular acceleration vector of each node under the global coordinate system; and generating a dynamic model of the thin-wall structure according to the translation inertia force and the rotation inertia force.

Description

Technical Field

[0001] This disclosure relates to the field of engineering machinery technology, and in particular to a method, apparatus, engineering machinery and medium for generating models of thin-walled structures. Background Technology

[0002] Thin-walled structures are commonly used in engineering practice; they can be composed of thin plates, thin shells, and slender rods. Thin-walled structures can withstand large loads with relatively little weight and material. Due to their strong flexibility and encapsulation properties, thin-walled structures are frequently used in packaging, transportation, and storage.

[0003] In the design of engineering machinery with thin-walled structures (such as solar panels, automobile chassis systems, crane booms, etc.), it is usually necessary to perform dynamic analysis on the thin-walled structure in order to accurately and efficiently predict the nonlinear dynamic response of the thin-walled structure and ensure that the designed engineering machinery has the corresponding performance.

[0004] In related technologies, the nonlinear dynamic response of thin-walled structures is predicted by constructing a dynamic model of the thin-walled structure. Summary of the Invention

[0005] The inventors of this disclosure have discovered the following problems in the above-mentioned related technologies: the accuracy of constructing dynamic models of thin-walled structures is low, resulting in low reliability of performance analysis of engineering machinery with thin-walled structures.

[0006] To address the aforementioned problems, the present disclosure provides the following solutions.

[0007] According to some embodiments of this disclosure, a method for generating a model of a thin-walled structure is provided, comprising: discretizing the thin-walled structure into multiple shell elements using finite element analysis, each shell element including multiple nodes; dividing a first mass value of the thin-walled structure into a second mass value corresponding to each of the multiple nodes, and determining the translational inertial force of each shell element based on the second mass value and the position vector of each node in the global coordinate system; dividing a first rotational inertia value of the thin-walled structure into a second rotational inertia value corresponding to each node, and determining the rotational inertial force of each shell element based on the second rotational inertia value, the angular velocity vector and the angular acceleration vector of each node in the global coordinate system; and generating a dynamic model of the thin-walled structure based on the translational inertial force and the rotational inertial force.

[0008] In some embodiments, determining the translational inertial force of each shell unit includes: determining the velocity vector and acceleration vector of each node in the global coordinate system based on the position vector of each node in the global coordinate system, and determining the translational inertial force based on the second mass value and the sum of the vector products of the velocity vector and acceleration vector of each node in the global coordinate system; and / or determining the rotational inertial force of each shell unit includes: determining the rotational inertial force based on the second moment of inertia value and the sum of the vector products of the angular velocity vector and angular acceleration vector of each node in the global coordinate system.

[0009] In some embodiments, the plurality of nodes includes a first node and at least one second node, wherein the first node coincides with the centroid of the thin-walled structure when the thin-walled structure is not deformed, and the first proportion of the second mass value corresponding to the first node in the first mass value is greater than the second proportion of the second mass value corresponding to the at least one second node in the first mass value.

[0010] In some embodiments, the at least one second node includes a plurality of second nodes, wherein the second quality value corresponding to each of the plurality of second nodes has a second proportion in the first quality value.

[0011] In some embodiments, each shell unit is a triangular shell unit, and the at least one second node includes the three vertices of the triangular shell unit, with the first proportion being three-quarters and the second proportion being one-twelfth.

[0012] In some embodiments, the plurality of nodes includes a first node and at least one second node, wherein the first node coincides with the center of mass of the thin-walled structure when the thin-walled structure is not deformed, and determining the translational inertial force of each shell element includes: determining the displacement vector of the first node in the co-rotation coordinate system based on the displacement vector of the center of mass in the co-rotation coordinate system; determining the position vector of the first node in the global coordinate system based on the displacement vector of the first node in the co-rotation coordinate system and the rotation matrix of the co-rotation coordinate system relative to the global coordinate system; and determining the translational inertial force based on the second mass value corresponding to the first node, the second mass value corresponding to the second node, the position vector of the first node in the global coordinate system, and the position vector of the at least one second node in the global coordinate system.

[0013] In some embodiments, the proportion of the second mass value corresponding to the first node in the first mass value is a first proportion, and the proportion of the second mass value corresponding to the at least one second node in the first mass value is a second proportion. Determining the displacement vector of the first node in the co-rotation coordinate system includes: determining the displacement vector of the first node in the co-rotation coordinate system based on the product of the displacement vector of the at least one second node in the co-rotation coordinate system and the second proportion, the displacement vector of the center of mass in the co-rotation coordinate system and the first proportion.

[0014] In some embodiments, the plurality of nodes includes a first node and at least one second node, wherein the first node coincides with the center of mass of the thin-walled structure when the thin-walled structure is not deformed, and the third proportion of the second moment of inertia value corresponding to the first node in the first moment of inertia value is greater than the fourth proportion of the second moment of inertia value corresponding to the at least one second node in the first moment of inertia value.

[0015] In some embodiments, the proportion of the second quality value corresponding to the first node in the first quality value is the first proportion, the proportion of the second quality value corresponding to the at least one second node in the first quality value is the second proportion, the third proportion is the same as the first proportion, and the fourth proportion is the same as the second proportion.

[0016] In some embodiments, the plurality of nodes includes a first node and at least one second node, wherein the first node coincides with the center of mass of the thin-walled structure when the thin-walled structure is not deformed, and determining the rotational inertia force of each shell element includes: determining the rotation vector of the first node in a co-rotational coordinate system based on the shape function of each shell element and the coordinates of the at least one second node in the natural coordinate system; and determining the angular velocity vector and angular acceleration vector of the first node in the global coordinate system based on the rotation vector of the first node in the co-rotational coordinate system.

[0017] In some embodiments, generating the dynamic model of the thin-walled structure based on the translational inertial force and the rotational inertial force includes: establishing the virtual power equation of the thin-walled structure based on the translational inertial force and the rotational inertial force; and generating the dynamic model of the thin-walled structure based on the virtual power equation.

[0018] According to some embodiments of this disclosure, a model generation apparatus for a thin-walled structure is provided, comprising: a discretization processing module configured to discretize the thin-walled structure into a plurality of shell elements using a finite element analysis method, each of the plurality of shell elements including a plurality of nodes; a first determining module configured to divide a first mass value of the thin-walled structure into a second mass value corresponding to each of the plurality of nodes, and determine the translational inertial force of each shell element based on the second mass value and the position vector of each node in a global coordinate system; a second determining module configured to divide a first rotational inertia value of the thin-walled structure into a second rotational inertia value corresponding to each node, and determine the rotational inertial force of each shell element based on the second rotational inertia value, the angular velocity vector and the angular acceleration vector of each node in the global coordinate system; and a generation module configured to generate a dynamic model of the thin-walled structure based on the translational inertial force and the rotational inertial force.

[0019] According to further embodiments of this disclosure, a model generation apparatus for thin-walled structures is provided, comprising: a memory; and a processor coupled to the memory, the processor being configured to execute the model generation method of any of the above embodiments based on instructions stored in the memory device.

[0020] According to further embodiments of this disclosure, an engineering machine is provided, including a thin-walled structure, wherein a dynamic model of the thin-walled structure is generated based on the model generation method in any of the above embodiments, and the dynamic model is used for performance analysis of the engineering machine.

[0021] According to further embodiments of the present disclosure, a computer-readable storage medium is provided that stores computer instructions thereon, which, when executed by a processor, implement the model generation method of any of the above embodiments.

[0022] According to further embodiments of this disclosure, a computer program product is also provided, including instructions that, when executed by a processor, cause the processor to perform the model generation method according to any of the foregoing embodiments.

[0023] In the above embodiments, the thin-walled structure is discretized into multiple shell elements using the finite element method. By distributing the mass and moment of inertia of the thin-walled structure to the nodes of each shell element, the translational and rotational inertial forces of each shell element are determined. This approach can accurately describe the influence of the distribution of the mass and moment of inertia of the thin-walled structure on the inertial forces generated by the thin-walled structure under bending, torsion, and other deformations, thereby effectively improving the accuracy of the dynamic model of the thin-walled structure. Attached Figure Description

[0024] The accompanying drawings, which form part of this specification, illustrate embodiments of this disclosure and, together with the specification, serve to explain the principles of this disclosure.

