Equivalent static collision load calculation method based on energy principle

Abstract

The invention belongs to the technical field of structural collision safety, and particularly relates to an equivalent static collision load calculation method based on an energy principle. The method comprises four processes of constructing a structure collision energy equation based on an energy principle, establishing a collision dynamic equilibrium equation based on a minimum energy principle, defining an equivalent static collision load based on a mechanical equilibrium principle and establishing an equivalent static collision load expression based on a position finite element method. The equivalent static collision load calculation method capable of visually representing the collision strength is constructed, and then a feasible technical scheme is provided for structural collision strength evaluation and structural collision optimization design. According to the equivalent static collision load calculation method based on the energy principle, calculation of the equivalent static collision load can be rapidly and directly achieved, and an effective solving method is provided for calculation of the equivalent static collision load.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural collision safety, and specifically relates to a method for calculating an equivalent static collision load based on the energy principle. Background Art

[0002] In recent years, with the rapid development of technologies such as automobiles and drones, automobiles and drones have been widely used in various industries. However, automobile collision accidents and drone collisions occur from time to time, posing a great threat to people's life safety. Therefore, it is highly necessary to scientifically evaluate the structural collision strength in order to better understand the collision risks and safety of structures, and provide a basis for structural design and the formulation of relevant policies and technologies.

[0003] However, the structural collision process is a typical non-linear dynamic process, involving geometric, material, and boundary non-linearity, which is one of the recognized research difficulties in the academic community. In contrast, the static mechanics process of structures is simpler and more intuitive, and scholars have been committed to finding a method that can equivalent the complex structural collision process to a simple static mechanics process, in order to provide a more easily understandable method for evaluating structural collision strength.

[0004] The existing methods for obtaining collision loads mainly include experimental methods, theoretical methods, and comprehensive methods. Experimental methods mainly measure collision contact forces through mechanical sensors. Such methods must be based on existing products and cannot be applied to the product concept design stage. A typical theoretical method is the equivalent static load method, which was proposed by Professor Park of Hanyang University in South Korea (B.S Kang and W.S Choi and G.J Park. Structural optimization under equivalent static loads transformed from dynamic loads based on displacement[J].”). The aim is to transform the complex collision process into a linear elastic problem under static load. However, when solving large deformation collision problems, there is a problem of magnification of the equivalent static load. There are also some literature materials that propose collision load calculation methods that combine experimental methods and theoretical methods. For example, in the patent of Wang Yuchao et al. (application number: 201310039923.3), a calculation method for equivalent average collision load (F = ma) based on the acceleration a of the target vehicle and the test mass m is proposed. This method preprocesses the collision acceleration curve of the target vehicle model and calculates the equivalent collision load using Newton's second law. This method belongs to a priori calculation methods, and reasonable calculation results can only be obtained by accumulating a large amount of data and experience. Guo Min et al. proposed a collision load calculation method based on finite element (application number: 202111683503.X). This method obtains the collision load between the vehicle and the bridge by building a refined finite element model and calibrating the model with necessary test data, and then using computational mechanics methods. This method must be based on accurate geometric models and finite element models, so it cannot be applied to the concept design stage and cannot avoid the difficult problems of collision dynamics.

[0005] In summary, the existing collision load calculation methods mainly have the following deficiencies: (1) The existing collision load calculation methods are too complex in theory and highly dependent on experimental techniques and sensors, and are mainly applicable to the performance verification process after structural design and manufacturing; (2) The existing equivalent collision load calculation methods based on the equivalent static load method cannot avoid the defect of magnification of the equivalent static load; (3) The existing collision load calculation methods cannot intuitively reflect the structural collision strength. Summary of the Invention

[0006] In view of the above problems, the present invention aims to provide an equivalent static collision load calculation method that can be widely applied to structural collision analysis and optimization. The method includes four processes: constructing a structural collision energy equation based on the energy principle, establishing a collision dynamics equilibrium equation based on the minimum energy principle, defining an equivalent static collision load based on the mechanical equilibrium principle, and establishing an equivalent static collision load expression based on the position finite element method. An equivalent static collision load calculation method that can intuitively represent the collision intensity is constructed, and further a feasible technical solution is provided for structural collision intensity evaluation and structural collision optimization design.

