A finite element structure simulation method, device, medium, equipment and product

Abstract

Embodiments of the present application disclose a finite element structure simulation method, device, medium, equipment and product, the method comprises: obtaining constraint equations of an augmented matrix group; the constraint equations are expressed as: the sum of the first product and the second product is zero, the dependent degree of freedom vector in the constraint equations is determined by the independent degree of freedom vector, the weight coefficient matrix, the displacement matrix and the distribution matrix, the distribution matrix is determined by the weight coefficient matrix and the displacement matrix; determine the target weight coefficient matrix and the target displacement matrix, and substitute the target weight coefficient matrix and the target displacement matrix into the constraint equations to obtain the target constraint equations of the augmented matrix group. The present application can automatically calculate the weight coefficient matrix which accurately reflects the physical coupling strength between nodes and the displacement matrix which represents the real deformation state, generate the constraint equations, effectively solve the calculation accuracy defect caused by the simple assumption of the constraint relationship, and therefore can improve the effectiveness of the construction of the constraint equations.

Description

Technical Field

[0001] This invention relates to the field of finite element simulation calculation technology in solid mechanics, and in particular to a finite element structural simulation method, device, medium, equipment and product. Background Technology

[0002] In engineering finite element analysis, the finite element method (FEM) has become a core tool for handling multiphysics simulation problems involving structures, heat, and fluids.

[0003] In dealing with load distribution in the field of mechanics, the effectiveness of finite element model simulation calculations largely depends on the accuracy of the constraint equations. These constraint equations, as an important component of the augmented matrix set, directly participate in the system solution process and are used to determine the load distribution at each node.

[0004] While traditional methods are relatively mature in identifying master and slave nodes, they often employ simplifications such as rigid connections or uniformly distributed loads when constructing the constraint equations of the augmented matrix set. This simplification results in the generated constraint equations failing to accurately reflect the true mechanical behavior of the system, leading to significant deviations between the solution results of the augmented matrix set and the actual physical model. This makes it difficult to meet the requirements of high-precision simulation and limits the effectiveness of constraint equations in solving load distribution. Therefore, traditional methods for constructing constraint equations have low effectiveness. Summary of the Invention

[0005] Based on this, it is necessary to propose a finite element structural simulation method, device, medium, equipment and products to address the above problems, aiming to solve the problem of low effectiveness in constructing constraint equations related to master nodes and slave nodes in traditional methods.

[0006] In a first aspect, embodiments of this application provide a method for determining constraint equations, the method comprising: Based on the augmented matrix set corresponding to the target object, determine the master node and the slave node corresponding to the master node among multiple nodes in the finite element model corresponding to the target object; wherein, the augmented matrix set defines the master node and the slave node corresponding to the master node in the finite element model; Obtain the constraint equations related to the master node and the slave node of the augmented matrix group; the constraint equations are expressed as follows: the sum of the first product and the second product is zero, the first product is the product of the first coefficient matrix and the dependent degree vector of the slave node, the second product is the product of the second coefficient matrix and the independent degree vector of the master node, the dependent degree vector is determined by the independent degree vector, the weight coefficient matrix, the displacement matrix and the allocation matrix, the weight coefficient matrix is ​​determined by the weight coefficient of the slave node relative to the master node, the displacement matrix is ​​determined by the coordinates of the slave node and the coordinates of the master node, and the allocation matrix is ​​determined by the weight coefficient matrix and the displacement matrix; Based on the finite element model, the target weight coefficient matrix and the target displacement matrix are determined, and the target weight coefficient matrix and the target displacement matrix are substituted into the constraint equation to obtain the target constraint equation of the augmented matrix set.

[0007] In some embodiments, the above method includes at least one of the following: The dependent degree-of-freedom vector of the slave node is the product of the independent degree-of-freedom vector, the weight coefficient matrix, the displacement matrix, and the allocation matrix; The allocation matrix is ​​the inverse of the product of the transpose of the weight coefficient matrix, the displacement matrix, and the weight coefficient matrix. The product of the inverse of the first coefficient matrix and the second coefficient matrix is ​​the product of the weight coefficient matrix, the displacement matrix, and the allocation matrix.

[0008] In some embodiments, the slave node includes a plurality of slave nodes, and the method includes at least one of the following: The weight coefficient matrix is ​​determined by the weight matrix corresponding to each slave node; wherein, for each slave node, the weight matrix corresponding to the slave node is determined by the element feature length and the weight coefficient corresponding to the slave node, the element feature length is the average length of each connecting component in the finite element model, and the connecting component is the element in the finite element model used to establish a coupling relationship between two or more nodes; The displacement matrix is ​​determined by the node displacement matrix corresponding to each slave node; wherein, for each slave node, The node displacement matrix corresponding to the slave node is determined by the coordinates of the slave node and the coordinates of the master node.

[0009] In some embodiments, the formula for calculating the weight matrix corresponding to the slave node is as follows: ; in, This represents the weight matrix corresponding to the slave node. Indicates the characteristic length of the unit.

[0010] In some embodiments, the formula for calculating the node displacement matrix corresponding to the slave node is as follows: ; in, This represents the node displacement matrix corresponding to the slave node. , , These represent the coordinates of the slave node along the x-axis, y-axis, and z-axis, respectively. , , These represent the coordinates of the master node on the x-axis, y-axis, and z-axis, respectively.

[0011] In some embodiments, determining the target weight coefficient matrix and the target displacement matrix based on the finite element model includes: determining the target weight coefficient of the slave node relative to the master node based on the finite element model, and substituting the target weight coefficient into the calculation formula of the weight coefficient matrix to obtain the target weight coefficient matrix; determining the target coordinates of the slave node and the master node based on the finite element model, and substituting the target coordinates of the slave node and the master node into the calculation formula of the displacement matrix to obtain the target displacement matrix.

