A method for topological optimization of automobile structure collision based on model order reduction

Abstract

The present invention is a method for topological optimization of automobile structure collision based on model order reduction. It is divided into a decomposition domain, an analysis domain, a transformation domain and a design domain. In the decomposition domain, the collision model is divided into a linear part and a nonlinear part, the nonlinear part is not processed, the linear model is reduced in model order, and the reduced-order stiffness matrix is ​​output; in the analysis domain, the nonlinear part and the reduced-order stiffness matrix are coupled to perform collision analysis to reduce the calculation cost of the structural collision analysis, and the collision response and model parameters are output at the same time; in the transformation domain, according to the collision model parameters and the collision response, the nonlinear dynamic model involved in the structural collision analysis is converted into a linear static model and output; in the topology optimization field, the static model is topologically optimized according to the preset optimization parameters, the optimal model is output, and the next cycle is entered; the entire optimization process is repeated until the optimization process meets the preset convergence conditions, then the optimization process is terminated and the optimization result is output.

Description

Technical Field

[0001] The invention relates to the field of automobile technology, in particular to an efficient structural collision topology optimization method based on model order reduction theory. Background Art

[0002] Research shows that structural collision topology optimization is a conceptual design method in the field of structural optimization design that can take into account both structural crashworthiness and lightweight requirements. However, structural collision topology optimization is a typical structural nonlinear dynamic response optimization problem, involving highly nonlinear problems such as materials, geometry, and contact, as well as complex dynamic processes such as collision impact. It is currently one of the most complex research problems in the field of structural optimization design.

[0003] Therefore, in practical applications, due to the complexity of the structural collision topology optimization problem, the solution speed of the structural collision finite element equations is slow. In addition, the optimization process requires hundreds of iterations, and each iteration requires solving the finite element equations and completing the nonlinear optimization iteration process, resulting in its computational efficiency always failing to meet the actual engineering needs.

[0004] The structural optimization method based on the equivalent static load method proposed by Professor Park et al. of Hanyang University in South Korea (“WS Choi and GJPark. Transformation of dynamic loads into equivalentstatic loads based on modal analysis[J]. International Journal for NumericalMethods in Engineering,1999, 46(1):29-43”, “BS Kang and WS Choi and G.JPark. Structural optimization under equivalent static loads transformed fromdynamic loads based on displacement[J]. Computers and Structures, 2001,79(2):145-154”, “WS Choi and GJ Park. Structural optimization using equivalentstatic loads at all time intervals[J]. Computer Methods in Applied Mechanicsand Engineering,2002, 191(19):2105-2122”, “Park, GJand BSKang. Validation of a Structural Optimization Algorithm Transforming Dynamic Loads intoEquivalent Static Loads[J].Journal of optimization theory and applications,2003,118(1):191-200”), which can transform complex nonlinear dynamic response optimization problems into simple and mature linear static optimization problems. This method can avoid the defect that each optimization iteration needs to solve the structural collision finite element equations, reduce the number of times the finite element equations are solved in the entire optimization process, and greatly improve the efficiency of the structural collision topology optimization method.However, when this method is directly used to solve the problem of large deformation collision topology optimization of structures, the mesh distortion caused by low-density units leads to high computational cost of the collision analysis process, and the node characteristics of the equivalent static load cause poor convergence of the structural topology optimization. As a result, this optimization method has high computational cost and low optimization efficiency when solving the problem of large deformation collision topology optimization of structures, and may even fail to obtain the optimal solution at all.