[0007] The technical solution of the present invention is as follows: An equivalent static collision load calculation method based on the energy principle, comprising: Establish the calculation formula for the equivalent static collision load as: ; Wherein, is the unit node position vector in the current configuration, is the total number of system units, is the volume of the unit in the initial configuration, is the dimension of the local coordinate system of the unit, is the second Piola - Kirchhoff stress, is the unit interpolation function, and are the components of the unit local coordinate system, the differential of the unit volume; Based on the established calculation formula, substitute the obtained parameters into the calculation formula to calculate the equivalent static collision load of the target , and obtain the equivalent static collision intensity of the target to intuitively evaluate the collision intensity of the structure or for implementing structural collision optimization.

[0008] Furthermore, the establishment process of the calculation formula includes: 1) Construct a structural collision energy equation based on the energy principle; 2) Establish a collision dynamics equilibrium equation based on the minimum energy principle; 3) Define an equivalent static collision load based on the mechanical equilibrium principle; 4) Establish an equivalent static collision load expression based on the position finite element method.

[0009] Furthermore, the specific method for constructing the structural collision energy equation based on the energy principle is: Express the total system energy using the strain energy stored in the system , the system kinetic energy and the virtual work of external forces , and the expression is ; Combining with the finite element method, convert the virtual work of external forces into the external force vector of system nodes and the displacement vector of system nodes , expressed as ; Convert the kinetic energy of the system into the velocity vector of system nodes and the mass matrix of the system as , thus obtaining the total energy expression of the system based on the finite element method; In the finite element method, the displacement vector of system nodes is obtained from the node position vector of the system under the target reference configuration and the node position vector of the system under the target current configuration, that is , thus establishing the relationship between the total energy of the system and the target node position vector.

[0010] Further, the specific method for establishing the collision dynamics equilibrium equation based on the minimum energy principle is: Differentiate the obtained structural collision energy equation using the chain rule, that is, by finding to obtain the collision dynamics equilibrium equation, thereby obtaining the internal force vector of system nodes , the acceleration vector of system nodes , the mass matrix of the system and the external force vector of system nodes relationship .

[0011] Further, the specific method for defining the equivalent static collision load based on the mechanical equilibrium principle is: According to the obtained collision dynamics equilibrium equation, define the equivalent static collision load as the internal force vector of system nodes .

[0012] Further, the specific method for establishing the equivalent static collision load expression based on the position finite element method is: Express the equivalent static collision load as a function of strain energy, thereby obtaining the relationship between the equivalent static collision load and the strain energy density ; Define the strain energy density as a function of the Green-Lagrange strain tensor , and define as the node position vector of the system under the target reference configuration and the node position vector of the system under the target current configuration and the component of the local coordinate system of the element and Differential equation; Combined with the interpolation expression of displacement in the finite element method for representation, the position vector of the element nodes in the current configuration of the target is obtained and relationship; Combined with the obtained relationship, the expression parameters of the original equivalent static collision load are replaced to obtain the final expression of the equivalent static collision load.

[0013] The beneficial effects of the present invention are: (1) The method of the present invention is derived and developed based on the energy principle, with rigorous theory and wide applicability; (2) The method of the present invention can directly calculate the equivalent collision load based on the position vector, with simple calculation; (3) The method of the present invention can be secondarily developed and calculated based on the existing mature commercial software platform, which is easy to realize programmed operation and engineering application; (4) The method of the present invention can effectively solve the problems caused by the amplification of the "equivalent static collision load" in the existing methods. Description of the Drawings

[0014] Figure 1 It is a schematic diagram of the construction process of the equivalent static collision load.

[0015] Figure 2 It is a schematic diagram of the deformation of a one-dimensional bar element.