[0025] This disclosure will become clearer with reference to the accompanying drawings and the following detailed description, wherein:

[0026] Figure 1 A flowchart illustrating a method for generating a model of a thin-walled structure according to some embodiments of the present disclosure is shown.

[0027] Figure 2 A flowchart illustrating a method for determining the position vector of a first node in a global coordinate system according to some embodiments of the present disclosure;

[0028] Figure 3 A flowchart illustrating a method for generating a model of a thin-walled structure according to other embodiments of the present disclosure is shown;

[0029] Figure 4 A block diagram of a model generation apparatus for thin-walled structures according to some embodiments of the present disclosure is shown;

[0030] Figure 5 A block diagram of a model generation apparatus for thin-walled structures according to other embodiments of the present disclosure is shown;

[0031] Figure 6 A block diagram of a model generation apparatus for thin-walled structures according to some embodiments of the present disclosure is shown. Detailed Implementation

[0032] Various exemplary embodiments of the present disclosure will now be described in detail with reference to the accompanying drawings. It should be noted that, unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the present disclosure.

[0033] At the same time, it should be understood that, for ease of description, the dimensions of the various parts shown in the accompanying drawings are not drawn according to actual scale.

[0034] The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit this disclosure or its application or use.

[0035] Techniques, methods, and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and equipment should be considered part of the specification.

[0036] In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values.

[0037] It should be noted that similar labels and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be discussed further in subsequent figures.

[0038] Flexible multibody systems composed of interconnected thin-walled structures exhibit geometrically nonlinear dynamic responses under dynamic external loads. As mentioned earlier, accurate and efficient prediction of the nonlinear dynamic response of thin-walled structures is of great significance for the structural design and maintenance of engineering machinery.

[0039] However, in related technologies, the dynamic models of thin-walled structures are usually constructed based on the assumption that the mass of the thin-walled structure is concentrated at its center of mass. While this approach is simple and computationally efficient, it neglects the continuous distribution of mass in the actual structure. For thin-walled structures (such as thin plates and shells), the mass distribution has a significant impact on the dynamic response to deformations such as bending and torsion. This simplification cannot accurately describe the dynamic characteristics of thin-walled structures under deformation, resulting in low accuracy of the constructed dynamic models.

[0040] The inventors of this disclosure have discovered that, in order to accurately reflect the dynamic characteristics of thin-walled structures, the constructed dynamic model needs to accurately describe the inertial forces of the thin-walled structure. The description of these inertial forces is influenced by both the mass of the thin-walled structure (corresponding to its translational inertial force) and its rotational inertia (corresponding to its rotational inertial force). If both the mass and rotational inertia of the thin-walled structure are treated equivalently at the center of mass, the constructed dynamic model will be unable to accurately describe the influence of mass distribution on the translational inertial force and the influence of rotational inertia distribution on the rotational inertial force, resulting in low accuracy of the dynamic model.

[0041] In view of this, this disclosure proposes a model generation method for thin-walled structures. First, the complex geometry of the thin-walled structure is accurately fitted by the flexible mesh generation in the finite element analysis method. Then, the mass and rotational inertia of the thin-walled structure are respectively distributed to each node of the shell element used to simulate the thin-walled structure, so as to accurately calculate the translational inertial force and rotational inertial force of each shell element. Thus, the dynamic model of the thin-walled structure is generated based on the translational inertial force and rotational inertial force of each shell element.

[0042] In this approach, by distributing the mass and moment of inertia of the thin-walled structure equally across the nodes of the shell element, compared to treating the mass and moment of inertia of the thin-walled structure equally at the center of mass, the influence of the distribution of the mass and moment of inertia of the thin-walled structure on the inertial forces generated by the thin-walled structure under bending, torsion, and other deformations can be accurately described. This effectively improves the accuracy of the dynamic model of the thin-walled structure and helps to analyze the dynamic response characteristics of the thin-walled structure more accurately.

[0043] Figure 1 A flowchart illustrating a method for generating a model of a thin-walled structure according to some embodiments of the present disclosure is shown.

[0044] like Figure 1 As shown, in step 110, the thin-walled structure is discretized into multiple shell elements using the finite element analysis method. Here, each shell element includes multiple nodes.

[0045] The finite element method (FEM) can discretize a continuous, complex solution domain (such as a mechanical structure) into a finite number of interconnected sub-regions (also called "elements"). Each element (e.g., triangular shell elements, quadrilateral shell elements, etc.) is connected to other elements through nodes, forming a "finite element mesh" for the entire structure; this process is called "meshing." Within each element, the physical quantities of the mechanical structure (such as displacement, temperature, stress, thickness, material properties, etc.) can be approximated using interpolation functions (also called "shape functions"), thus constructing a digital model corresponding to the mechanical structure that can be analyzed and calculated in a computer.

[0046] In some embodiments, triangular shell elements can be used to describe thin-walled structures. For example, each shell element is a triangular shell element, and each triangular shell element has corresponding thickness and material information, which can simulate the mechanical behavior of thin-walled structures such as stress and deformation. Each node of the triangular shell element has at least 6 degrees of freedom. For example, each node has 3 translational degrees of freedom (e.g., translational motion along the X, Y, and Z axes of the global coordinate system) and 3 rotational degrees of freedom (e.g., rotational motion about the X, Y, and Z axes of the global coordinate system).

[0047] Thus, compared to quadrilateral shell elements or other curved shell elements, triangular shell elements can more accurately fit the local geometric details of thin-walled structures, effectively improving the accuracy of describing the dynamic behavior of thin-walled structures without increasing the overall degrees of freedom.

[0048] In step 120, the first mass value of the thin-walled structure is divided into a second mass value corresponding to each of the multiple nodes, and the translational inertial force of each shell element is determined based on the second mass value corresponding to each node and the position vector of each node in the global coordinate system.

[0049] In some embodiments, the proportion of the second quality value corresponding to different nodes in the first quality value may be the same or different.

[0050] For example, the proportion of the second mass value corresponding to different nodes in each shell element to the first mass value can be the same, that is, the first mass value can be proportionally distributed to different nodes.

[0051] For example, the proportion of the second mass value in the first mass value is different for any two nodes in each shell element.

[0052] For example, each shell element includes multiple groups of nodes of different types, and each group of nodes includes one or more nodes. Within the same group of nodes, the proportion of the second mass value corresponding to each node in the first mass value is the same; however, the proportion of the second mass value corresponding to nodes in different groups of nodes is different.

[0053] In some embodiments, based on the position vector of each node in the global coordinate system, the velocity vector and acceleration vector of each node in the global coordinate system can be determined, and then based on the second mass value corresponding to each node, the velocity vector and acceleration vector of each node in the global coordinate system, the translational inertial force of each shell element can be determined.

[0054] For example, by taking the first derivative of the position vector of each node in the global coordinate system with respect to time, we can obtain the velocity vector of each node in the global coordinate system; by taking the second derivative of the position vector of each node in the global coordinate system with respect to time, we can obtain the acceleration vector of each node in the global coordinate system.

[0055] In step 130, the first moment of inertia of the thin-walled structure is divided into a second moment of inertia corresponding to each node, and the rotational inertia force of each shell element is determined based on the second moment of inertia corresponding to each node, the angular velocity vector and the angular acceleration vector of each node in the global coordinate system.

[0056] In some embodiments, the proportion of the second moment of inertia value corresponding to different nodes in the first moment of inertia value may be the same or different.

[0057] For example, the proportion of the second moment of inertia value corresponding to different nodes in each shell element to the first moment of inertia value can be the same, that is, the first moment of inertia value can be proportionally distributed to different nodes.

[0058] For example, the proportion of the second moment of inertia value in the first moment of inertia value is different for any two nodes in each shell element.

[0059] For example, each shell element includes multiple groups of nodes of different types, and each group of nodes includes one or more nodes. The proportion of the second moment of inertia value in the first moment of inertia value is the same for each node in the same group, while the proportion of the second moment of inertia value in the first moment of inertia value is different for nodes in different groups.

