The present invention relates to the technical field of crashworthiness optimization of thin-walled frame structures, and specifically to a material-based subdomain hybrid cellular automata algorithm for solving material optimization of thin-walled frame structures.
Bodies of car, rail transit and engineering machinery are typical space frame structures assembled by a variety of thin-walled structures of different materials. To use multi-material thin-walled frame structures is an effective way and an inevitable trend to optimize the safety and cost requirements of automotive, rail transit and engineering machinery. To select the best material and to do optimization design of the multi-material thin-walled frame structures can not only improve the mechanical properties (such as crashworthiness) of thin-walled frame structures, but also reduce their costs. The multi-material matching optimization of thin-walled frame structures with considering crashworthiness and cost is a typical nonlinear dynamic response optimization problem including many discrete variables. Due to the high level of non-linearity in the output response of crash simulation and the presence of numerical noise and oscillation, the gradient-based optimization algorithm is difficult to effectively solve the crashworthiness optimization problem of thin-walled frame structures. Evolutionary algorithms usually need to perform thousands of finite element analyses (FEAs), which leads to a very long optimization time. The optimization algorithms based on the surrogate model is the main way to solve the problems mentioned above. However, when the number of design variables is large (such as more than 30 or even more), the optimization efficiency of the optimization algorithm based on the surrogate model will also be greatly reduced.
Hybrid Cellular Automata (HCA) method is a non-gradient heuristic algorithm that can solve nonlinear dynamic response optimization problems including many discrete variables (such as material density or thickness). However, the existing methods are mainly based on the idea of uniform distribution of internal energy density (IED) to update material density or thickness. It is difficult to solve the multi-material optimization problem of thin-walled frame structures with multiple performance constraint functions, and easy to fall into local optimal solution. Presently, few efficient algorithms can be employed to solve the nonlinear dynamic response optimization problem with many material variables in the discrete design space.
In view of the deficiencies in the prior art, the present invention provides a material-based subdomain hybrid cellular automata algorithm for solving material optimization of thin-walled frame structures which can efficiently solve a nonlinear dynamic response optimization problem with many material variables.
The present invention achieves the technical object mentioned above by the following technical means.
A material-based subdomain hybrid cellular automata(M-SHCA) algorithm for solving material optimization of thin-walled frame structures includes the following steps:
Specifically: defining a candidate material library and a nominal flow stress of each material, updating the nominal flow stress of a current cell, comparing a nominal flow stress with the true flow stress of each material in the candidate material library, selecting a candidate material closest to the nominal flow stress as a selected material of current cell, and replacing material parameters of current cell with the mechanical parameters of the selected material;
where, ρs is a density of the sth material in the candidate material library; Es is an elastic modulus of the sth material in the candidate material library; σys is a yield strength of the sth material in the candidate material library;
is a flow stress of the sth material in the candidate material library; σus is a tensile strength of the sth material in the candidate material library; :1≥2 is the number of materials in the candidate library.
Furthermore, a nominal flow stress is a non-physical parameter, which is a positive real number. Further, a nominal flow stress of each cell is updated as follows:
where, σΩ
ΔσΩ
where, eΩ
where, Kp is a proportional control coefficient; Ki is an integral control coefficient; Kd is a differential control coefficient; eΩ
Furthermore, the following equation is used to select a candidate material closest to the nominal flow stress as the selected material of the current cell by comparing the nominal flow stress with the true flow stress of each material in the candidate material library:
where, p denotes a position of the selected material in the candidate material library, σfp is an actual flow stress of the selected material; σΩ
Further, the following equation is employed to replace material parameters of a current cell with mechanical parameters of selected material:
where, ρΩ
Furthermore, global convergence conditions comprise:
|C(h,k)−C*(k)|<ε1 or k1≥k1max
where
is a total cost in the hth inner loop and the kth outer loop, here CΩ
C
Ω
(h+1,k)=ξΩ
where, ξΩ
The present invention has the following beneficial effects:
The present invention is further illustrated below with reference to the accompanying drawings and specific embodiments, but the protection scope of the present invention is not limited thereto.