[0005] In order to solve the mesh distortion problem caused by low-density units in the process of solving structural nonlinear finite element equations, Luo et al. used adaptive hyperelastic technology to convert the material of low-density units into hyperelastic materials, which effectively solved the numerical instability problem caused by low-density units. However, this method cannot be applied to engineering practice ("LUO, Yangjun; WANG, Michael Yu; KANG, Zhan. Topology optimization of geometrically nonlinear structures based on an additive hyperelasticity technique. Computer methods in applied mechanics and engineering, 2015, 286: 422-441."); In order to solve the difficulties in practical applications, Qi Chen et al. equated low-density units to overlapping units composed of standard units and shared node units based on additional hyperelastic materials. This method can be modeled using existing commercial software, which improves the engineering practicality of this method. However, since this method increases the difficulty of modeling and expands the number of units in the model, it does not solve the problem of low computational efficiency ("CHEN, Qi; ZHANG, Xianmin; ZHU, Benliang. A 213-line topology optimization code for geometrically nonlinear structures based on an additive hyperelasticity technique. Computer methods in applied mechanics and engineering, 2015, 286: 422-441."). structures. Structural and Multidisciplinary Optimization, 2019, 59.5:1863-1879.").

[0006] In order to solve the numerical instability problem of topology optimization caused by the node characteristics of the equivalent static load method, Duddeck et al. proposed a solution of ignoring some equivalent static loads or deleting the units in the area where they act. However, due to the node characteristics of the equivalent static loads, deleting the equivalent static loads or units may lead to infeasibility of the optimization results and errors in the optimization process (“Duddeck, Volz. A new Topology Optimization Approach for Crashworthiness of Passenger Vehicles Based on Physically Defined Equivalent Static Loads[J]. In Proceedings ICRASH conference, Milano, 2012”); Davoudi, M et al. proposed a method of capturing the nonlinear dynamic characteristics of thin-walled structures during collision by refining the time step. However, it did not solve the problem of low optimization efficiency or poor convergence caused by the node characteristics of the equivalent static load (“Davoudi, M. and C. Kim. Topology optimization for crashworthiness of thin-walled structures under axial crash considering nonlinear plastic buckling and locations of plastic hinges[J]. Engineering Optimization, 2018.51(5):775-795”).

[0007] In summary, the existing structural optimization method based on equivalent static load still has the following shortcomings in solving the problem of structural large deformation collision topology optimization:

[0008] (1) When solving the topology optimization problem of large deformation collision, the existing structural optimization method based on equivalent static load requires the entire model to participate in the collision analysis process, so there is a problem of high computational cost. In particular, when a large number of low-density units exist, the computational efficiency of the collision analysis process is significantly reduced.

[0009] (2) When solving the topology optimization problem of large structural deformation collision, the existing structural optimization method based on equivalent static load has a serious impact on the convergence of topology optimization due to the node characteristics of equivalent static load.

[0010] (3) The existing unit superposition technology based on hyperelastic materials can effectively solve the grid distortion problem caused by low-density units during structural collision, but it is not conducive to reducing the cost of structural collision analysis;

[0011] (4) The existing structural optimization method based on equivalent static loads cannot solve the problems of low optimization efficiency and poor convergence caused by the node characteristics of equivalent static loads. Summary of the invention

[0012] The present invention provides an efficient structural collision topology optimization method based on model order reduction theory, which can take into account both collision analysis cost and optimization efficiency; the present invention is centered on model order reduction and is divided into a decomposition domain, an analysis domain, a transformation domain and a design domain. In the decomposition domain, the collision model is divided into a linear part and a nonlinear part, and no processing is done on the nonlinear part, while the model is reduced for the linear model, and the reduced-order stiffness matrix is ​​output; in the analysis domain, the nonlinear part and the reduced-order stiffness matrix are coupled for collision analysis to reduce the computational cost of the structural collision analysis, and the collision response and model parameters are output at the same time; in the transformation domain, according to the collision model parameters and the collision response, the nonlinear dynamic model involved in the structural collision analysis is converted into a linear static model and output; in the design domain, the static model is topologically optimized according to the pre-set optimization parameters, the optimal model is output, and the next cycle is entered; the entire optimization process is repeated until the optimization process meets the pre-set convergence conditions, then the optimization process is terminated and the optimization result is output.