[0060] In step 140, a dynamic model of the thin-walled structure is generated based on the translational and rotational inertial forces of each shell element. For example, the dynamic model of the thin-walled structure can be used to perform performance analysis on engineering machinery with thin-walled structures.

[0061] In some embodiments, a virtual power equation for the thin-walled structure is established based on the translational and rotational inertial forces of each shell element, and a dynamic model of the thin-walled structure is generated based on this virtual power equation. For example, a virtual power equation for each shell element is established based on the translational and rotational inertial forces of each shell element, and a dynamic model of the thin-walled structure is established based on the virtual power equation of each shell element and the positional distribution of each shell element.

[0062] In the above embodiments, the thin-walled structure is discretized into multiple shell elements using the finite element method. By distributing the mass and moment of inertia of the thin-walled structure to the nodes of each shell element, the translational and rotational inertial forces of each shell element are determined. This approach can accurately describe the influence of the distribution of the mass and moment of inertia of the thin-walled structure on the inertial forces generated by the thin-walled structure under bending, torsion, and other deformations, thereby effectively improving the accuracy of the dynamic model of the thin-walled structure.

[0063] The following examples illustrate the method for determining the translational inertial force of each shell element in the model generation method proposed in this disclosure.

[0064] In some embodiments, the velocity vector and acceleration vector of each node in the global coordinate system are determined based on the position vector of each node in the global coordinate system. Then, the translational inertial force of each shell element is determined based on the second mass value corresponding to each node and the sum of the vector products of the velocity vector and acceleration vector of each node in the global coordinate system.

[0065] For example, each shell element includes n nodes, where the second mass value corresponding to the i-th node is... The position vector of the i-th node in the global coordinate system is The velocity vector of the i-th node in the global coordinate system is The acceleration vector is The translational inertial force of each shell element can be expressed as: , where the operator Represents the imaginary variation operation, operator Represents a vector or matrix ( The transpose operation of ).

[0066] It should be noted that if dynamic modeling is performed on every point on the thin-walled structure (e.g., calculating the velocity and acceleration vectors at each point), and then the inertial force of the overall structure is calculated by surface domain integration, then the quadratic continuous integral needs to be discretized into nested multi-level Gaussian integrals during the surface domain integration process. Although this process can improve the accuracy of the inertial force description, it significantly increases the computational complexity of the inertial force and the amount of computation required to generate the dynamic model, resulting in a large consumption of computational resources in the dynamic model generation process.

[0067] In other words, the method of establishing a dynamic model of a thin-walled structure through surface domain integration is difficult to simultaneously meet the requirements of modeling accuracy and computational cost in practical applications.

[0068] Therefore, in the above embodiments, by equivalently distributing the first mass value of the thin-walled structure to a finite number of nodes in the shell element, the translational inertial force corresponding to each node can accurately describe the influence of the mass distribution on the translational inertial force. Based on this, the translational inertial force of each shell element can be obtained by summing the vector products of the second mass value, velocity vector, and acceleration vector corresponding to each node (i.e., multi-point summation).

[0069] This approach effectively reduces the computational complexity of inertial forces compared to establishing a dynamic model of a thin-walled structure through surface domain integration. It also reduces the amount of computation required to generate the dynamic model, thereby improving the accuracy of the dynamic model of the thin-walled structure while effectively reducing the consumption of computational resources in the generation process and lowering the computational cost.

[0070] In some embodiments, the plurality of nodes in each shell element include a first node and a second node, wherein the first node (also referred to as an auxiliary node of each shell element) coincides with the centroid of the thin-walled structure when the thin-walled structure is not deformed.

[0071] In some embodiments, the first proportion of the second quality value corresponding to the first node in the first quality value is greater than the second proportion of the second quality value corresponding to the second node in the first quality value.

[0072] In this approach, considering that the center of mass of the thin-walled structure will shift before and after deformation, the dynamic characteristics of the center of mass before and after deformation are described by introducing a first node (i.e., an auxiliary node) and giving the first node a larger equivalent mass. This effectively improves the ability of the dynamic model to represent the inertial response of the thin-walled structure before and after deformation, thereby improving the accuracy of the generated dynamic model of the thin-walled structure.

[0073] In some embodiments, the number of first nodes and second nodes can be one or more. For example, the plurality of nodes in each shell unit includes one first node and at least one second node.

[0074] In some embodiments, at least one second node may include multiple second nodes, i.e., the number of second nodes is multiple. The second mass value corresponding to each of the multiple second nodes has a second proportion in the first mass value equal to this proportion. For example, the multiple second nodes in each shell element may include multiple vertices of each shell element.

[0075] In the above embodiments, the proportion of the second mass value corresponding to each second node in each shell element, excluding the first node (i.e., the auxiliary node) used to describe the dynamic characteristics of the center of mass, is kept consistent within the first mass value. In this way, by having the first node bear a large portion of the mass of the thin-walled structure, while each second node shares the remaining mass in the same proportion, the generated dynamic model can effectively characterize the translational inertial force response of the overall structure while retaining sensitivity to local strain, thereby further improving the accuracy of the generated dynamic model of the thin-walled structure.

[0076] In some embodiments, each shell element is a triangular shell element, and the plurality of second nodes include the three vertices of the triangular shell element.

[0077] In this way, when solving the translational inertial force of each shell element by multi-point summation, since the position vector of each shell element vertex in the global coordinate system is a constant value that can be determined after mesh generation, no additional solution is required. Therefore, the computational complexity of the inertial force is further reduced, and the amount of computation required to generate the dynamic model is reduced. Thus, while improving the accuracy of the dynamic model of the thin-walled structure, the computational resources consumed in the generation process of the dynamic model are effectively reduced, and the computational cost is lowered.

[0078] In some embodiments, the first proportion of the second quality value corresponding to the first node in the first quality value can be set to three-quarters, and the second proportion of the second quality value corresponding to each second node in the first quality value can be one-twelfth.

[0079] In this way, mass allocation based on this allocation ratio ensures that the introduction of the first node (i.e., the auxiliary node) enhances the representation capability of the centroid. It also ensures that the translational inertial force of the shell element remains equivalent before and after the calculation method is changed from continuous surface domain integration to discrete multi-point summation (i.e., translational kinetic energy is equivalent). This reduces computational complexity and amount without sacrificing the accuracy of the inertial force representation, thus improving the accuracy of the dynamic model of the thin-walled structure.

[0080] The process of determining the scheme in which the first proportion is three-quarters and the second proportion is one-twelfth is described below through some embodiments.

[0081] Considering that thin-walled structures exhibit rigid body motion with large displacements and rotations under dynamic loads, while maintaining relatively small local strain, the corotational coordinate method can accurately calculate the elastic strain of shell elements in a corotational coordinate system that moves with the shell elements. Furthermore, its calculation process is independent of the type of shell element, exhibiting good shell element reusability and simplifying the modeling process. Therefore, this disclosure combines finite element analysis with the corotational coordinate method for dynamic analysis of thin-walled structures.

[0082] In the global coordinate system, the moment of inertia J of the triangular shell element can be expressed as:

[0083] Formula (1)

[0084] in, Let be the moment of inertia of the triangular shell element in the co-rotational coordinate system. Let be the rotation matrix of the co-rotating coordinate system relative to the global coordinate system. , , These represent the thickness, density, and area of ​​the triangular shell unit, respectively. (Operator) Represents a vector or matrix ( The antisymmetric tensor of ) The natural coordinates of the three second nodes of the triangular shell element in the natural coordinate system can be used to determine the natural coordinates of the elements. Sure.

[0085] For example, ,in, The three vertices of the triangular shell unit The coordinate vector in the global coordinate system when the thin-walled structure is deformed.

[0086] Will Substituting into the above formula (1), the moment of inertia J of the triangular shell element can be obtained as:

[0087] Formula (2)

[0088] in, Let be the coordinate vector of the centroid of the triangular shell element in the global coordinate system when the thin-walled structure is not deformed, and m represent the first mass value of the thin-walled structure (i.e., the total mass of the thin-walled structure).

[0089] Based on the above formula (2), it can be determined that, in the case that the thin-walled structure does not deform, the equivalent mass allocated to the first node (coinciding with the center of mass) of the triangular shell element is 9m / 12, that is, 3m / 4, and the equivalent mass allocated to each second node of the triangular shell element is 1m / 12.