As shown in
A finite element preprocessor software (such as HyperMesh or LS-Prepost) is used to discrete a full-vehicle geometric model into its finite element meshes, and then assign attributes, materials, boundary conditions and initial conditions for each part of the finite element meshes to complete the full-vehicle crash finite element model for the material and cost optimization of thin-walled frame structures.
The concept of “subdomain Cellular Automata (CA) model” is introduced in a discrete design space based on a conventional CA model, as shown in
Ω(CAΩ,αΩ)=Ω1(CAΩ
where Ω1 denotes an ith subdomain of the global design space Ω, αΩ
As shown in
in which, MatΩ
Wherein, UΩ
A main purpose of the outer loop is to carry out finite element simulation analysis, calculate an output response, and update an TED and a target cost:
To improve the stability for updating the cell material and avoid the oscillation in the outer loop, an IED SΩ
When multiple performance constraint functions exist in the outer loop, a target cost updating rule is proposed based on the penalty function method, in which the penalty value of a target cost ΔC*(k) is used to indicate an extent to a current design point violating the constraint boundary in the kth outer loop and then the target cost is updated in the kth outer loop. The penalty value of the target cost ΔC*(k) is calculated as follows:
in which, ng is the number of constraint functions, Kq is a scale factor of the penalty value of the target cost, Oi(k) is a response of the ith constraint function in the kth outer loop, Oi* is a specified boundary condition of the ith constraint function, δ(k) is a relative deviation between ng constraint functions and a specified boundary condition, C*(0) denotes an initial total cost of thin-walled frame structures, ΔC denotes a maximum penalty of the target cost.
Then a target cost C*(k) in the kth outer loop is updated by the following equation:
C*
(k)=min(C*(k−l)+ΔC*(k),C*(k′)) (7)
in which, k′ denotes the position of the last feasible solution in the outer loop iterations. If there is no feasible solution in the outer loop iterations until current design point, k′ will vanish (k′=0).
To improve the convergence efficiency of the M-SHCA. algorithm, pf is defined to indicate the iteration number for the consecutive infeasible solutions, of which an initial value is set to be zero; pf* is defined to indicate the maximum iteration number for the consecutive infeasible solutions. If the current design point is a feasible solution during iterations, pf=0; if the current design point is an infeasible solution, pf=pf+1. If the iteration number for the consecutive infeasible solutions is greater than the maximum iteration number for the consecutive infeasible solutions (pf>pf*), the M-SHCA algorithm will be convergent and the iterations of the M-SHCA algorithm will be terminated.
As shown in
A side collision simulation of car body frames is employed to exemplify the construction and the updating rule of the SIED* function:
An index id of the cell Ωi,j with its subscripts i and j is defined by equation (8), that is, id is a function about the subscripts i and j of the cell Ωi,j, and then Sid(i,j)(k)=S106
id(i,j)={circumflex over (N)}Ω
in which, {circumflex over (N)}Ω
ΔSid(k)=Sid(k)−
where,
is an average IED of all cells in the kth outer loop,
All cells are traversed to judge whether equation (10) is satisfied. A subscript id of ΔSid(k) is defined as a “step point” and denoted as idi if equation (10) is satisfied. The m “step points” determined by equation (10) can construct m+1 “step ranges” denoted as [idi−1, idi], where
ΔSid(k)*ΔSid+1(k)<0 (10)
A width threshold of the “step range” is defined as Hthreshold. All “step ranges” are traversed. to judge whether equation (11) is satisfied. If equation (11) is satisfied (that is, the width of “step range” [idi−1, idi] is very small), the “step points” are deleted and the “step ranges” are updated in the following manner: when i=1, a “step point” id1 is deleted, the “step range” is updated from [id0,id1] to [id0,id2]; when i>1, a “step point” idi−1 is deleted, and the “step range” is updated from [idi−1,idi] to [idi−2,idi]. The original “step points” and “step ranges” are retained if equation (11) is not satisfied. If the number of the updated “step points” is m′, the number of the updated “step ranges” is m′+1.
idi+1−idi+1<Hthreshold (11)
where, Si*(h,k) is a target IED in the “step range”[idi−1,idi] in the kth outer loop and the hth inner loop.