[0013] The technical solution of the present invention is described as follows in conjunction with the accompanying drawings:

[0014] A method for automobile structure collision topology optimization based on model order reduction includes the following steps:

[0015] Step 1: Before performing the vehicle structure collision analysis in the decomposition domain, the entire collision model is divided into a linear part and a nonlinear part based on a clustering algorithm;

[0016] Step 2: For the nonlinear part, a unit-level standard nonlinear dynamic collision model is established based on the explicit finite element method;

[0017] Step 3: For the linear part, the internal force vector F int (t) Solve using linear finite element method;

[0018] Step 4: Select the common node degrees of freedom of the linear part and the nonlinear part as the master degrees of freedom and the other node degrees of freedom as the slave degrees of freedom, and represent them with subscripts m (master) and s (slave) respectively, reduce the model order of the linear part, and output the reduced-order stiffness matrix;

[0019] Step 5: In the analysis domain, the reduced-order stiffness matrix and the nonlinear part are coupled to form a reduced-order collision model to reduce the computational cost of the collision analysis;

[0020] Step 6: In the transformation domain, the reduced-order equivalent static load F is obtained by multiplying the reduced-order stiffness matrix of the structure with the node displacement vector. req ;

[0021] Step 7: Equivalent the structural collision topology optimization problem to the critical time t c Linear static topology optimization problem of multi-case structures under the action of nearby reduced-order equivalent static loads;

[0022] Step 8. According to the objective function values ​​and design variables of two adjacent external loops and their changes, the convergence of the optimization process is judged. If it converges, the optimization process is called out. If it does not converge, the model is updated and returned to step 1. The model is updated in such a way that the degrees of freedom of the corresponding design area in the collision model are reduced to the boundary degrees of freedom according to the values ​​of the design variables in the topology optimization results, and then coupled to the collision model in the form of a super unit for collision analysis again.

[0023] The unit-level standard nonlinear dynamics collision model described in step 2 is as follows:

[0024]

[0025] in, represents the acceleration vector; M represents the unit mass matrix; F int (t) represents the internal force vector; F ext (t) represents the external force vector.

[0026] The specific method of step three is as follows:

[0027] According to the definition of equivalent static load, the internal force is expressed as the product of the node displacement vector and the structural stiffness matrix; under the premise of ensuring the calculation accuracy, the internal force vector F of the collision model at any time point is int (t) is equivalent to:

[0028]

[0029] Among them, u e (t) is the unit node displacement vector; ρ e is the cell density, is the element tangent stiffness matrix;

[0030] In the linear range, the tangent stiffness matrix of the element is It is further degenerated into a linear stiffness matrix, namely:

[0031]

[0032] Among them, Ke(ρ e ) is the unit linear stiffness matrix, then the structural collision dynamics equation for the linear part is further expressed as:

[0033]

[0034] Among them, M(ρ) represents the structural mass matrix; K(ρ) represents the structural stiffness matrix; X(t) and denote the node displacement and acceleration vectors respectively; F(t) denotes the external load vector;

[0035] The reduced stiffness matrix described in step 4 is as follows:

[0036] K R (ρ)=K(ρ) mm -K(ρ) ms ((ρ)K ss ) -1 K(ρ) sm

[0037] in, K(ρ) mm represents the block corresponding to the principal degree of freedom in the structural stiffness matrix; K(ρ) ms and K(ρ) sm The structural stiffness matrix corresponds to a mixed block of master and slave degrees of freedom, and K(ρ) ss Represents the block in the structural stiffness matrix corresponding to the slave degrees of freedom.

[0038] The collision control equation of the linear part in step 5 is expressed as:

[0039]

[0040] Where M(ρ) represents the structural mass matrix; X(t) and represent the node displacement and acceleration vector respectively; K(ρ) represents the structural stiffness matrix.