[0090] Thus, it can be determined that the first proportion of the second mass value corresponding to the first node (i.e., the auxiliary node) used to describe the dynamic characteristics of the center of mass in each shell element is 3 / 4, and the second proportion of the second mass value corresponding to each second node in each shell element other than the first node is 1 / 12.

[0091] It should be noted that, as those skilled in the art will understand, the global coordinate system is a fixed reference coordinate system that does not change with structural deformation, the co-rotation coordinate system is a local coordinate system that translates and rotates with the deformation of the particle, and the natural coordinate system is a local coordinate system that moves with the motion of the particle. The natural coordinate system follows the trajectory of the particle and is mainly used to analyze the motion of the particle along its path (such as changes in the tangential and normal directions); the co-rotation coordinate system follows the rigid body rotation of the particle in the deformable body and is mainly used to analyze the local deformation of the object.

[0092] In the above embodiments, based on the introduction of a first node (i.e., an auxiliary node) to describe the dynamic characteristics of the center of mass, and considering that the first node and the center of mass coincide when the thin-walled structure is not deformed, the first proportion and the second proportion are solved by using the natural coordinates of each vertex in the triangular shell element in the natural coordinate system, with the goal of keeping the mass and moment of inertia of the discretized shell element consistent with the mass and moment of inertia of the continuous structure before discretization when the thin-walled structure is not deformed.

[0093] In this way, mass allocation based on this ratio ensures that the translational inertial force of the shell element remains equivalent before and after the calculation method is changed from continuous surface domain integration to discrete multi-point summation (i.e., translational kinetic energy is equivalent). This reduces computational complexity and amount without sacrificing the accuracy of the inertial force representation, thus improving the accuracy of the dynamic model of thin-walled structures.

[0094] The following examples illustrate how to determine the position vector of the first node (i.e., the auxiliary node) in the global coordinate system.

[0095] Figure 2 A flowchart illustrating a method for determining the position vector of a first node in a global coordinate system according to some embodiments of the present disclosure is shown.

[0096] like Figure 2As shown, in step 210, the displacement vector of the first node in the co-rotation coordinate system is determined based on the displacement vector of the centroid of the thin-walled structure in the co-rotation coordinate system.

[0097] It should be noted that the position vector of any node in each shell element in the global coordinate system refers to a directed line segment originating from the origin of the global coordinate system and ending at the location of that node. The displacement vector of any node in the co-rotational coordinate system refers to a directed line segment originating from the node's position before deformation and ending at its position after deformation. For example, any node can be the first node, the second node, or the centroid.

[0098] When the thin-walled structure remains unchanged, the first node coincides with the centroid of the thin-walled structure. Therefore, the position vector of the first node in the global coordinate system is the same as the position vector of the centroid of the thin-walled structure in the global coordinate system. When the thin-walled structure deforms, the first node does not coincide with the centroid of the thin-walled structure. In this case, considering that the co-rotation coordinate method can decompose the motion of the shell element into rigid body motion with the translation and rotation of the thin-walled structure in the global coordinate system and local deformation occurring in the co-rotation coordinate system, the position vector of the first node in the global coordinate system can be determined based on the displacement vector of the centroid of the thin-walled structure in the co-rotation coordinate system, taking advantage of the characteristic that the co-rotation coordinate system moves with the deformation of the mass.

[0099] In step 220, the position vector of the first node in the global coordinate system is determined based on the displacement vector of the first node in the co-rotation coordinate system and the rotation matrix of the co-rotation coordinate system relative to the global coordinate system.

[0100] In some embodiments, the rotation matrix of the co-rotating coordinate system relative to the global coordinate system converts the displacement vector of the first node in the co-rotating coordinate system into the position vector in the global coordinate system.

[0101] Taking a triangular shell element as an example, the vector consisting of the global motion description parameters of the triangular shell element is defined as follows: , and These represent the three second nodes of the triangular shell element. And the first node (i.e., the auxiliary node) (i=4) Position and rotation vectors in the global coordinate system.

[0102] The rotation matrix of the co-rotating coordinate system relative to the global coordinate system is: Angular velocity vector is Angular acceleration vector is The corresponding expression is:

[0103] Formula (3)

[0104] in, The coordinate vectors of the three basis vectors in a co-rotating coordinate system can be obtained using... Fully defined This is the coefficient matrix of the angular velocity vector.

[0105] The vector consisting of the local motion description parameters of the triangular shell element is defined as follows: , and These represent the three second nodes of the triangular shell element. And the first node (i.e., the auxiliary node) (i=4) Displacement and rotation vectors in the co-rotating coordinate system.

[0106] Establish First-order rate of change vector With the second-order rate of change vector The relation is:

[0107] Formula (4)

[0108] in, is the projection matrix of the co-rotating coordinate system.

[0109] After the thin-walled structure deforms, the displacement vector of the origin of the corotating coordinate system is:

[0110] Formula (5)

[0111] Based on the rotation matrix in formula (3) The displacement vector of the first node in the co-rotation coordinate system can be... Convert to position vector in global coordinate system .

[0112] It should be noted that, since the center of mass will shift when a thin-walled structure deforms, if the position vector of the center of mass before deformation in the global coordinate system is still determined as the position vector of the first node in the global coordinate system, the position vector of the first node in the global coordinate system will not accurately reflect the position of the center of mass after deformation, which will have an adverse effect on the determination of the subsequent inertial force.

[0113] Therefore, in the above embodiments, considering that the displacement vector of the center of mass in the co-rotation coordinate system can reflect the displacement of the center of mass during deformation, the position vector of the first node in the global coordinate system can be determined by the displacement vector of the center of mass in the co-rotation coordinate system. This can accurately describe the position vector of the first node in the global coordinate system before and after deformation, improve the accuracy of the subsequently determined inertial force, and thus improve the accuracy of the dynamic model of the generated thin-walled structure.

[0114] In some embodiments, in step 210, the displacement vector of the first node in the co-rotation coordinate system can be determined based on the displacement vector of at least one second node in the co-rotation coordinate system and the displacement vector of the centroid of the thin-walled structure in the co-rotation coordinate system.

[0115] For example, the displacement vector of the first node in the co-rotation coordinate system is determined based on the product of the displacement vector of at least one second node in the co-rotation coordinate system and the second proportion, the first proportion, and the displacement vector of the centroid of the thin-walled structure in the co-rotation coordinate system.

[0116] Continuing with the example above where each shell element is a triangular shell element, the displacement vector of the centroid of the thin-walled structure in the co-rotational coordinate system is: It can be represented as:

[0117] Formula (6)

[0118] in, Let be the coefficient matrix of the displacement vector of the centroid in the corotating coordinate system, and it is a constant matrix. The coordinates of the three second nodes of the triangular shell element in the co-rotation coordinate system can be determined. Here, the coordinates of the three second nodes of the triangular shell element in the co-rotation coordinate system are constant values ​​that are determined after meshing using the triangular shell element. These constant values ​​are related to the dimensions of the triangular shell element in the case of a thin-walled structure without deformation.

[0119] Assuming the second proportion is 1 / 12 and the first proportion is 3 / 4, using this mass distribution ratio as the displacement distribution ratio, the relationship between the displacement vector of the centroid of the thin-walled structure in the co-rotation coordinate system and the displacement vector of at least one second node in the co-rotation coordinate system, as well as the displacement vector of the first node in the co-rotation coordinate system, can be obtained as follows:

[0120] Formula (7)

[0121] According to formulas (4) and (5), the displacement vector of the first node in the co-rotation coordinate system can be obtained. for:

[0122] Formula (8)

[0123] in, It is a constant matrix.

[0124] In the above embodiments, the mass distribution ratio (such as the first ratio and the second ratio) is used as the displacement distribution ratio, and the displacement vector of the first node in the co-rotation coordinate system is determined accordingly by using the displacement vector of at least one second node in the co-rotation coordinate system.