[0012] Secondly, embodiments of this application also provide a device for determining constraint equations, the device comprising: The node determination module is used to determine the master node and the slave node corresponding to the master node among multiple nodes in the finite element model corresponding to the target object, based on the augmented matrix group corresponding to the target object; wherein, the augmented matrix group defines the master node and the slave node corresponding to the master node in the finite element model; A constraint acquisition module is used to acquire the constraint equations related to the master node and the slave node of the augmented matrix group; the constraint equations are expressed as follows: the sum of a first product and a second product is zero, the first product is the product of a first coefficient matrix and the dependent degree vector of the slave node, the second product is the product of a second coefficient matrix and the independent degree vector of the master node, the dependent degree vector is determined by the independent degree vector, the weight coefficient matrix, the displacement matrix, and the allocation matrix, the weight coefficient matrix is ​​determined by the weight coefficients of the slave node relative to the master node, the displacement matrix is ​​determined by the coordinates of the slave node and the coordinates of the master node, and the allocation matrix is ​​determined by the weight coefficient matrix and the displacement matrix; The equation determination module is used to determine the target weight coefficient matrix and the target displacement matrix based on the finite element model, and substitute the target weight coefficient matrix and the target displacement matrix into the constraint equation to obtain the target constraint equation of the augmented matrix set.

[0013] Thirdly, embodiments of this application also provide a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the following steps: Based on the augmented matrix set corresponding to the target object, determine the master node and the slave node corresponding to the master node among multiple nodes in the finite element model corresponding to the target object; wherein, the augmented matrix set defines the master node and the slave node corresponding to the master node in the finite element model; Obtain the constraint equations related to the master node and the slave node of the augmented matrix group; the constraint equations are expressed as follows: the sum of the first product and the second product is zero, the first product is the product of the first coefficient matrix and the dependent degree vector of the slave node, the second product is the product of the second coefficient matrix and the independent degree vector of the master node, the dependent degree vector is determined by the independent degree vector, the weight coefficient matrix, the displacement matrix and the allocation matrix, the weight coefficient matrix is ​​determined by the weight coefficient of the slave node relative to the master node, the displacement matrix is ​​determined by the coordinates of the slave node and the coordinates of the master node, and the allocation matrix is ​​determined by the weight coefficient matrix and the displacement matrix; Based on the finite element model, the target weight coefficient matrix and the target displacement matrix are determined, and the target weight coefficient matrix and the target displacement matrix are substituted into the constraint equation to obtain the target constraint equation of the augmented matrix set.

[0014] Fourthly, embodiments of this application also provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the following steps: Based on the augmented matrix set corresponding to the target object, determine the master node and the slave node corresponding to the master node among multiple nodes in the finite element model corresponding to the target object; wherein, the augmented matrix set defines the master node and the slave node corresponding to the master node in the finite element model; Obtain the constraint equations related to the master node and the slave node of the augmented matrix group; the constraint equations are expressed as follows: the sum of the first product and the second product is zero, the first product is the product of the first coefficient matrix and the dependent degree vector of the slave node, the second product is the product of the second coefficient matrix and the independent degree vector of the master node, the dependent degree vector is determined by the independent degree vector, the weight coefficient matrix, the displacement matrix and the allocation matrix, the weight coefficient matrix is ​​determined by the weight coefficient of the slave node relative to the master node, the displacement matrix is ​​determined by the coordinates of the slave node and the coordinates of the master node, and the allocation matrix is ​​determined by the weight coefficient matrix and the displacement matrix; Based on the finite element model, the target weight coefficient matrix and the target displacement matrix are determined, and the target weight coefficient matrix and the target displacement matrix are substituted into the constraint equation to obtain the target constraint equation of the augmented matrix set.

[0015] Fifthly, embodiments of this application also provide a computer program product, wherein instructions in the computer program product, when executed by a processor of a computer device, cause the computer device to perform the following steps: Based on the augmented matrix set corresponding to the target object, determine the master node and the slave node corresponding to the master node among multiple nodes in the finite element model corresponding to the target object; wherein, the augmented matrix set defines the master node and the slave node corresponding to the master node in the finite element model; Obtain the constraint equations related to the master node and the slave node of the augmented matrix group; the constraint equations are expressed as follows: the sum of the first product and the second product is zero, the first product is the product of the first coefficient matrix and the dependent degree vector of the slave node, the second product is the product of the second coefficient matrix and the independent degree vector of the master node, the dependent degree vector is determined by the independent degree vector, the weight coefficient matrix, the displacement matrix and the allocation matrix, the weight coefficient matrix is ​​determined by the weight coefficient of the slave node relative to the master node, the displacement matrix is ​​determined by the coordinates of the slave node and the coordinates of the master node, and the allocation matrix is ​​determined by the weight coefficient matrix and the displacement matrix; Based on the finite element model, the target weight coefficient matrix and the target displacement matrix are determined, and the target weight coefficient matrix and the target displacement matrix are substituted into the constraint equation to obtain the target constraint equation of the augmented matrix set.

[0016] The method, apparatus, computer-readable storage medium, computer device, and computer program product for determining constraint equations in this application obtain constraint equations related to the master node and the slave node of the augmented matrix set. The constraint equations are expressed as follows: the sum of a first product and a second product is zero. The first product is the product of a first coefficient matrix and the dependent degree-of-freedom vector of the slave node, and the second product is the product of a second coefficient matrix and the independent degree-of-freedom vector of the master node. The dependent degree-of-freedom vector is determined by the independent degree-of-freedom vector, the weight coefficient matrix, the displacement matrix, and the allocation matrix. The weight coefficient matrix is ​​determined by the weight coefficient of the slave node relative to the master node. The displacement matrix is ​​determined by the coordinates of the slave node and the coordinates of the master node. The allocation matrix is ​​determined by the weight coefficient matrix and the displacement matrix. Based on the finite element model, the target weight coefficient matrix and the target displacement matrix are determined, and the target weight coefficient matrix and the target displacement matrix are substituted into the constraint equations to obtain the target constraint equations of the augmented matrix set. Thus, the weighting coefficients can characterize the physical coupling strength between nodes, while the coordinate information can characterize the deformation state of the nodes. This application can automatically calculate the weighting coefficient matrix that accurately reflects the physical coupling strength between nodes and the displacement matrix that characterizes the actual deformation state, and generate constraint equations. This effectively solves the problem of insufficient calculation accuracy caused by simple assumptions about constraint relationships. Ultimately, while ensuring computational efficiency, it significantly improves the accuracy and reliability of finite element simulation results. Therefore, the method of this application can improve the effectiveness of constructing constraint equations. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] in: Figure 1 A flowchart illustrating the method for determining constraint equations provided in an embodiment of this application; Figure 2 A structural block diagram of the constraint equation determination device provided in the embodiments of this application; Figure 3 This is a structural block diagram of a computer device provided in an embodiment of this application. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] The method for determining the constraint equations can be applied to computer equipment, which can be a cloud server or other server, or an electronic product including a cloud server or other server. The method for determining the constraint equations can be executed by the aforementioned computer equipment.