[0041] The optimized numerical sequence model in step seven is:

[0042] find:ρ∈R n

[0043]

[0044] subjectto:K(ρ)X(L c )=F req (L c )

[0045] v T ρ≤fv V

[0046] 0.0<ρ min ≤ρ≤1.0,j=1,…,n

[0047] Among them, ρ∈R n represents the topology design variable vector; ρ min represents the lower limit of unit density defined to prevent numerical singularity problems during the optimization process; the objective function g is defined as the weighted sum of structural flexibility under the action of reduced-order equivalent static load; w c represents the weighting coefficient of the cth reduced-order equivalent static load case; v represents the unit volume vector; f v represents the given volume fraction; V represents the volume of the entire design area, and outputs the optimized structural unit density and objective function value; X(L c ) represents the critical time point t c The equivalent static displacement vector of the node at the moment; F req (L c ) represents the critical time point t c Reduced-order equivalent static load at time t.

[0048] The beneficial effects of the present invention are:

[0049] 1) The present invention extends the model reduction theory to the nonlinear field and reduces the cost of collision analysis technology by reducing the order of the collision model;

[0050] 2) The present invention transfers the equivalent static load acting on all nodes in the design domain to some characteristic nodes (such as the common nodes of the linear part and the nonlinear part, and the boundary nodes of the design area), which effectively solves the convergence difficulty problem caused by the node characteristics of the equivalent static load;

[0051] 3) The model updating method of the present invention does not delete any low-density units when updating the model, but reduces the internal degrees of freedom of the design area where the low-density units are located, and couples the output stiffness matrix to the collision model in a super-unit manner, thereby avoiding the numerical instability problem caused by low-density units during the collision analysis process, and maximally ensuring the consistency of the topology optimization results and the collision analysis model, thereby improving the convergence of the topology optimization results;

[0052] 4) The present invention can make full use of the advantages of the existing mature commercial software platform on the basis of the standard equivalent static load calculation method, realize the equivalent transfer of equivalent static load and the order reduction processing of low-density areas, ensure that the equivalent static load acts on some characteristic nodes of the structure, and is easy to realize programming and engineering applications;

[0053] 5) The method described in the present invention can solve the mesh distortion problem involved in the structural large deformation collision topology optimization and the node characteristic defects inherent in the equivalent static load method, enrich the connotation of topology optimization, effectively expand the application scope of the structural optimization method based on equivalent static load, and solve the problems of high computational cost and low optimization efficiency of structural collision topology optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0055] Figure 1 It is a schematic diagram of the present invention;

[0056] Figure 2 is a flow chart of the present invention;

[0057] Figure 3a To simplify the body structure and reduce the collision model schematic;

[0058] Figure 3b Simplified schematic diagram for actual model;

[0059] Figure 3c It is a schematic diagram of the reduced-order collision model;

[0060] Figure 4 This is a schematic diagram of the collision topology optimization model;

[0061] Figure 5 It is a schematic diagram of the iterative process of the objective function;

[0062] Figure 6 This is a schematic diagram of the topology optimization results;

[0063] Figure 7 Schematic diagram for comparison of structural collision force-displacement curves. DETAILED DESCRIPTION

[0064] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0065] See also Figure 1 and Figure 2The core of the technical solution of the present invention is the collision model reduction and equivalent static load calculation method based on the model reduction theory, and the model update technology based on the super unit technology. The model reduction theory is mainly applied to the structural collision analysis, which reduces the calculation cost of the collision analysis on the one hand, and solves the grid distortion problem caused by low-density units on the other hand, and defines a new equivalent static load calculation method and model update method, thereby solving the problems of high calculation cost and low optimization efficiency in solving the structural large deformation collision topology optimization due to the structural optimization method based on equivalent static load, and reducing the difference between the topology optimization results and the collision model, further improving the convergence of the algorithm. The method proposed by the present invention includes several steps including model decomposition, structural collision analysis, reduced-order equivalent static load calculation, structural linear static topology optimization and model update, and each step is mainly:

[0066] 1. Model decomposition

[0067] In a car collision accident, some structures will absorb a lot of energy through plastic deformation, while most other structures will only experience small linear vibrations. Therefore, the decomposition domain is responsible for dividing the entire collision model into linear and nonlinear parts based on the clustering algorithm before performing the car structure collision analysis.