[0125] In this way, since the displacement vector in the co-rotating coordinate system can reflect the relative displacement caused by structural deformation, the displacement vector of the center of mass in the co-rotating coordinate system is equivalent to the weighted average of the displacement vectors of the second node and the first node in the co-rotating coordinate system, according to the same displacement distribution ratio as the mass distribution ratio. This allows for an accurate description of the relative displacement of the center of mass after deformation in the co-rotating coordinate system, thereby accurately deriving the displacement vector of the first node in the co-rotating coordinate system. This helps improve the accuracy of subsequent determination of inertial forces, and further helps improve the accuracy of the generated dynamic model of the thin-walled structure.

[0126] In some embodiments, after step 220, the translational inertial force of each shell element can be determined based on the second mass value corresponding to the first node, the second mass value corresponding to the second node, the position vector of the first node in the global coordinate system, and the position vector of at least one second node in the global coordinate system.

[0127] For example, based on the multi-point summation method described above, the translational inertial force of each shell element can be determined as follows: ,in, (i=1,2,3) represents the second quality value corresponding to the i-th second node. This represents the velocity vector of the i-th second node in the global coordinate system. The acceleration vector of the i-th second node in the global coordinate system This represents the second quality value corresponding to the first node. This represents the velocity vector of the first node in the global coordinate system. This represents the acceleration vector of the first node in the global coordinate system.

[0128] Next, we will provide an exemplary description of how the rotational inertia force of each shell element is determined in the model generation method proposed in this disclosure, with reference to some embodiments.

[0129] In some embodiments, the rotational inertia force of each shell element is determined based on the second moment of inertia value corresponding to each node, the sum of the vector products of the angular velocity vector and the angular acceleration vector of each node in the global coordinate system.

[0130] For example, each shell element includes n nodes, where the second moment of inertia corresponding to the i-th node is value The angular velocity vector of the i-th node in the global coordinate system is The angular acceleration vector of the i-th node in the global coordinate system is The rotational inertial force of each shell element can be expressed as: , where the operator Represents the imaginary variation operation, operator Represents a vector or matrix ( The transpose operator () Represents a vector or matrix ( The antisymmetric tensor.

[0131] In the above embodiments, by equivalently distributing the first moment of inertia of the thin-walled structure to a finite number of nodes in the shell element, the rotational inertia force corresponding to each node can accurately describe the influence of the moment of inertia distribution on the rotational inertia force. Based on this, the rotational inertia force of each shell element can be obtained by summing the vector products of the second moment of inertia, angular velocity vector, and angular acceleration vector corresponding to each node (i.e., multi-point summation).

[0132] This approach effectively reduces the computational complexity of inertial forces compared to establishing a dynamic model of a thin-walled structure through surface domain integration. It also reduces the amount of computation required to generate the dynamic model, thereby improving the accuracy of the dynamic model of the thin-walled structure while effectively reducing the consumption of computational resources in the generation process and lowering the computational cost.

[0133] In some embodiments, the third proportion of the second moment of inertia value corresponding to the first node in the first moment of inertia value is greater than the fourth proportion of the second moment of inertia value corresponding to at least one second node in the first moment of inertia value.

[0134] In this approach, considering that the center of mass of the thin-walled structure will shift before and after deformation, the dynamic characteristics of the center of mass before and after deformation are described by introducing a first node (i.e., an auxiliary node) and giving the first node a larger equivalent moment of inertia. This effectively improves the ability of the dynamic model to characterize the inertial response of the thin-walled structure before and after deformation, thereby improving the accuracy of the generated dynamic model of the thin-walled structure.

[0135] In some embodiments, the third proportion of the second moment of inertia value corresponding to the first node in the first moment of inertia value is the same as the first proportion of the second mass value corresponding to the first node in the first mass value; the fourth proportion of the second moment of inertia value corresponding to at least one second node in the first moment of inertia value is the same as the second proportion of the second mass value corresponding to the second node in the first mass value.

[0136] For example, at least one second node may include multiple second nodes, each having a second proportion in the first mass value equal to the second mass value corresponding to each of the multiple second nodes. Correspondingly, each second moment of inertia value has a fourth proportion in the first moment of inertia value corresponding to each of the multiple second nodes.

[0137] Therefore, by using the mass distribution ratio as the rotational inertia distribution ratio for calculating the rotational inertia value, the generated dynamic model can retain the sensitivity to local strain while effectively characterizing the rotational inertia force response of the overall structure, thereby further improving the accuracy of the generated dynamic model of the thin-walled structure.

[0138] For example, the second moment of inertia value corresponding to the first node can be set to account for three-quarters of the first moment of inertia value, and the second moment of inertia value corresponding to each second node can account for one-twelfth of the first moment of inertia value.

[0139] In this way, the rotational inertial force of the shell element can remain equivalent before and after the calculation method is changed from continuous surface domain integration to discrete multi-point summation (i.e., rotational kinetic energy is equivalent). This reduces the computational complexity and amount of computation without sacrificing the accuracy of the inertial force representation, thus improving the accuracy of the dynamic model of thin-walled structures.

[0140] Next, we will illustrate, with reference to some embodiments, how to determine the angular velocity vector and angular acceleration vector of the first node (i.e., the auxiliary node) in the global coordinate system.

[0141] In some embodiments, the co-rotation coordinate method can decompose the motion of the shell element into rigid body motion with the translation and rotation of the thin-walled structure in the global coordinate system and local deformation occurring in the co-rotation coordinate system. When the thin-walled structure is not deformed, the rotation vector of the first node in the co-rotation coordinate system is 0; when the thin-walled structure is deformed, the angular velocity vector and angular acceleration vector of the first node in the global coordinate system can be determined based on the rotation vector of the first node in the co-rotation coordinate system.

[0142] In some embodiments, the rotation vector of the first node in the co-rotation coordinate system is determined based on the shape function of each shell element and the coordinates of at least one second node in the natural coordinate system. Then, the angular velocity vector and angular acceleration vector of the first node in the global coordinate system are determined based on the rotation vector of the first node in the co-rotation coordinate system.

[0143] For example, the shape function of each triangular shell element is: The rotation vector of the first node in the co-rotation coordinate system for:

[0144] Formula (9)

[0145] in, It is a constant matrix. This represents the natural coordinates of the i-th second node among the three second nodes of the triangular shell element in the natural coordinate system.

[0146] Based on the rotation vector of the first node in the co-rotation coordinate system The first-order rate of change determines the angular velocity vector of the first node in the co-rotation coordinate system, based on the rotation vector of the first node in the co-rotation coordinate system. The second-order rate of change determines the angular acceleration vector of the first node in the co-rotating coordinate system.

[0147] It should be understood that shape functions are continuous functions defined within shell elements and related to coordinates in the finite element analysis method.

[0148] Next, combined Figure 3 The model generation method proposed in this disclosure will be further explained.

[0149] Figure 3 A flowchart illustrating a method for generating a model of a thin-walled structure according to other embodiments of the present disclosure is shown. For example... Figure 3 As shown, Figure 3 The model generation method shown can be used as Figure 1 An example of the model generation method shown is used to perform this.

[0150] In step 310, the mesh data for the thin-walled structure is prepared. For example, the thin-walled structure is discretized into multiple shell elements using the finite element method. Each shell element includes multiple nodes.

[0151] In some embodiments, a geometric model of a thin-walled structure is established, and a mesh with multiple shell elements (e.g., triangular shell elements) is generated using mesh generation software based on the finite element analysis method. The material information and thickness information of each shell element are then assigned.

[0152] In step 320, the co-rotation coordinate system of the shell element is established.

[0153] For example, the co-rotation coordinate system of the shell unit can be established by referring to the relevant processes in formulas (3) to (5) above. The relevant explanations can be found in the descriptions in the previous embodiments, and will not be repeated here.

[0154] In step 330, the velocity vector, acceleration vector, angular velocity vector, and angular acceleration vector of each node in the shell element in the global coordinate system are determined.

[0155] In some embodiments, each shell element includes a first node and at least one second node. For example, each shell element is a triangular shell element, the first node coincides with the centroid of the thin-walled structure when the thin-walled structure is not deformed, and at least one second node includes the three vertices of the triangular shell element.

[0156] In some embodiments, the displacement vector of the first node in the co-rotation coordinate system is determined based on the displacement vector of the center of mass in the co-rotation coordinate system. The position vector of the first node in the global coordinate system is determined based on the displacement vector of the first node in the co-rotation coordinate system and the rotation matrix of the co-rotation coordinate system relative to the global coordinate system. The velocity vector and acceleration vector of each node in the global coordinate system are determined based on the position vector of each node in the global coordinate system.