[0021] refer to Figure 1 , Figure 1 This is a flowchart illustrating the method for determining constraint equations provided in an embodiment of this application. Specifically, it includes the following steps S1-S3: Step S1: Based on the augmented matrix group corresponding to the target object, determine the master node and the slave node corresponding to the master node among multiple nodes in the finite element model corresponding to the target object.

[0022] The aforementioned target object can be understood as the structural object of the constraint equation to be determined. The aforementioned target object can be a mechanical model, such as aerospace vehicles (e.g., aircraft wings, rocket fairings), vehicles (e.g., car bodies, high-speed rail frames), building structures (e.g., bridges, skyscrapers), mechanical equipment (e.g., excavator booms, wind turbine blades), etc.

[0023] The augmented matrix set described above defines the master nodes and corresponding slave nodes in the finite element model. This augmented matrix set can be known, meaning it has already been determined before step S1. The augmented matrix set implicitly reflects the master and slave nodes in the finite element model through its inherent mathematical structure, thereby automatically acquiring and determining the division of master and slave nodes.

[0024] In finite element analysis, the aforementioned master node refers to a node whose displacement degrees of freedom are defined as independent variables and are used to drive or control the motion of other nodes, while slave node refers to a node whose displacement degrees of freedom depend on the displacements of one or more master nodes through the constraint equations. For example, when simulating a rigid plate, the node at the center of the plate is defined as a master node, whose displacement is independent, while the nodes at the edge of the plate are defined as slave nodes, whose displacement is completely determined by the displacements of the master nodes through the rigid constraint equations.

[0025] The aforementioned finite element model can be constructed before step S1. The finite element model can be constructed by discretizing the continuous physical domain of the target object into a mesh model connected by a finite number of nodes and elements. Its construction process has a direct mapping relationship with the target object. Specifically, firstly, mesh nodes (whose coordinates represent the spatial morphology of the target object) are generated according to the geometry of the target object. Then, the element type and parameters are defined according to the material properties, connection relationships and other physical characteristics of the target object. The final finite element model is essentially a digital representation of the mechanical and physical behavior of the target object. Its accuracy directly determines the degree of reproduction of the simulation results to the actual physical system.

[0026] Step S2: Obtain the constraint equations related to the master and slave nodes of the augmented matrix group.

[0027] The constraint equations are expressed as follows: the sum of the first product and the second product is zero. The first product is the product of the first coefficient matrix and the dependent degree vector of the slave node. The second product is the product of the second coefficient matrix and the independent degree vector of the master node. The dependent degree vector is determined by the independent degree vector, the weight coefficient matrix, the displacement matrix, and the allocation matrix. The weight coefficient matrix is ​​determined by the weight coefficient of the slave node relative to the master node. The displacement matrix is ​​determined by the coordinates of the slave node and the coordinates of the master node. The allocation matrix is ​​determined by the weight coefficient matrix and the displacement matrix.

[0028] In finite element analysis, the aforementioned weighting coefficients can be scalar values ​​calculated based on at least one of the physical properties, geometric relationships, and topological connections of nodes in the finite element model. They are used to quantify the degree to which the displacement of a slave node is affected by the displacement of the master node. Generally speaking, the closer a slave node is to the master node, the larger its corresponding weighting coefficient.

[0029] In finite element analysis, the displacement matrix mentioned above can refer to a column vector that assembles the displacement degrees of freedom of all nodes in the system in a predetermined order, used to completely characterize the overall deformation state of the target object under load. This displacement matrix typically contains the translational and rotational degrees of freedom of each node, and can be divided into two sub-blocks according to the node type: master node displacement vector and slave node displacement vector, thus providing a mathematical basis for establishing the constraint relationship between dependent and independent degrees of freedom.

[0030] In the construction of finite element constraint equations, the aforementioned allocation matrix refers to the transformation matrix generated by specific mathematical operations based on the weight coefficient matrix and the displacement matrix. Its core function is to accurately allocate the displacement response of the subordinate degree of freedom to the corresponding independent degree of freedom. This allocation matrix combines the scalar relationship of the weight coefficient matrix with the geometric information of the displacement matrix by quantifying the spatial correlation and physical coupling strength between the master and slave nodes.

[0031] In some embodiments, the sum of the first product and the second product being zero can be characterized by the following formula: ; in, These represent the first coefficient matrix and the second coefficient matrix, respectively. These represent the dependent degree-of-freedom vector of the slave node and the independent degree-of-freedom vector of the master node, respectively.

[0032] Step S3: Based on the finite element model, determine the target weight coefficient matrix and the target displacement matrix, and substitute the target weight coefficient matrix and the target displacement matrix into the constraint equations to obtain the target constraint equations of the augmented matrix set.

[0033] Based on the finite element model, the specific values ​​of the weight coefficient matrix and position matrix in the above constraint equations can be determined to obtain the target weight coefficient matrix and target displacement matrix.

[0034] Substituting the specific target weight coefficient matrix and target displacement matrix into the constraint equations yields the final target constraint equations for the augmented matrix set.

[0035] This embodiment of the application obtains the constraint equations related to the master node and the slave node of the augmented matrix set. The constraint equations are expressed as follows: the sum of the first product and the second product is zero. The first product is the product of the first coefficient matrix and the dependent degree-of-freedom vector of the slave node, and the second product is the product of the second coefficient matrix and the independent degree-of-freedom vector of the master node. The dependent degree-of-freedom vector is determined by the independent degree-of-freedom vector, the weight coefficient matrix, the displacement matrix, and the allocation matrix. The weight coefficient matrix is ​​determined by the weight coefficient of the slave node relative to the master node. The displacement matrix is ​​determined by the coordinates of the slave node and the coordinates of the master node. The allocation matrix is ​​determined by the weight coefficient matrix and the displacement matrix. Based on the finite element model, the target weight coefficient matrix and the target displacement matrix are determined, and these are substituted into the constraint equations to obtain the target constraint equations of the augmented matrix set. In this way, the weight coefficient matrix that accurately reflects the physical coupling strength between nodes and the displacement matrix that characterizes the actual deformation state can be automatically calculated to generate the constraint equations. This effectively solves the problem of insufficient calculation accuracy caused by simple assumptions about constraint relationships, and ultimately significantly improves the accuracy and reliability of finite element simulation results while ensuring computational efficiency.