[0068] For the nonlinear part, the following unit-level standard nonlinear dynamic collision model is established based on the explicit finite element method; for the linear part, the structure is reduced in model order under small deformation and linear material constitutive relations and the reduced-order stiffness matrix is ​​output:

[0069]

[0070] in, represents the acceleration vector; M represents the unit mass matrix; F int (t) represents the internal force vector; F ext (t) represents the external force vector.

[0071] 2. Structural collision analysis

[0072] In the structural collision analysis module, the structural large deformation collision analysis is carried out. The reduced-order stiffness matrix is ​​coupled with the nonlinear part in the form of a super-element to form a reduced-order collision model to reduce the computational cost of the collision analysis. The structural collision control equation and the reduced-order collision control equation are respectively expressed as:

[0073]

[0074]

[0075] Where ρ represents the artificial density vector of the material; M(ρ), C(ρ) and K N(ρ) represent the structural mass matrix, damping matrix and nonlinear stiffness matrix respectively; F(t) represents the external load vector, which is a function of any time t; x N (t) and Represent the node displacement, velocity and acceleration vectors respectively; the subscript N indicates the nonlinearity involved in the structural collision analysis; for the linear part, K R (ρ) represents the reduced-order stiffness matrix; and X(t) represent the vibration acceleration and displacement vector of the linear part respectively.

[0076] 3. Reduced-order equivalent static load calculation

[0077] The equivalent static load calculation realizes the equivalent linear static transformation of the collision model. The reduced-order equivalent static load calculation described in the present invention utilizes the model reduction theory to calculate on the basis of the reduced-order stiffness matrix. By selecting the boundary nodes as the main nodes, it can ensure that the equivalent static load is equivalently transferred to the boundary nodes, thereby solving the convergence problem caused by the equivalent static load node characteristics. The specific principle is as follows:

[0078] (1) Model proposal

[0079] According to the principle of dynamics, under the premise of ensuring that the overall dynamic characteristics of the model remain unchanged, based on the stiffness design characteristics of the body structure, during the frontal collision, the entire body structure is divided into a front collision energy absorption area with smaller stiffness and a passenger safety protection area with larger stiffness, with the firewall as the dividing line. The front structure is mainly used to absorb collision energy during the collision, and the middle part is mainly used to ensure that the survival space of the occupants is not invaded during the collision. Therefore, under the frontal collision condition, the body structure will undergo severe plastic deformation during the collision; the remaining part will only undergo linear vibration during the collision. Based on the above characteristics, in order to improve the calculation efficiency and reduce the calculation cost, the linear part with smaller deformation is linearly reduced in the frontal collision analysis process, and coupled to the whole vehicle collision model in the form of a super unit, so as to obtain a global reduced-order model of the simplified body structure under the frontal collision condition.

[0080] (2) Calculation of equivalent static load

[0081] The node located at the junction of the nonlinear part and the linear part is called the interface node, and its corresponding degree of freedom is the main node degree of freedom. According to the collision model reduction theory proposed by the present invention, the specific equivalent static load calculation formula can be expressed as:

[0082] F req (L c )=K R ·x B (t c ) (3)

[0083] In the formula, the equivalent static condition L c The critical time point t of the collision process c Strictly correspond; F req (L c ) represents the key time point t c The reduced-order equivalent static load vector of K R represents the reduced-order stiffness matrix of the structure; x B (t c ) corresponds to the critical time point t c The dynamic displacement vector.