[0157] The following example uses a triangular shell element for each shell element. First, we determine the three second nodes of the triangular shell element. The implementation of velocity and acceleration vectors in the global coordinate system is explained.

[0158] The three second nodes of the triangular shell element The position vector in the global coordinate system is:

[0159] Formula (10)

[0160] in, Let be the position vector of the i-th second node of the triangular shell element in the global coordinate system when the thin-walled structure has not deformed; is a constant vector.

[0161] The position vector of the i-th second node in the global coordinate system Calculate the first and second derivatives with respect to time to obtain the velocity vector of the i-th second node in the global coordinate system. and acceleration vector for:

[0162] Formula (11)

[0163] in, It is a constant matrix. , and The identity matrix and the zero matrix are 3×3 respectively.

[0164] The three second nodes of the triangular shell element Angular velocity vector in global coordinate system for:

[0165] Formula (12)

[0166] in, The coefficient matrix, , This is the global angular velocity operator matrix. , , operator Represents a vector or matrix ( The antisymmetric tensor.

[0167] The angular velocity vector of the i-th second node in the global coordinate system Take the first derivative with respect to time to obtain the angular acceleration vector of the i-th second node in the global coordinate system. for:

[0168] Formula (13)

[0169] in, The coefficient matrix, .

[0170] The following section determines the first node of the triangular shell element. The implementation of velocity and acceleration vectors in the global coordinate system is explained.

[0171] When the thin-walled structure does not deform, the first node coincides with the centroid of the thin-walled structure. Therefore, the position vector of the first node in the global coordinate system is the same as the position vector of the centroid of the thin-walled structure in the global coordinate system.

[0172] When a thin-walled structure deforms, the position vector of the first node in the global coordinate system Displacement vector of the centroid of a thin-walled structure in a corotating coordinate system Sure.

[0173] As shown in the previous formula (6), the displacement vector of the centroid of the thin-walled structure in the co-rotation coordinate system is: It can be represented as ,in, Let be the coefficient matrix of the displacement vector of the centroid in the corotating coordinate system, and it is a constant matrix.

[0174] Assuming the triangular shell element is obtained by combining OPT membrane elements and DKT plate elements, then the coefficient matrix is:

[0175] Formula (14)

[0176] in, , , , and Let x and y be the x-axis and y-axis coordinates of the i-th second node of the triangular shell element in the co-rotation coordinate system when the thin-walled structure has not undergone deformation.

[0177] Assuming the second proportion is 1 / 12 and the first proportion is 3 / 4, this mass distribution ratio is used as the displacement distribution ratio. As shown in the aforementioned formula (7), the displacement vector of the centroid of the thin-walled structure in the co-rotation coordinate system, the displacement vector of at least one second node in the co-rotation coordinate system, and the displacement vector of the first node in the co-rotation coordinate system satisfy the following relationship: .

[0178] Therefore, as shown in the aforementioned formula (8), the displacement vector of the first node in the co-rotation coordinate system can be obtained. for: ,in, It is a constant matrix.

[0179] Based on the displacement vector of the first node in the co-rotating coordinate system and the rotation matrix in formula (3) This allows us to obtain the displacement vector of the first node in the global coordinate system. , that is ,for:

[0180] Formula (15)

[0181] in, is the position vector of the origin of the corotating coordinate system in the global coordinate system.

[0182] The position vector of the first node in the global coordinate system Take the first and second derivatives with respect to time to obtain the velocity vector of the first node in the global coordinate system. and acceleration vector for:

[0183] Formula (16)

[0184] in, , It is a constant matrix. , .

[0185] Next, the implementation method for determining the angular velocity vector and angular acceleration vector of the first node of the triangular shell element in the global coordinate system will be explained.

[0186] The rotation vector of the first node in the co-rotation coordinate system can be determined according to the aforementioned formula (9). According to the rotation vector of the first node in the co-rotation coordinate system Determine the angular velocity vector of the first node in the co-rotating coordinate system. for:

[0187] Formula (17)

[0188] in, The local angular velocity vector operator matrix, This is the projection matrix of the corotating coordinate system in formula (4). Those skilled in the art are familiar with the local angular velocity vector operator matrix. The derivation of will not be repeated here.

[0189] Based on the principle of angular velocity superposition, determine the angular velocity vector of the first node in the global coordinate system. for:

[0190] Formula (18)

[0191] In formula (3) Substituting into formula (8), we get:

[0192] Formula (19)

[0193] in, .

[0194] The angular velocity vector of the first node in the global coordinate system Taking the first derivative with respect to time, we obtain the angular acceleration vector of the first node in the global coordinate system. for:

[0195] Formula (20)

[0196] in, .

[0197] In step 340, the translational inertial force and rotational inertial force of each shell element are determined.

[0198] In some embodiments, the velocity vector and acceleration vector of each node in the global coordinate system are determined based on the position vector of each node in the global coordinate system, and the translational inertial force of each shell element is determined based on the second mass value and the sum of the vector products of the velocity vector and acceleration vector of each node in the global coordinate system.

[0199] In some embodiments, the rotational inertia force of each shell element is determined based on the second moment of inertia value corresponding to each node, the sum of the vector products of the angular velocity vector and the angular acceleration vector of each node in the global coordinate system.

[0200] The following example illustrates how to determine the translational and rotational inertial forces of each shell element, taking a triangular shell element as an example, where each shell element includes a first node and at least one second node.

[0201] For example, at least one second node includes multiple second nodes. The translational inertial force of each shell element is determined based on the second mass value corresponding to the first node, the second mass value corresponding to each second node, the velocity vector and acceleration vector of the first node in the global coordinate system, and the velocity vector and acceleration vector of each second node in the global coordinate system.

[0202] Assume that the first proportion of the second quality value corresponding to the first node in the first quality value is 3 / 4, and the second proportion of the second quality value corresponding to each second node in the first quality value is 1 / 12.

[0203] By distributing the first mass value of the thin-walled structure to each node of the triangular shell element according to this mass distribution ratio, the translational inertial force of each shell element can be converted from the calculation method of continuous surface domain integration to the calculation method of discrete multi-point summation. For example, the translational inertial force of each shell element is:

[0204] Formula (21)

[0205] Where m represents the first quality value, and the operator... Represents the imaginary variation operation, operator Represents a vector or matrix ( The transpose operation of ).

[0206] The velocity vector of the first node in the global coordinate system in formula (16) and acceleration vector Substituting into formula (21), we get:

[0207] Formula (22)

[0208] in, , , and These can be referred to as the translational inertial force vector contributed by the acceleration vector of the shell element and the translational inertial force vector contributed by the velocity vector of the shell element, respectively.

[0209] Using the aforementioned mass distribution ratio as the rotational inertia distribution ratio (i.e., the third proportion of the second rotational inertia value corresponding to the first node in the first rotational inertia value is 3 / 4, and the fourth proportion of the second rotational inertia value corresponding to each second node in the first rotational inertia value is 1 / 12), the first rotational inertia value of the thin-walled structure is distributed to each node of the triangular shell element, thus obtaining the first rotational inertia value of each shell element relative to the i-th (i=1,2,3) second node. The corresponding second moment of inertia value and the first node The corresponding second moment of inertia value They are respectively:

[0210] , Formula (23)

[0211] Based on this, the rotational inertial force of each shell element can be calculated by converting the method of continuous surface domain integration into a method of discrete multi-point summation. For example, the rotational inertial force of each shell element is:

[0212] Formula (24)

[0213] in, , For nodes The local rotation matrix relative to the co-rotating coordinate system.

[0214] Angular velocity vector of each node and angular acceleration vector Substituting into formula (24), we get:

[0215] Formula (25)

[0216] in, , coefficient matrix The expression is , For nodes The global angular velocity vector operator matrix, and Calculated using formulas (19) and (20), and These can be referred to as the rotational inertial force vector contributed by the acceleration vector of the shell element and the rotational inertial force vector contributed by the velocity vector of the shell element, respectively.