[0036] In some embodiments, the dependent degree-of-freedom vector of the slave node is the product of the independent degree-of-freedom vector, the weight coefficient matrix, the displacement matrix, and the assignment matrix, and the calculation formula can be as follows: ; in, This represents the vector of dependent degrees of freedom from the node. , , These represent the weighting matrix, displacement matrix, and allocation matrix, respectively. This represents the independent degrees of freedom vector of the master node.

[0037] In some embodiments, the above allocation matrix is ​​the inverse matrix of the transpose of the weight coefficient matrix, the shift matrix, and the product of the weight coefficient matrices, and the calculation formula can be as follows: ; in, Represents the allocation matrix. Represents the displacement matrix. This represents the weight coefficient matrix.

[0038] In some embodiments, the product of the inverse of the first coefficient matrix and the second coefficient matrix is ​​the product of the weight coefficient matrix, the displacement matrix, and the allocation matrix, and the calculation formula can be as follows: ; in, These are the inverse matrix of the first coefficient matrix and the second coefficient matrix, respectively. These are the weighting coefficient matrix, the displacement matrix, and the allocation matrix, respectively.

[0039] In other embodiments, the product of the inverse of the first coefficient matrix and the second coefficient matrix is ​​the product of the inverse of the allocation matrix, the transpose of the displacement matrix, and the weight coefficient matrix, and the calculation formula can be as follows: = W.

[0040] In this embodiment, the parameters in the constraint equation are jointly defined by the weight coefficient matrix, displacement matrix and allocation matrix, which can improve the simulation accuracy. The weight coefficient matrix ensures the authenticity of the mechanical transmission path by quantifying the physical coupling strength between nodes, the displacement matrix maintains geometric consistency by preserving the spatial coordinate information of nodes, and the allocation matrix merges the two through mathematical transformation, together overcoming the distortion problem caused by traditional rigid constraints or empirical assumptions.

[0041] In some embodiments, the slave node may include multiple slave nodes, and the value of i may range from 1 to c, where c is the number of slave nodes included in the multiple slave nodes, and i is a positive integer.

[0042] The aforementioned weight coefficient matrix is ​​determined by the weight matrix corresponding to each slave node, and the calculation formula can be as follows: ; in, This is the weight coefficient matrix. Let represent the weight matrix corresponding to the i-th slave node, where i ranges from 1 to c.

[0043] In some embodiments, for each slave node, the weight matrix corresponding to the slave node is determined by the cell feature length and the weight coefficient corresponding to the slave node, and the calculation formula can be as follows: ; in, This represents the weight matrix corresponding to the node. This represents the weight coefficient corresponding to the node. Indicates the characteristic length of the unit.

[0044] In some embodiments, the aforementioned element feature length is the average length of each connecting component in the finite element model, and the calculation formula can be as follows: ; in, Indicates the characteristic length of the unit. This represents the length of the k-th connecting component, where k ranges from 1 to... , This indicates the number of connecting parts, where k is a positive integer.

[0045] The aforementioned connecting components are elements used in the finite element model to establish coupling relationships between two or more nodes.

[0046] In finite element or mechanical models, connecting components refer to those units or elements in the model used to establish mechanical or physical coupling relationships between two or more nodes and to transfer loads (such as force, torque, heat, current, etc.), such as the interface where two components intersect.

[0047] The displacement matrix mentioned above is determined by the nodal displacement matrix corresponding to each slave node, and the calculation formula can be as follows: ; in, Represents the displacement matrix. Let represent the node displacement matrix corresponding to the i-th slave node, where i ranges from 1 to c.

[0048] In some embodiments, for each slave node, the node displacement matrix corresponding to the slave node is determined by the coordinates of the slave node and the coordinates of the master node, and the calculation formula can be as follows: ; in, This represents the node displacement matrix corresponding to the i-th slave node. , , These represent the coordinates of the node along the x-axis, y-axis, and z-axis, respectively. , , These represent the coordinates of the master node on the x-axis, y-axis, and z-axis, respectively.

[0049] In some embodiments, step S3 may include, but is not limited to, the following steps: Based on the finite element model, the target weight coefficients of the slave nodes relative to the master nodes are determined, and the target weight coefficients are substituted into the calculation formula of the weight coefficient matrix to obtain the target weight coefficient matrix.

[0050] Based on the finite element model, the target coordinates of the slave node and the master node are determined, and then the target coordinates of the slave node and the master node are substituted into the calculation formula of the displacement matrix to obtain the target displacement matrix.

[0051] In some implementations, the weighting coefficient can be proportional to the physical property value of the connecting component linking the slave node and the master node, such as stiffness. The determination of the target weighting coefficient of the slave node relative to the master node based on the finite element model can be achieved using existing conventional methods.

[0052] The calculation formula for the weight coefficient matrix has been explained above. In this embodiment, the target weight coefficient is substituted into the calculation formula for the weight coefficient matrix to obtain the specific target weight coefficient matrix.

[0053] The finite element model contains the coordinate information of each node. In some implementations, the determination of the target coordinates of the slave node and the master node based on the finite element model can be achieved using existing conventional methods.

[0054] In this embodiment, the weight coefficient matrix and displacement matrix in the constraint equation are automatically calculated and determined by the algorithm, realizing the automation and intelligence of constraint equation generation. This completely overcomes the problems of low efficiency and poor consistency caused by the reliance on human experience in traditional methods. At the same time, since the weight coefficient matrix and target displacement matrix are strictly derived from the finite element model, they can accurately characterize the real mechanical behavior of the system, significantly improving the accuracy and reliability of the simulation results.