[0084] 4. Structural linear static topology optimization

[0085] The structural collision topology optimization problem can be equivalent to the critical time t c The linear static topology optimization problem of multi-condition structures under the action of nearby reduced-order equivalent static loads. The specific optimization mathematical model is:

[0086] find:ρ∈R n (4a)

[0087]

[0088] subject to:K(ρ)X(L c )=F req (L c ) (4c)

[0089] v T ρ≤f v V (4d)

[0090] 0.0<ρ min ≤ρ≤1.0,j=1,…,n (4e)

[0091] Among them, ρ∈R n represents the topology design variable vector; ρ min represents the lower limit of unit density defined to prevent numerical singularity problems during the optimization process; the objective function g is defined as the weighted sum of structural flexibility under the action of reduced-order equivalent static load; w c represents the weighting coefficient of the cth reduced-order equivalent static load case; v represents the unit volume vector; f v represents the given volume fraction; V represents the volume of the entire design area, and outputs the optimized structural unit density and objective function value; X(L c ) represents the key time point t c The equivalent static displacement vector of req (L c ) represents the key time point t cThe reduced-order equivalent static load vector of .

[0092] 5. Model update

[0093] The convergence of the optimization process is judged according to the objective function values ​​and design variables of two adjacent external cycles and their changes. If converged, the optimization process is called out. If not converged, the model is updated and returned to step 1. The model is updated in such a way that the degrees of freedom of the corresponding design area in the collision model are reduced to the boundary degrees of freedom according to the values ​​of the design variables in the topology optimization results, and then coupled to the collision model in the form of a super unit for collision analysis again.

[0094] like Figure 2 As shown in the figure, it is a flowchart of efficient structural collision topology optimization based on model reduction theory. The specific optimization process is as follows:

[0095] Step 1: Model decomposition;

[0096] Based on multiple collision analysis data, the collision structure is divided into a large deformation nonlinear energy absorption part and a small deformation vibration part using clustering algorithms or engineering experience;

[0097] Step 2: Construct a reduced-order collision model and perform nonlinear dynamic collision analysis;

[0098] Based on the model decomposition results of step 1, the interface node degrees of freedom of the linear and nonlinear regions are first selected as the main degrees of freedom, the nonlinear model of the small deformation region is linearized and the model is reduced to generate a reduced-order stiffness matrix; then the reduced-order stiffness matrix is ​​coupled with the nonlinear model in the form of a super-element to form a reduced-order collision model; finally, the reduced-order collision model is subjected to collision analysis and collision responses such as displacement, acceleration and energy are output;

[0099] Step 3: Calculate the reduced-order equivalent static load;

[0100] Using the reduced-order stiffness matrix and corresponding displacement vector calculated in step 2, calculate the reduced-order equivalent static load corresponding to the key time point;

[0101] F req (L c )=K R ·x B (t c ) (5)

[0102] Step 4: Establish a reduced-order topology optimization model;

[0103] First, the linear region in step 1 is used as the design space for topology optimization and the objective function, volume constraint, and convergence coefficient are defined. Then, the non-design region under the action of the reduced-order equivalent static load is reduced in model order and coupled with the design region to form a global reduced-order topology optimization model. Finally, the reduced-order optimization model is topologically optimized. The specific optimization mathematical model is:

[0104] find:ρ∈R n (6a)

[0105]

[0106] subject to:K(ρ)X(L c )=F req (L c ) (6c)

[0107] v T ρ≤f v V (6d)

[0108] 0.0<ρ min ≤ρ≤1.0,j=1,…,n (6e)

[0109] Step 5: Determine convergence;

[0110] The convergence of the optimization process is judged according to the objective function values ​​and design variables of two adjacent external cycles and their changes. If converged, the optimization process is called out. If not, the model is updated and returned to step 1. The model is updated in such a way that the degrees of freedom of the corresponding design area in the collision model are reduced to the boundary degrees of freedom according to the values ​​of the design variables in the topology optimization results, and then coupled to the collision model in the form of super-units for collision analysis again.