[0016] Figure 3 It is a schematic diagram of the relationship between the equivalent collision load and the position. Detailed Embodiments

[0017] The following describes the present invention in detail with reference to the drawings.

[0018] The core of the technical solution of the present invention is the calculation of the equivalent static collision load based on the energy principle. First, the collision dynamics equation is derived based on the energy principle, then the equivalent static collision load is defined, and finally the analytical expression of the equivalent static collision load is derived in the finite element mode based on displacement. The method proposed by the present invention includes constructing an energy balance equation, deriving a collision dynamics equation, defining an equivalent static collision load, and establishing an analytical expression of the equivalent static collision load in the finite element mode based on position. The specific steps are mainly as follows: 1. Construct the structural collision energy equation based on the energy principle Considering that the duration of the collision process is very short, and ignoring the influence of system damping, the total energy H of the system is: (1) Where: \(U\) is the strain energy stored in the system, and \(T\) is the kinetic energy of the system, is the virtual work of external forces; In the finite element-based method, the total energy \(H\) can be further expressed as: (2) Where: is the system nodal displacement vector, is the system nodal velocity vector, is the system nodal external force vector, is the system mass matrix; (3) Where: and are the system nodal position vectors in the reference configuration and the current configuration, respectively; 2. Establish the collision dynamics equilibrium equation based on the principle of minimum energy Differentiate Equation (2) using the chain rule based on the principle of minimum energy, and considering Equation (3), we get: (4) Where: is the system nodal internal force vector, is the system nodal acceleration vector; 3. Define the equivalent static collision load based on the principle of mechanical equilibrium Based on the principle of mechanical equilibrium, the equivalent static collision load can be defined as: (5) Numerically, the equivalent static collision load can also be further expressed as a function of the strain energy: (6) Where: is the strain energy density, is the volume of the element in the initial configuration, is the total number of elements in the system; 4. Establish the expression of the equivalent static collision load based on the position finite element method Considering that the collision process involves geometric nonlinearity and material nonlinearity, the strain energy density of the element can be expressed as a function of the Green-Lagrange strain tensor : (7) Considering the work conjugate relationship between the Green-Lagrange strain tensor and the second Piola-Kirchhoff stress we have: (8) Under large deformations, the Green-Lagrange strain tensor can be expressed as: (9) where: and are the components of the local coordinate system of the element, and the values of i and j range from 1 to , is the dimension of the local coordinate system of the element; Considering the interpolation expression form of displacement in the finite element method: (10) where, is the displacement vector of the element nodes, and are the position vectors of the element nodes in the current configuration and the reference configuration, respectively.

[0019] Then equation (9) can be further expressed as: (11) where: and are the element interpolation function and the displacement vector of the element nodes, respectively.

[0020] Furthermore, the derivative of the strain can be expressed as: (12) Applying the chain rule of differentiation to equation (6) and considering equations (7), (8), and (11), the expression for the equivalent static collision load can be obtained: (13) Furthermore, considering equations (8) and (12), the final analytical expression of the equivalent static collision load can be expressed as: (14) where, is the volume of the element in the initial configuration, is the total number of elements in the system.

[0021] Example

[0022] In this example, an isoparametric rod element is considered for the general form of the equivalent collision load. For simplicity, a one-dimensional rod element with 2 nodes ( ) is considered here, and the nodes are and (as shown in Figure 2 ). Let and respectively represent the cross-sectional area and length of the element in the reference configuration Consider the local coordinate system of the element ( ), that is, establish the local coordinate system along the axis direction of the bar element (and this method is consistent with the X direction of the global coordinate system and shares the same origin), then there is .