[0055] In some embodiments, the above It can be a value in the global coordinate system, if the above... The values ​​are in the global coordinate system. To obtain the values ​​in the local coordinate system, the constraint equations can be modified by adding the following equations: ; ; in, This represents the transformation matrix between the global coordinate system and the local coordinate system. This represents the subordinate degrees of freedom in the local coordinate system.

[0056] In some embodiments, the above-mentioned target constraint equations can be solved by finite element method in combination with a known augmented matrix set to obtain the load distribution of each node.

[0057] To better understand the above solution, the embodiments of this application provide the following specific descriptions: In engineering finite element analysis, the simulation method of connecting components has a crucial impact on the reliability of the results and computational efficiency. When dealing with complex assemblies or interface force transmission problems, it is often necessary to use different types of rigid elements to simplify the model, and the choice depends on the physical behavior of the actual structure and the simulation objectives.

[0058] In the aerospace field, aircraft wings and fuselages are often connected by high-strength bolts or welded structures. These interfaces have extremely high stiffness, and local deformation is negligible. However, directly creating detailed bolt contacts or weld details in the finite element model leads to difficulties in mesh generation and a sharp increase in computational cost. At this point, rigid elements (RBE2 elements) are widely used. Through the rigid binding of master and slave nodes, the rigid body motion of the wing (such as bending or torsion) is directly transmitted to the connection nodes of the fuselage, thus simplifying the modeling of the force transmission path. Its constraint equations ensure that the slave nodes strictly follow the displacement and rotation of the master node, as if "fusing" multiple points into a rigid body. However, the forced rigidity of RBE2 completely suppresses local deformation in the connection area, which may lead to artificially high stress in adjacent elements. It is more suitable for evaluating the overall structural stiffness or motion attitude than for strength analysis of connection details.

[0059] For different scenarios, a constraint element for load distribution is proposed. In vehicle engineering, the connection between the vehicle body and the suspension system often involves flexible components such as bushings or rubber pads. Loads cannot be transmitted through a single node but must be distributed across multiple connection points, taking into account the influence of elastic deformation. For example, the impact force on the wheel needs to be transmitted to the frame through multiple supports of the suspension system. If a traditional rigid connection is used, the local stiffness of the frame will be overestimated, leading to stress concentration and misleading the direction of structural optimization. This element, through weight definition, "flexibly" distributes the load of the master node to multiple slave nodes (e.g., by assigning weights based on geometric distance or material stiffness), ensuring the static equivalence of force and moment, while allowing relative displacement of slave nodes after being subjected to force, preserving the local flexibility of the connection area. This characteristic enables it to more realistically simulate bolt preload diffusion, force transmission behavior under elastic support, or, in collision simulation, distribute concentrated collision forces to the vehicle body structure along the actual path.

[0060] The deeper difference in application context lies in their "physical orientation." Traditional RBE2 elements are suitable for dominant force transmission scenarios where the stiffness of the connection domain is much higher than the surrounding structure and there is no significant deformation; while this type of element is suitable for scenarios where the connection area itself is elastic (such as a flexible joint) or where artificial stiffness needs to be avoided. In the aerospace field, RBE2 can be used to simulate the synchronous motion of rigid deployment hinges, while this type of element can be used to simulate the load redistribution between plates due to thermal deformation after deployment. The essential difference between the two can be compared to "welding" and "spring." Traditional elements eliminate degrees of freedom through constraint equations, while this type of element coordinates degrees of freedom through weight functions. These different choices reflect a balance between simplified assumptions about the physical world and computational requirements.

[0061] In traditional mechanical simulations, rigid kinematic coupling elements transfer loads through rigid body constraints between master and slave nodes. The core theory requires that the displacements of all slave nodes strictly conform to the rigid body motion laws of the master node. While this "one-point-controls-the-world" load equivalence principle simplifies the modeling process, it fundamentally conflicts with the mechanical response of real connection interfaces. The core issue is that the load transfer mechanism of rigidly bound elements forcibly covers the strain field physics of the connection region with the assumption of geometric rigidity, leading to the loss of topological fidelity in the stress diffusion path.

[0062] In engineering practice, the force transmission behavior in the connection region is essentially governed by a combination of local stiffness distribution, contact surface geometry, and material nonlinearity. Traditional methods forcibly simplify this complex force transmission process into a rigid body kinematic projection, maintaining a rigid constraint between the return force from the slave node and the master node, resulting in errors in the stress field. Mechanical error: The equivalent return force of the master node of a rigidly bonded element only reflects the global static equilibrium. This leads to an underestimation of the stress in the connection edge region far from the master node, while the region near the master node is forced to bear an excessive load, forming a false "stress funnel" phenomenon.

[0063] Geometric error: The load transfer direction of the connection interface is absolutely dominated by the master node coordinate system, which cannot be compatible with the adaptive adjustment characteristics of the actual contact surface for eccentric loads.

[0064] Taking bolt connection analysis as an example, the equivalent return force of the main node in traditional methods can only statically reflect the initial load balance during the assembly pre-tightening stage. In this scenario, the micro-slippage of the real interface and the creep behavior of the tapered gasket are directly masked by the displacement of the rigid binding element, causing the prediction of bolt loosening risk to completely lose its physical basis. This kind of defect exposes the contradiction of traditional rigid motion coupling elements: the contradiction between the rigid body assumption and actual engineering.

[0065] This application proposes a load distribution constraint element designed to more realistically simulate structural connections and address the stress concentration and mechanical behavior distortion problems caused by traditional rigid elements (such as RBE2). The core idea of ​​this element is to flexibly transfer the load on an independent point (reference point or master node) to a set of subordinate connection nodes (slave nodes) in a weighted distribution manner, thereby achieving static equivalence of force and moment, while allowing local relative deformation in the connection area that conforms to physical reality.

[0066] To clearly describe the technical solution of this invention, the core terms are first defined: Reference point: An independent, virtual or real node, denoted by the subscript q. It is the control point for applying external loads (forces and moments). Its motion (displacement and rotation) determines the macroscopic motion trend of the entire connected structure. The "reference point" is also called the "master node".

[0067] Connection nodes: A group of physical nodes located on the actual structural model and subordinate to the reference point, denoted by the subscript i. They are load-receiving points, and their motion is a superposition of the reference point's motion and their own local deformation. "Connection nodes" are also called "slave nodes".