To achieve the specified target mass in the outer loop, a target IED of each “step range” in the inner loop is updated according to equation (13):
where, C*(k) denotes a target cost updated in the kth outer loop, C(h,k) denotes a current cost updated in the kth outer loop and the hth inner loop. An initial target IED Si*(0,k) of each “step range” when the process enters the inner loop is calculated by equation (14):
Where, Vthreshold is a target IED threshold coefficient in the “step range”,
A schematic diagram of the step target IED function constructed by the above steps is shown in
A cell material updating rule with a certain control strategy is to make a current cost in the inner loop converged to a target cost. The larger the flow stress of the cell material, the more difficult thin-walled frame structure is to deform in the local region, and the smaller its IED. Conversely, the smaller the flow stress of the cell material, the more easily thin-walled frame structure is to deform in the local region, and the larger its IED. A current IED of each cell is compared with the value of the SIED* function to make the current cost of the inner loop converge to the target cost: if the cell IED is lower than the SIED*, the cell material should be changed to the material with a lower flow stress.
The energy absorption capacity of thin-walled frame structures is dependent of the geometrical characteristics and material properties, in which, the key indicators affecting material properties include yield strength, tensile strength, hardening index and so on. The flow stress calculated by equation (16) can be generally employed to measure the overall material strength, which is adopted as a basis to select material.
where, σy is a yield strength, σu is a tensile strength, and n=0.1 is a hardening index.
Since body material is a discrete variable, its optimization design belongs to the optimization problem with discrete variable. In addition, a specified material normally has an assured combination of different material parameters. Therefore, large amount of complex relationships among material parameters would also be introduced, which would no doubt lead to a high computational complexity of the optimization problems. To handle the difficulties mentioned above, A so-called nominal flow stress (continuous variable) is defined and updated by equations (17)-(20), which is compared with the actual flow stress of the candidate material in turn. Then the candidate material, of which the actual flow stress is closest to the nominal flow stress, is selected as the material of current cell. Finally, the material parameters of the current cell are replaced by the mechanical parameters of the selected material, i.e., density, elastic modulus, yield stress and so on.
The specific steps of cell material update are listed as follows:
A candidate material library of l (l≥2) materials is defined as follows:
Where,
is a flow stress of the sth material in the candidate library, ρs is a material density of the sth material in the candidate library, and Es is an elastic modulus of the sth material in the candidate library.
To solve the discrete optimal problems of body materials, we define a nominal flow stress, which is a positive non-physical parameter.
in which, σΩ
ΔσΩ
where eΩ
f(eΩ
where, Kp is a proportional control coefficient, Ki is an integral control coefficient, Kd is a differential control coefficient, eΩ
in which, p denotes a position of the selected material in the candidate material library, σfp is an actual flow stress of the selected material, σΩ
Material properties of a cell are replaced by the selected material properties mentioned above by equation (22):
where, ρΩ
According to the above steps, a cell cost CΩ
C
Ω
(h+1,k)=ξΩ
where, CΩ
The convergence condition of the inner loop is:
|C(h,k)−C*(k)|<εi or ki≥k1max (24)
where,
denotes a total cost in the kth outer loop and the hth inner loop, C*(k) is a target cost defined in the kth outer loop, ε1 is a cost convergence factor, k1 denotes the number of iterations in the inner loop, and k1max denotes a maximum number of iterations in the inner loop.
The M-SFICA algorithm will be terminated if one of the following three convergence conditions is satisfied:
in which, N is the total number of cells, and ε2 represents a global convergence factor.