[0023] The element shape function matrix can be defined as:

[0024] The derivative of the element shape function matrix can be expressed as:

[0025] For a bar element, since its local coordinate system has only one degree of freedom ( ), so when , the axial strain of the bar is calculated by formula (11) as:

[0026] Consider the simplest case, that is, only one element is included ( ), so when , the axial strain of the bar is calculated by formula (11) as:

[0027] Considering the material nonlinearity under the collision condition, here choose the incompressible neo-Hookean material model, then there is:

[0028]

[0029] It can be seen from the above formula that although the equivalent collision load is a highly nonlinear function of the nodal position vector , it is uniquely determined by the nodal position vector (the relationship between the equivalent static collision load and the position is as shown in Figure 3 ).

[0030] It can be seen that the method for calculating the equivalent static collision load based on the energy principle proposed by the present invention can quickly and directly realize the calculation of the equivalent static collision load, providing an effective solution method for the calculation of the equivalent static collision load. At the same time, current commercial software can all output the nodal position vector. Therefore, this method can also be used for secondary development based on existing large-scale finite element software, providing a feasible approach for engineering applications.

Claims

1. A method for calculating equivalent static collision load based on energy principle, characterized in that: include: The calculation formula for establishing the equivalent static collision load is: in, is the node position vector of the unit in the current configuration, is the total number of system units, is the volume of the unit in the initial configuration, is the dimension of the local coordinate system of the element, is the second kind of Piola-Cochhof stress, is the interpolation function of the unit, and are the components of the local coordinate system of the element, is the unit volume; Based on the established calculation formula, the acquired parameters are brought into the calculation formula to calculate the equivalent static collision load of the target. , obtain the equivalent static collision strength of the target to intuitively evaluate the collision strength of the structure or to implement structural collision optimization.

2. The method for calculating equivalent static collision load based on energy principle according to claim 1, characterized in that: The process of establishing the calculation formula includes: 1) Construct the structural collision energy equation based on the energy principle; 2) Establish the collision dynamics equilibrium equation based on the minimum energy principle; 3) Define equivalent static collision load based on the principle of mechanical equilibrium; 4) Establish the equivalent static collision load expression based on the position finite element method.

3. The method for calculating equivalent static collision load based on energy principle according to claim 2, characterized in that: The specific method of constructing the structural collision energy equation based on the energy principle is: The total energy of the system Strain energy stored in the system 、System kinetic energy and external force virtual work To express it, the expression is ; Combined with the finite element method, the virtual work of external force Convert to system node external force vector and the system node displacement vector , expressed as ; Convert system kinetic energy into system node velocity vector and the system mass matrix for , thus obtaining the total energy expression of the system based on the finite element method; in the finite element method, the system node displacement vector is the node position vector of the system in the reference configuration and the node position vector of the system in the current configuration Get, that is , thereby establishing the relationship between the total system energy and the target node position vector.

4. The method for calculating equivalent static collision load based on energy principle according to claim 3 is characterized in that: The specific method of establishing the collision dynamics equilibrium equation based on the minimum energy principle is: The obtained structural collision energy equation is differentiated by using the chain rule, that is, by finding The collision dynamics equilibrium equation is obtained, and thus the internal force vector of the system node is obtained , system node acceleration vector , system quality matrix and the system node external force vector The relationship between .

5. The method for calculating equivalent static collision load based on energy principle according to claim 4, characterized in that: The specific method of defining the equivalent static collision load based on the principle of mechanical equilibrium is: According to the collision dynamics equilibrium equation obtained, the equivalent static collision load is defined as the system node internal force vector .

6. The method for calculating equivalent static collision load based on energy principle according to claim 5, characterized in that: The specific method for establishing the equivalent static collision load expression based on the position finite element method is: Equivalent static collision load Expressed as a function of strain energy, the equivalent static collision load is obtained and strain energy density the relationship between; Definition of strain energy density is the Green-Lagrange strain tensor Function , and define is the node position vector of the system under the target reference configuration and the node position vector of the system under the target current configuration and the local coordinate system components of the element and Differential equations of Combined with the interpolation expression of displacement in the finite element method Represented, the unit node position vector under the current configuration of the target is obtained and relationship; Combined with the obtained relationship, the original equivalent static collision load The expression parameters are replaced to obtain the final equivalent static collision load expression.

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