[0068] Weighting coefficients (as mentioned above): A set of numerical coefficients assigned to each connected node, using... This indicates how the total load transferred from the reference point should be distributed among the various connection nodes. Weighting coefficients can be determined based on geometric distance, material stiffness, or user-defined rules to simulate different physical connection characteristics.

[0069] Technical implementation steps: Step 1: Define constraint elements In the finite element model, the user first selects the composition of the constraint elements.

[0070] Select Master Node: Specify a node as an independent reference point (master node). This node can be an existing node in the model or a virtual node created to apply loads.

[0071] Select slave nodes: Specify one or more physical nodes on the model as connection nodes (slave nodes). These nodes are typically located on the interfaces where the connection needs to be simulated, such as nodes around bolt holes, nodes on welds, or interface nodes between different meshes.

[0072] The aforementioned master and slave nodes are determined by a known set of augmented matrices.

[0073] Step 2: Calculate the weighting coefficients The system calculates the weighting coefficient for each slave node based on preset rules or user input. A common automated method is distance-based weighting: slave nodes closer to the master node are assigned higher weights, and vice versa. This aligns with the tendency for loads to concentrate towards the stiffness center in most physical connections. The sum of the weights of all slave nodes is typically normalized.

[0074] Step 3: Construct the constraint equations for load distribution The core of this unit lies in establishing a set of multi-point constraint (MPC) equations that correlate the displacements of the master node with those of the slave node. This is achieved by constructing a series of matrices (such as the displacement transformation matrix S, the weighting coefficient matrix W, etc.), ultimately forming the force and displacement transfer relationship between the master and slave nodes.

[0075] Step 4: Finite Element Solution During the solution process, when an external load is applied to the master node, the solver uses the constraint equations established in step three to distribute the load to all slave nodes in real time and calculates the displacement and stress response of the entire structure. Because the constraints are flexible, relative displacement is allowed between slave nodes, thus avoiding spurious stresses introduced by rigid elements.

[0076] Specifically, in finite element analysis, multi-point constraints (MPC) are a technique for establishing linear relationships between specific degrees of freedom. The core of any MPC equation is its integration into the global system equilibrium equations.

[0077] Global equilibrium equations and constraint equations: The standard finite element static analysis equation is: ; Where K, U, and F are the global stiffness matrix, nodal displacement vector, and nodal load vector, respectively.

[0078] An MPC equation defines a linear relationship between a set of degrees of freedom, and its general homogeneous form is: ; Here, R is the constraint matrix, which selects the relevant degrees of freedom from the global displacement vector U and applies constraints.

[0079] Integration of constraint equations: Matrix dimensionality expansion method To integrate constraints into the solution process, the force balance equations and constraint equations can be combined into a higher-dimensional linear system of equations. This process involves changing the constraint equations... Directly added to the stiffness matrix equation This forms a system equation with expanded dimensions. To ensure the system of equations has a solution, a set of unknowns corresponding to the constraints needs to be introduced. Thus, the following augmented matrix is ​​constructed: ; Solving this extended set of equations yields the displacement U that simultaneously satisfies force equilibrium and constraint conditions.

[0080] Construction of the constraint matrix R (described by the G matrix in this paper) In finite element theory, the MPC relationship is usually represented by a set of dependent degrees of freedom (DoFs, denoted as {u i}) can be expressed as a set of independent degrees of freedom (DoFs, denoted as {u q Linear combinations of}): .

[0081] in, It is a transformation matrix.

[0082] In order to construct a general homogeneous constraint equation The above equation can be rearranged as follows: =0; This equation directly defines the constraint matrix R and the transformation matrix. The relationship. If we separate the degrees of freedom involved in the constraints from the global degree-of-freedom vector U, denoted as... Then the constraint equations can be written as: =0; Therefore, the constraint matrix R is a sparse matrix in the global degrees of freedom U space, whose non-zero elements exist only in the space between R and U. and In the corresponding columns, their values ​​are the identity matrix I and - .

[0083] In the specific computational implementation, the transformation matrix It is often derived from more basic matrices through operations. A common form of expression is: ; Here and It comes from a more general constraint equation The coefficient matrix is ​​separated from the constraint matrix R. Therefore, the non-zero part of the constraint matrix R is ultimately defined by these fundamental matrices.

[0084] When a load is applied to the master node, the load must be applied equally to each slave node through a distribution relationship: ; Assume "P" qin"P" represents an arbitrary force system at a reference point. qin The input load applied to the master node, beamed out to the connected nodes (slave nodes), can be represented as (where "X" is an unknown matrix): ; in, The matrix is: ; Variable meaning: : The weight coefficient of the i-th slave node.

[0085] Characteristic length of the cell; This represents the load distributed on the slave nodes, where i ranges from 1 to c, and c is the number of slave nodes.

[0086] To ensure dimensional uniformity, the weights related to rotational degrees of freedom are multiplied by the feature length. The square of.

[0087] Considering all slave nodes on the element, calculate the element feature length: ; Variable meaning: : The length of each connecting component; The number of connecting parts; c: Number of slave nodes.

[0088] If a node's degree of freedom is not subject to constraints, then... The corresponding diagonal term is set to 0.

[0089] in The matrix is: ; (x i y i , z i ): The coordinates of the i-th slave node.

[0090] (x q y q , z q ): The coordinates of the master node.

[0091] The matrix describes how the displacement of the i-th slave node is generated by the displacement (translation and rotation) of the master node q. It is based on the principles of rigid body kinematics and is a mathematical representation of the geometric relationships between nodes.

[0092] If the j-th degree of freedom of the master node i is not involved, then (j, j) can be set to 0.0.

[0093] The forces acting on the connection nodes should be balanced with the loads on the reference nodes.

[0094] ; P qout P represents the output load on the master node. i This indicates the load assigned to the slave node.

[0095] In summary: ; Considering We get X: ; Finally, the relationship of nodal forces is obtained: ; Based on the duality of force and displacement: ; Therefore, we obtain matrix: ; Consider the coordinate transformation of the connecting nodes Displacement of connecting nodes in the global coordinate system (basic coordinate system) Displacement in the local coordinate system (element coordinate system) : ; in, This represents the transformation matrix between the global coordinate system and the local coordinate system.