[0111] Example

[0112] Taking Figure 3(a) as an example of a simplified body structure and reduced-order collision model, the length is 1520 mm, the width and height are both 1000 mm, and the length of the front end of the body is 400 mm. As shown in Figure 3(b), the body collision finite element model simulates a 1000 kg rigid pendulum hitting a rigid wall along the axial direction at a speed of 15 km / h. When modeling, a 5 mm four-node quadrilateral unit is selected for meshing. The material is Young's modulus, Poisson's ratio and density are 210000 MPa, 0.33 and 7.9×10 -9 T / mm 3 The steel has a tangent modulus of 107 GPa and a yield stress of 340 MPa, and the stress-strain curve is shown in Figure 3(c).

[0113] On the basis of the above collision finite element model, 2.0 mm and 5.0 mm thick materials are used before and after the node EFHG as shown in FIG3(c), respectively, to ensure that the structure of the rear part of the point EFHG remains within the linear vibration range during the collision process. The reduced-order collision model construction method and the reduced-order equivalent static load calculation method proposed in the present invention are used to optimize the structure of the rear linear part through topology optimization under the collision condition. The specific optimization process is as follows: Figure 2 As shown. In the collision topology optimization, the rear end area with smaller deformation is defined as the design space. The entire optimization model uses the relative density of each unit as the design variable, and the constraint condition is that the volume fraction is less than 20%. The specific topology optimization model is shown in Figure 4. In addition. In order to ensure complete collision deformation and realize the axial telescopic deformation mode, no displacement constraint is set here, and the weighted flexibility and minimum of the structure under the action of the reduced-order equivalent static load near the critical time point are used as the objective function to ensure that the structure has sufficient stiffness throughout the collision process to avoid excessive intrusion and cause damage to the occupants in the car.

[0114] The iterative process of the objective function is as follows Figure 5 As shown in Figure 2, the optimization process is stable and efficient, and the objective function decreases steadily. The topology optimization results and the optimization model obtained after engineering interpretation and process modification are shown in Figure 2. Figure 6 As shown in the figure, the high-density areas are mainly distributed near the interface between the linear part and the nonlinear part and near the four corners, which is conducive to improving the bearing capacity of the structure. The load transfer path is reasonable and reliable, which helps to efficiently and robustly transfer the collision load. In addition, in order to meet the lightweight requirements (volume constraints), two circular and three triangular low-density areas are formed in the structure. This topological layout is conducive to reducing stress concentration and improving the robustness of the structure while ensuring the bearing capacity of the structure.

[0115] In order to verify the effectiveness of this method, the model obtained by topology optimization was remodeled, and a collision analysis was performed under the same conditions. The crashworthiness of the optimized model was evaluated by comparing it with the original structure. Figure 7 The comparison of the collision force-displacement curves of the two models is shown. It can be found that the deformation of the nonlinear energy absorption part of the new model has increased significantly, while the deformation of the linear part has hardly increased. It can be seen that the collision energy absorption area of ​​the model designed after collision topology optimization has a larger deformation and the energy absorption effect is more fully exerted. In summary, the automobile structure collision topology optimization method based on model order reduction proposed in the present invention can solve the topology optimization problem of thin-walled structures under large deformation collision conditions, effectively reducing the calculation cost and improving the optimization efficiency.