[0217] In step 350, based on the principle of virtual power, the virtual power equation for each shell element is determined to generate a dynamic model of the thin-walled structure.

[0218] For example, by summing the translational inertial force shown in formula (22) and the rotational inertial force shown in formula (25), we can obtain the inertial force of each shell element as follows:

[0219] Formula (26)

[0220] in, This represents the mass matrix of each shell element. It can be called the inertial force vector contributed by the acceleration vector of the shell element. It can be called the inertial force vector contributed by the velocity vector of the shell element.

[0221] Based on the principle of virtual power and formula (26), the virtual power equation for each shell element is established as follows:

[0222] Formula (27)

[0223] in, This represents the virtual power of the elastic force in each shell element. This represents the virtual power of external forces for each shell element. Those skilled in the art are familiar with the derivation methods of the virtual power of elastic forces and the virtual power of external forces, which will not be elaborated here.

[0224] Based on the virtual power equation shown in formula (27), the dynamic model for generating the thin-walled structure is as follows:

[0225] Formula (28)

[0226] in, , The external force vector is determined by the virtual power of the external forces in each shell element. The external elastic force vector is determined by the virtual power of the elastic force in each shell element. It is the inertial force vector.

[0227] In some embodiments, after establishing a dynamic model of the thin-walled structure, the performance of engineering machinery with a thin-walled structure can be analyzed using this dynamic model. For example, explicit integration algorithms or implicit integration algorithms (such as the Newmark method) can be used to perform numerical integration on the dynamic model of the thin-walled structure to obtain one or more performance curves of the engineering machinery with a thin-walled structure, including displacement response curve, velocity response curve, kinetic energy curve, strain energy curve, and total energy curve. The performance of the engineering machinery can then be analyzed based on these performance curves.

[0228] It should be noted that, as can be understood here, Figure 3 The implementation of each step in the method shown is consistent with the previous text. Figures 1 to 2The implementation of the corresponding steps in the method shown is similar and can be achieved by referring to the methods in the relevant embodiments above. Related explanations can be found in the relevant embodiments above. They will not be repeated here.

[0229] Figure 4 A block diagram of a model generation apparatus for thin-walled structures according to some embodiments of the present disclosure is shown.

[0230] like Figure 4 As shown, the thin-walled structure model generation device 400 includes a discretization processing module 410, a first determination module 402, a second determination module 403, and a generation module 404.

[0231] The discretization module 401 can be configured to discretize the thin-walled structure into multiple shell elements using the finite element analysis method, wherein each shell element includes multiple nodes.

[0232] The first determining module 402 can be configured to divide the first mass value of the thin-walled structure into a second mass value corresponding to each of the multiple nodes, and determine the translational inertial force of each shell element based on the second mass value and the position vector of each node in the global coordinate system.

[0233] The second determining module 403 can be configured to divide the first moment of inertia of the thin-walled structure into a second moment of inertia corresponding to each node, and determine the rotational inertia force of each shell element based on the second moment of inertia, the angular velocity vector and the angular acceleration vector of each node in the global coordinate system.

[0234] The generation module 404 can be configured to generate a dynamic model of a thin-walled structure based on translational and rotational inertial forces.

[0235] In some embodiments, the first determining module 402 may be configured to determine the velocity vector and acceleration vector of each node in the global coordinate system based on the position vector of each node in the global coordinate system, and to determine the translational inertial force of each shell element based on the second mass value corresponding to each node and the sum of the vector products of the velocity vector and acceleration vector of each node in the global coordinate system.

[0236] In some embodiments, the second determining module 403 may be configured to determine the rotational inertia force of each shell element based on the second moment of inertia value corresponding to each node, the sum of the vector products of the angular velocity vector and the angular acceleration vector of each node in the global coordinate system.

[0237] In some embodiments, the plurality of nodes include a first node and at least one second node. The first node coincides with the centroid of the thin-walled structure when the thin-walled structure is not deformed. The first proportion of the second mass value corresponding to the first node in the first mass value is greater than the second proportion of the second mass value corresponding to the at least one second node in the first mass value.

[0238] In some embodiments, at least one second node includes a plurality of second nodes, wherein the second quality value corresponding to each of the plurality of second nodes has a second proportion in the first quality value.

[0239] In some embodiments, each shell element is a triangular shell element, and at least one second node includes the three vertices of the triangular shell element, with a first proportion of three-quarters and a second proportion of one-twelfth.

[0240] In some embodiments, the first determining module 402 may be configured to determine the displacement vector of the first node in the co-rotation coordinate system based on the displacement vector of the center of mass in the co-rotation coordinate system; determine the position vector of the first node in the global coordinate system based on the displacement vector of the first node in the co-rotation coordinate system and the rotation matrix of the co-rotation coordinate system relative to the global coordinate system; and determine the translational inertial force of each shell element based on the second mass value corresponding to the first node, the second mass value corresponding to the second node, the position vector of the first node in the global coordinate system, and the position vector of at least one second node in the global coordinate system.

[0241] In some embodiments, the proportion of the second mass value corresponding to the first node in the first mass value is the first proportion, and the proportion of the second mass value corresponding to at least one second node in the first mass value is the second proportion. The first determining module 402 can be configured to determine the displacement vector of the first node in the co-rotation coordinate system based on the product of the displacement vector of at least one second node in the co-rotation coordinate system and the second proportion, the displacement vector of the centroid in the co-rotation coordinate system, and the first proportion.

[0242] In some embodiments, the plurality of nodes include a first node and at least one second node. The first node coincides with the center of mass of the thin-walled structure when the thin-walled structure is not deformed. The third proportion of the second moment of inertia value corresponding to the first node in the first moment of inertia value is greater than the fourth proportion of the second moment of inertia value corresponding to the at least one second node in the first moment of inertia value.

[0243] In some embodiments, the proportion of the second quality value corresponding to the first node in the first quality value is the first proportion, the proportion of the second quality value corresponding to at least one second node in the first quality value is the second proportion, the third proportion is the same as the first proportion, and the fourth proportion is the same as the second proportion.

[0244] In some embodiments, the plurality of nodes include a first node and at least one second node. The first node coincides with the centroid of the thin-walled structure when the thin-walled structure is not deformed. The second determining module 403 can be configured to determine the rotation vector of the first node in the co-rotation coordinate system based on the shape function of each shell element and the coordinates of the at least one second node in the natural coordinate system; and to determine the angular velocity vector and angular acceleration vector of the first node in the global coordinate system based on the rotation vector of the first node in the co-rotation coordinate system.

[0245] In some embodiments, the generation module 404 can be configured to establish a virtual power equation for the thin-walled structure based on translational inertial force and rotational inertial force; and generate a dynamic model of the thin-walled structure based on the virtual power equation.

[0246] Figure 5 A block diagram of a model generation apparatus for thin-walled structures according to other embodiments of the present disclosure is shown.

[0247] like Figure 5 As shown, the thin-walled structure model generation apparatus 500 of this embodiment includes: a memory 501 and a processor 502 coupled to the memory 501. The processor 502 is configured to execute the model generation method of any embodiment of this disclosure based on instructions stored in the memory 501.

[0248] The memory 501 may include, for example, system memory, fixed non-volatile storage media, etc. The system memory may store, for example, an operating system, application programs, a boot loader, a database, and other programs.

[0249] Figure 6 A block diagram of a model generation apparatus for thin-walled structures according to some embodiments of the present disclosure is shown.

[0250] like Figure 6 As shown, the thin-walled structure model generation apparatus 600 of this embodiment includes: a memory 601 and a processor 602 coupled to the memory 601. The processor 602 is configured to execute the model generation method of any of the foregoing embodiments based on instructions stored in the memory 601.

[0251] The memory 601 may include, for example, system memory, fixed non-volatile storage media, etc. The system memory may store, for example, an operating system, application programs, a boot loader, and other programs.

[0252] The thin-walled structure model generation device 600 may also include an input / output interface 603, a network interface 604, and a storage interface 605. These interfaces 603, 604, and 605, as well as the memory 601 and processor 602, can be connected, for example, via a bus 606. Specifically, the input / output interface 603 provides a connection interface for input / output devices such as a monitor, mouse, keyboard, touchscreen, microphone, and speakers. The network interface 604 provides a connection interface for various networked devices. The storage interface 605 provides a connection interface for external storage devices such as SD cards and USB flash drives.