[0096] The reference coordinate system (global coordinate system) still uses the Cartesian coordinate system (Basic coordinate system), resulting in: ; Among them, here For the above , Represents the value in the local coordinate system; get: ; Also governed by duality: ; Code calculation implementation process: Considering all nodes on the element, calculate the element feature length: ; Calculate the corresponding weight matrix: ; ; Calculate the corresponding transformation matrix: ; ; Assembly In and The matrix (and other constraint elements) are in the same form. Consider the local coordinate system and make corrections.

[0097] To better implement the above method, embodiments of this application provide a device for determining constraint equations, referring to... Figure 2 , Figure 2 A structural block diagram of the constraint equation determination device provided in the embodiments of this application is shown below. Figure 2 As shown, the constraint equation determining device 200 specifically includes the following: The node determination module 201 is used to determine the master node and the corresponding slave node among multiple nodes in the finite element model corresponding to the target object based on the augmented matrix group corresponding to the target object; wherein, the augmented matrix group defines the master node and the corresponding slave node in the finite element model; The constraint acquisition module 202 is used to acquire the constraint equations related to the master node and slave node of the augmented matrix group. The constraint equations are expressed as follows: the sum of the first product and the second product is zero. The first product is the product of the first coefficient matrix and the dependent degree vector of the slave node. The second product is the product of the second coefficient matrix and the independent degree vector of the master node. The dependent degree vector is determined by the independent degree vector, the weight coefficient matrix, the displacement matrix, and the allocation matrix. The weight coefficient matrix is ​​determined by the weight coefficient of the slave node relative to the master node. The displacement matrix is ​​determined by the coordinates of the slave node and the coordinates of the master node. The allocation matrix is ​​determined by the weight coefficient matrix and the displacement matrix. The equation determination module 203 is used to determine the target weight coefficient matrix and the target displacement matrix based on the finite element model, and substitute the target weight coefficient matrix and the target displacement matrix into the constraint equation to obtain the target constraint equation of the augmented matrix set.

[0098] In some embodiments, the dependent degree-of-freedom vector of a node is the product of the independent degree-of-freedom vector, the weight coefficient matrix, the displacement matrix, and the allocation matrix. The allocation matrix is ​​the inverse of the product of the transpose of the weight coefficient matrix, the displacement matrix, and the weight coefficient matrix. The product of the inverse of the first coefficient matrix and the second coefficient matrix is ​​the product of the weight coefficient matrix, the displacement matrix, and the allocation matrix.

[0099] In some embodiments, a slave node includes multiple slave nodes, and the weight coefficient matrix is ​​determined by the weight matrix corresponding to each slave node. For each slave node, the weight matrix is ​​determined by the element feature length and the weight coefficient corresponding to the slave node. The element feature length is the average length of each connecting component in the finite element model, and the connecting component is the element used to establish coupling between two or more nodes in the finite element model. In some embodiments, the displacement matrix is ​​determined by the node displacement matrix corresponding to each slave node. For each slave node, the node displacement matrix is ​​determined by the coordinates of the slave node and the coordinates of the master node.

[0100] In some embodiments, in the constraint acquisition module 202, the formula for calculating the weight matrix corresponding to the node is as follows:

[0101] in, This represents the weight matrix corresponding to the node. Indicates the characteristic length of the unit.

[0102] In some embodiments, in the constraint acquisition module 202, the formula for calculating the node displacement matrix corresponding to the node is as follows: ; in, This represents the nodal displacement matrix corresponding to the node. , , These represent the coordinates of the node along the x-axis, y-axis, and z-axis, respectively. , , These represent the coordinates of the master node on the x-axis, y-axis, and z-axis, respectively.

[0103] In some embodiments, the equation determination module 203 is specifically used to: determine the target weight coefficient of the slave node relative to the master node according to the finite element model, and substitute the target weight coefficient into the calculation formula of the weight coefficient matrix to obtain the target weight coefficient matrix; determine the target coordinates of the slave node and the master node according to the finite element model, and substitute the target coordinates of the slave node and the master node into the calculation formula of the displacement matrix to obtain the target displacement matrix.

[0104] The constraint equation determination device 200 provided in this application embodiment can execute the technical solution shown in the above method embodiment. Its implementation principle and beneficial effects are similar, and will not be described again here.

[0105] Figure 3 An internal structural diagram of a computer device in one embodiment is shown. This computer device can specifically be a terminal or a server. Figure 3 As shown, the computer device includes a processor, memory, and network interface connected via a system bus. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and may also store a computer program, which, when executed by the processor, causes the processor to implement the method of the present invention. The internal memory may also store a computer program, which, when executed by the processor, causes the processor to perform the method of the present invention. Those skilled in the art will understand that... Figure 3 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0106] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the following steps: Based on the augmented matrix set corresponding to the target object, determine the master node and the corresponding slave node among multiple nodes in the finite element model corresponding to the target object; wherein, the augmented matrix set defines the master node and the corresponding slave node in the finite element model; Obtain the constraint equations related to the master and slave nodes of the augmented matrix group; the constraint equations are expressed as follows: the sum of the first product and the second product is zero. The first product is the product of the first coefficient matrix and the dependent degree vector of the slave node. The second product is the product of the second coefficient matrix and the independent degree vector of the master node. The dependent degree vector is determined by the independent degree vector, the weight coefficient matrix, the displacement matrix, and the assignment matrix. The weight coefficient matrix is ​​determined by the weight coefficient of the slave node relative to the master node. The displacement matrix is ​​determined by the coordinates of the slave node and the coordinates of the master node. The assignment matrix is ​​determined by the weight coefficient matrix and the displacement matrix. Based on the finite element model, the target weight coefficient matrix and the target displacement matrix are determined, and then substituted into the constraint equations to obtain the target constraint equations of the augmented matrix set.