[0116] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for automobile structure collision topology optimization based on model order reduction, characterized in that: The following steps are involved: Step 1: Before performing the vehicle structure collision analysis in the decomposition domain, the entire collision model is divided into a linear part and a nonlinear part based on a clustering algorithm; Step 2: For the nonlinear part, a unit-level standard nonlinear dynamic collision model is established based on the explicit finite element method; Step 3: For the linear part, the internal force vector F int (t) Solving using linear finite element method; Step 4: Select the common node degrees of freedom of the linear part and the nonlinear part as the master degrees of freedom and the other node degrees of freedom as the slave degrees of freedom, and represent them with subscripts m (master) and s (slave) respectively, reduce the model order of the linear part, and output the reduced-order stiffness matrix; Step 5: In the analysis domain, the reduced-order stiffness matrix and the nonlinear part are coupled to form a reduced-order collision model to reduce the computational cost of the collision analysis; Step 6: In the transformation domain, the reduced-order equivalent static load F is obtained by multiplying the reduced-order stiffness matrix of the structure with the node displacement vector. req ; Step 7: Equivalent the structural collision topology optimization problem to the critical time t c Linear static topology optimization problem of multi-case structures under the action of nearby reduced-order equivalent static loads; Step 8. According to the objective function values ​​and design variables of two adjacent external loops and their changes, the convergence of the optimization process is judged. If it converges, the optimization process is called out. If it does not converge, the model is updated and returns to step 1. The model is updated in such a way that the degrees of freedom of the corresponding design area in the collision model are reduced to the boundary degrees of freedom according to the values ​​of the design variables in the topology optimization results, and then coupled to the collision model in the form of a super unit for collision analysis again.

2. The method for automobile structure collision topology optimization based on model order reduction according to claim 1, characterized in that: The unit-level standard nonlinear dynamics collision model described in step 2 is as follows: in, represents the acceleration vector; M represents the unit stiffness matrix; F int (t) represents the internal force vector; F ext (t) represents the external force vector.

3. The method for automobile structure collision topology optimization based on model order reduction according to claim 1, characterized in that: The specific method of step three is as follows: According to the definition of equivalent static load, the internal force is expressed as the product of the node displacement vector and the structural stiffness matrix; under the premise of ensuring the calculation accuracy, the internal force vector F of the collision model at any time point is int (t) is equivalent to: Among them, u e (t) is the unit node displacement vector; ρ e is the cell density, is the element tangent stiffness matrix; In the linear range, the tangent stiffness matrix of the element is It is further degenerated into a linear stiffness matrix, namely: Among them, K e (ρ e ) is the unit linear stiffness matrix, then the structural collision dynamics equation for the linear part is further expressed as: Among them, M(ρ) represents the structural mass matrix; K(ρ) represents the stiffness matrix; X(t) and represent the node displacement and acceleration vector respectively; F(t) represents the external load vector.

4. The method for automobile structure collision topology optimization based on model order reduction according to claim 1, characterized in that: The reduced stiffness matrix described in step 4 is as follows: K R (ρ)=K(ρ) mm -K(p) ms (K(p) ss ) -1 K(p) sm in, K(ρ) mm represents the block corresponding to the principal degree of freedom in the structural stiffness matrix; K(ρ) ms and K(ρ) sm The structural stiffness matrix corresponds to a mixed block of master and slave degrees of freedom, and K(ρ) ss Represents the block in the structural stiffness matrix corresponding to the slave degrees of freedom.

5. The method for automobile structure collision topology optimization based on model order reduction according to claim 1, characterized in that: The collision control equation of the linear part in step 5 is expressed as: Where M(ρ) represents the structural mass matrix; X(t) and represent the node displacement and acceleration vector respectively; K(ρ) represents the stiffness matrix.

6. The method for automobile structure collision topology optimization based on model order reduction according to claim 1, characterized in that: The optimized numerical sequence model in step seven is: find:ρ∈R n subject to:K(ρ)X(L c )=F req (L c ) v T ρ≤f v V 0.0<ρ min ≤ρ≤1.0,j=1,…,n Among them, ρ∈R n represents the topology design variable vector; ρ min represents the lower limit of unit density defined to prevent numerical singularity problems during the optimization process; the objective function g is defined as the weighted sum of structural flexibility under the action of reduced-order equivalent static load; w c represents the weighting coefficient of the cth reduced-order equivalent static load case; v represents the unit volume vector; f v Represents a given volume fraction; V represents the volume of the entire design area, and outputs the optimized structural unit density and objective function value; X(L c ) represents the critical time point t c The equivalent static displacement vector of the node at the moment; F req (L c ) represents the critical time point t c Reduced-order equivalent static load at time t.

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