[0253] This disclosure also provides an engineering machinery, including a thin-walled structure. The dynamic model of the thin-walled structure is generated based on the model generation method in any of the foregoing embodiments. The dynamic model is used to perform performance analysis on the engineering machinery.

[0254] This disclosure also provides a computer-readable storage medium including computer program instructions that, when executed by a processor, implement the model generation method of any of the above embodiments.

[0255] This disclosure also provides a computer program product, including a computer program that, when executed by a processor, implements the model generation method of any of the above embodiments.

[0256] Those skilled in the art will understand that embodiments of this disclosure can be provided as methods, systems, or computer program products. Therefore, this disclosure can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this disclosure can take the form of a computer program product embodied on one or more computer-usable non-transitory storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0257] The model generation technique for thin-walled structures according to this disclosure has now been described in detail. To avoid obscuring the concept of this disclosure, some details known in the art have not been described. Those skilled in the art can fully understand how to implement the technical solutions disclosed herein based on the above description.

[0258] The methods and systems of this disclosure may be implemented in many ways. For example, they may be implemented by software, hardware, firmware, or any combination of software, hardware, and firmware. The above-described order of steps for the methods is for illustrative purposes only, and the steps of the methods of this disclosure are not limited to the specific order described above unless otherwise specifically stated. Furthermore, in some embodiments, this disclosure may also be implemented as a program recorded on a recording medium, the program including machine-readable instructions for implementing the methods according to this disclosure. Thus, this disclosure also covers recording media storing programs for performing the methods according to this disclosure.

[0259] While specific embodiments of this disclosure have been described in detail by way of example, those skilled in the art should understand that the examples are for illustrative purposes only and not intended to limit the scope of this disclosure. Those skilled in the art should understand that modifications can be made to the above embodiments without departing from the scope and spirit of this disclosure. The scope of this disclosure is defined by the appended claims.

Claims

1. A method for generating a model of a thin-walled structure, comprising: The thin-walled structure is discretized into multiple shell elements using the finite element analysis method, and each shell element includes multiple nodes. The first mass value of the thin-walled structure is divided into a second mass value corresponding to each of the plurality of nodes, and the translational inertial force of each shell element is determined based on the second mass value and the position vector of each node in the global coordinate system. The first moment of inertia of the thin-walled structure is divided into a second moment of inertia corresponding to each node, and the rotational inertia force of each shell element is determined based on the second moment of inertia, the angular velocity vector and the angular acceleration vector of each node in the global coordinate system. A dynamic model of the thin-walled structure is generated based on the translational inertial force and the rotational inertial force.

2. The model generation method according to claim 1, wherein: Determining the translational inertial force of each shell element includes: determining the velocity vector and acceleration vector of each node in the global coordinate system based on the position vector of each node in the global coordinate system, and determining the translational inertial force based on the second mass value and the sum of the vector products of the velocity vector and acceleration vector of each node in the global coordinate system; and / or Determining the rotational inertia force of each shell unit includes: determining the rotational inertia force based on the second moment of inertia value and the sum of the vector products of the angular velocity vector and the angular acceleration vector of each node in the global coordinate system.

3. The model generation method according to claim 1, wherein, The plurality of nodes includes a first node and at least one second node, wherein the first node coincides with the centroid of the thin-walled structure when the thin-walled structure does not deform. The first proportion of the second quality value corresponding to the first node in the first quality value is greater than the second proportion of the second quality value corresponding to the at least one second node in the first quality value.

4. The model generation method according to claim 3, wherein, The at least one second node includes a plurality of second nodes, wherein the second mass value corresponding to each of the plurality of second nodes has a second proportion in the first mass value that is equal.

5. The model generation method according to claim 3, wherein, Each shell unit is a triangular shell unit, and the at least one second node includes the three vertices of the triangular shell unit, with the first proportion being three-quarters and the second proportion being one-twelfth.

6. The model generation method according to any one of claims 1-5, wherein, The plurality of nodes includes a first node and at least one second node, wherein the first node coincides with the centroid of the thin-walled structure when the thin-walled structure does not deform. The determination of the translational inertial force of each shell unit includes: The displacement vector of the first node in the co-rotation coordinate system is determined based on the displacement vector of the centroid in the co-rotation coordinate system. The position vector of the first node in the global coordinate system is determined based on the displacement vector of the first node in the co-rotation coordinate system and the rotation matrix of the co-rotation coordinate system relative to the global coordinate system. The translational inertial force is determined based on the second mass value corresponding to the first node, the second mass value corresponding to the second node, the position vector of the first node in the global coordinate system, and the position vector of the at least one second node in the global coordinate system.

7. The model generation method according to claim 6, wherein, The proportion of the second quality value corresponding to the first node in the first quality value is the first proportion, and the proportion of the second quality value corresponding to the at least one second node in the first quality value is the second proportion. Determining the displacement vector of the first node in the co-rotating coordinate system includes: The displacement vector of the first node in the co-rotation coordinate system is determined based on the product of the displacement vector of the at least one second node in the co-rotation coordinate system and the second proportion, the displacement vector of the centroid in the co-rotation coordinate system and the first proportion.

8. The model generation method according to any one of claims 1-5, wherein, The plurality of nodes includes a first node and at least one second node, wherein the first node coincides with the centroid of the thin-walled structure when the thin-walled structure does not deform. The third proportion of the second moment of inertia value corresponding to the first node in the first moment of inertia value is greater than the fourth proportion of the second moment of inertia value corresponding to the at least one second node in the first moment of inertia value.

9. The model generation method according to claim 8, wherein, The proportion of the second quality value corresponding to the first node in the first quality value is the first proportion, and the proportion of the second quality value corresponding to the at least one second node in the first quality value is the second proportion. The third percentage is the same as the first percentage, and the fourth percentage is the same as the second percentage.

10. The model generation method according to any one of claims 1-5, wherein, The plurality of nodes includes a first node and at least one second node, wherein the first node coincides with the centroid of the thin-walled structure when the thin-walled structure does not deform. The determination of the rotational inertial force of each shell unit includes: Based on the shape function of each shell unit and the coordinates of the at least one second node in the natural coordinate system, determine the rotation vector of the first node in the co-rotation coordinate system; Based on the rotation vector of the first node in the co-rotation coordinate system, determine the angular velocity vector and angular acceleration vector of the first node in the global coordinate system.

11. The model generation method according to any one of claims 1-5, wherein, The process of generating the dynamic model of the thin-walled structure based on the translational inertial force and the rotational inertial force includes: Based on the translational inertial force and the rotational inertial force, establish the virtual power equation for the thin-walled structure; Based on the virtual power equation, a dynamic model of the thin-walled structure is generated.

12. A model generation device for thin-walled structures, comprising: The discretization module is configured to discretize the thin-walled structure into multiple shell elements using the finite element analysis method, each of the multiple shell elements including multiple nodes; The first determining module is configured to divide the first mass value of the thin-walled structure into a second mass value corresponding to each of the plurality of nodes, and determine the translational inertial force of each shell element based on the second mass value and the position vector of each node in the global coordinate system. The second determining module is configured to divide the first moment of inertia value of the thin-walled structure into a second moment of inertia value corresponding to each node, and determine the rotational inertia force of each shell unit based on the second moment of inertia value, the angular velocity vector and angular acceleration vector of each node in the global coordinate system; The generation module is configured to generate a dynamic model of the thin-walled structure based on the translational inertial force and the rotational inertial force.

13. A model generation device for thin-walled structures, comprising: Memory; and A processor coupled to the memory, the processor being configured to execute the model generation method of any one of claims 1-11 based on instructions stored in the memory.

14. An engineering machine, comprising: A thin-walled structure, wherein the dynamic model of the thin-walled structure is generated based on the model generation method according to any one of claims 1-11, and the dynamic model is used for performance analysis of the engineering machinery.

15. A computer-readable storage medium having stored thereon computer instructions that, when executed by a processor, implement the model generation method according to any one of claims 1-11.

16. A computer program product comprising instructions that, when executed by a processor, cause the processor to perform the model generation method according to any one of claims 1-11.

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