[0107] In one embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, causes the processor to perform the following steps: Based on the augmented matrix set corresponding to the target object, determine the master node and the corresponding slave node among multiple nodes in the finite element model corresponding to the target object; wherein, the augmented matrix set defines the master node and the corresponding slave node in the finite element model; Obtain the constraint equations related to the master and slave nodes of the augmented matrix group; the constraint equations are expressed as follows: the sum of the first product and the second product is zero. The first product is the product of the first coefficient matrix and the dependent degree vector of the slave node. The second product is the product of the second coefficient matrix and the independent degree vector of the master node. The dependent degree vector is determined by the independent degree vector, the weight coefficient matrix, the displacement matrix, and the assignment matrix. The weight coefficient matrix is ​​determined by the weight coefficient of the slave node relative to the master node. The displacement matrix is ​​determined by the coordinates of the slave node and the coordinates of the master node. The assignment matrix is ​​determined by the weight coefficient matrix and the displacement matrix. Based on the finite element model, the target weight coefficient matrix and the target displacement matrix are determined, and then substituted into the constraint equations to obtain the target constraint equations of the augmented matrix set.

[0108] In some embodiments, this application also provides a computer program product, wherein the instructions in the computer program product, when executed by the processor of a computer device, cause the computer device to perform the following steps: Based on the augmented matrix set corresponding to the target object, determine the master node and the corresponding slave node among multiple nodes in the finite element model corresponding to the target object; wherein, the augmented matrix set defines the master node and the corresponding slave node in the finite element model; Obtain the constraint equations related to the master and slave nodes of the augmented matrix group; the constraint equations are expressed as follows: the sum of the first product and the second product is zero. The first product is the product of the first coefficient matrix and the dependent degree vector of the slave node. The second product is the product of the second coefficient matrix and the independent degree vector of the master node. The dependent degree vector is determined by the independent degree vector, the weight coefficient matrix, the displacement matrix, and the assignment matrix. The weight coefficient matrix is ​​determined by the weight coefficient of the slave node relative to the master node. The displacement matrix is ​​determined by the coordinates of the slave node and the coordinates of the master node. The assignment matrix is ​​determined by the weight coefficient matrix and the displacement matrix. Based on the finite element model, the target weight coefficient matrix and the target displacement matrix are determined, and then substituted into the constraint equations to obtain the target constraint equations of the augmented matrix set.

[0109] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc.

[0110] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0111] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A finite element structural simulation method, characterized in that, The method includes: A finite element model is constructed for the target entity structure. Based on the augmented matrix set corresponding to the target entity structure, the master node used to apply external loads and the slave nodes distributed on the structural connection interface corresponding to the master node are determined among multiple nodes in the finite element model. The augmented matrix set defines the master node and the slave node corresponding to the master node in the finite element model. Obtain the constraint equations related to the master node and the slave node of the augmented matrix group; the constraint equations are expressed as follows: the sum of the first product and the second product is zero, the first product is the product of the first coefficient matrix and the dependent degree-of-freedom vector of the slave node, the second product is the product of the second coefficient matrix and the independent degree-of-freedom vector of the master node, the dependent degree-of-freedom vector is determined by the independent degree-of-freedom vector, the weight coefficient matrix, the displacement matrix, and the allocation matrix, the weight coefficient matrix is ​​determined by the weight coefficient of the slave node relative to the master node, the weight coefficient matrix is ​​used to characterize the physical coupling strength between nodes, the displacement matrix is ​​determined by the coordinates of the slave node and the coordinates of the master node, the displacement matrix is ​​used to characterize the overall deformation state of the target entity structure under load; the allocation matrix is ​​determined by the weight coefficient matrix and the weight coefficient matrix. The displacement matrix is ​​determined by combining the scalar relationship of the weight coefficient matrix with the geometric information of the displacement matrix by quantifying the spatial correlation and physical coupling strength between master and slave nodes. The slave nodes include multiple slave nodes, and the weight coefficient matrix is ​​determined by the weight matrix corresponding to each slave node. For each slave node, the weight matrix corresponding to the slave node is determined by the element feature length and the weight coefficient corresponding to the slave node. The element feature length is the average length of each connecting component in the finite element model, and the connecting component is the element in the finite element model used to establish coupling relationships between two or more nodes. The displacement matrix is ​​determined by the node displacement matrix corresponding to each slave node. For each slave node, the node displacement matrix corresponding to the slave node is determined by the coordinates of the slave node and the coordinates of the master node. Based on the finite element model, the target weight coefficient matrix and the target displacement matrix are determined, and the target weight coefficient matrix and the target displacement matrix are substituted into the constraint equation to obtain the target constraint equation of the augmented matrix set. Based on the stated objective constraint equations, the finite element model is used for simulation.

2. The method according to claim 1, characterized in that, The method includes at least one of the following: The dependent degree-of-freedom vector of the slave node is the product of the independent degree-of-freedom vector, the weight coefficient matrix, the displacement matrix, and the allocation matrix; The allocation matrix is ​​the inverse of the product of the transpose of the weight coefficient matrix, the displacement matrix, and the weight coefficient matrix. The product of the inverse of the first coefficient matrix and the second coefficient matrix is ​​the product of the weight coefficient matrix, the displacement matrix, and the allocation matrix.

3. The method according to claim 1, characterized in that, The formula for calculating the weight matrix corresponding to the slave node is as follows: ； in, This represents the weight matrix corresponding to the slave node. This represents the weight coefficient corresponding to the node. Indicates the characteristic length of the unit.

4. The method according to claim 1, characterized in that, The formula for calculating the node displacement matrix corresponding to the slave node is as follows: ； in, This represents the node displacement matrix corresponding to the slave node. , , These represent the coordinates of the slave node along the x-axis, y-axis, and z-axis, respectively. , , These represent the coordinates of the master node on the x-axis, y-axis, and z-axis, respectively.

5. The method according to claim 1, characterized in that, The step of determining the target weight coefficient matrix and the target displacement matrix based on the finite element model includes: Based on the finite element model, the target weight coefficient of the slave node relative to the master node is determined, and the target weight coefficient is substituted into the calculation formula of the weight coefficient matrix to obtain the target weight coefficient matrix; Based on the finite element model, the target coordinates of the slave node and the master node are determined, and the target coordinates of the slave node and the master node are substituted into the calculation formula of the displacement matrix to obtain the target displacement matrix.

6. A computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the steps of the method as claimed in any one of claims 1 to 5.

7. A computer device comprising a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the steps of the method as claimed in any one of claims 1 to 5.

8. A computer program product, characterized in that, When the instructions in the computer program product are executed by the processor of the computer device, they implement the steps of the method as described in any one of claims 1 to 5.

Images