To verify the convergence and efficiency of the M-SHCA algorithm, it is employed to optimize the material distribution and cost of a car body frame under side collisions. The total weight of the full-vehicle crash FE model is 1346 kg including 276838 elements and 284961 nodes, in which body in white (BIW) adopts the shell elements and engine, gearbox, suspension system, etc. adopt the solid elements. The piecewise elastoplastic materials are used for the deformable structures and the rigid materials are adopted for the undeformable structures. The automatic single surface, automatic surface to surface, automatic node to surface algorithms are defined for the possible contact positions during side collisions. According to the requirements of the regulation titled “The protection of the occupants in the event of a lateral collision” (GB 20071-2006), a mobile deformable barrier (MDB) with a weight of 950 kg should hit a target vehicle perpendicularly at an initial velocity of 50 km/h, as shown in
Step 1: Definition of the Subdomain CA Model and Design Variable
During the vehicle side collisions, B-pillar, sill, doors, and roof middle crossbeam appear large deformation which are the main energy absorbing structures and A-pillar, roof rail, seat crossbeam, and roof crossbeam are the main structures to transfer impact loading. Therefore, the material of 34 parts of 14 assemblies, such as the A-pillar, B-pillar, sill, roof rail, front and rear doors, rear side member, seat crossbeam, and roof crossbeam are defined as the design variables,
The detailed steps to define the subdomain. CA model for the car body beam frame are provided as follows:
Following the above 4 steps, a total of 14 subdomains and a total of 34 thickness variables are defined for the car body beam frame model, as shown in TABLE 2. The material parameters of the candidate material library are listed in
Step 2: Definition of Output Response
In the side collisions simulation of the car body frame, B-pillar is a key component that resists excessive deformation of the body structure and reduces the speed of body intrusion, Excessive deformation of B-pillar will lead the body structure to invade a passenger compartment significantly while reducing the living space of the passenger compartment and causing crash injuries to the passenger. The soft -tissue organs such as heart and lungs of passenger are very sensitive to speed changing of the chest position, If the intrusion velocity is too high, the vital organs in chest will be damaged seriously. Therefore, the maximum intrusion amounts and maximum intrusion velocities of B-pillar corresponding to the chest and pelvic positions are respectively selected as the crashworthiness indexes and output responses under side collisions, which are denoted as d1(Mat), v1(Mat), d2(Mat) and v2(Mat), respectively. As depicted in
Step 3: Definition of Optimization Formulation
In this embodiment, the total cost of 34 parts in TABLE 2 is used as the objective function in which the initial cost is CNY 1291. The maximum invasion amounts and maximum intrusion speeds corresponding to the measuring points at B-pillar (points A and B) are defined as the constraint functions, in which the maximum intrusions at points A and B are 204.70 mm of 270.30 mm, respectively; the maximum initial intrusion velocities at points A and B are 7.78 m/s and 7.85 m/s, respectively. To make the initial full vehicle model meet the requirements of GB 20071-2006, the maximum intrusion amount and the maximum intrusion velocity should be less than or equal to 180 mm and 7.50 m/s, respectively. The initial values and design goals of the output response of B-pillar corresponding to the chest and pelvic positions are shown in TABLE 4, and the corresponding optimization equation is given as follows:
in which, ξi is price of the ith cell material, ρi is material density of the ith cell material, ti is thickness of the ith cell, Ai is area of the ith cell, Mati is material number of the ith cell, and DC01, B170P1, B210P1, B280VK, HC340, HC420, 980DP, 1180DP, B1500HS are candidate materials in the material library.
Step 4: Optimization Results and Discussion
The horizontal IED target (HIED*) function is commonly calculated by the conventional HCA method in each iteration of the inner loop to make the current cost of the inner loop converged to the target mass by updating material with the PID control strategy.
In this embodiment, the M-SHCA algorithm adopting the. HIED* function for cell material updating in the inner loop is referred to as “M-SHCA#1” and the M-SHCA algorithm adopting the SIED* function for cell material updating in the inner loop is referred to as “M-SHCA#2”. To validate the convergence and efficiency of T-SHCA#2, the optimization equation in Equation (25) is separately solved by T-SHCA#1, T-SHCA#2 and parallel EGO-PCEI. The optimization results and the FEAs' numbers of the three algorithms are compared. The detail parameters used by T-SHCA#1, T-SHCA#2 are listed in TABLE 5, while those of parallel EGO-PCEI are listed in TABLE 6.
The iteration processes of M-SHCA#1 are illustrated in
With the comparison and analysis of
The optimization effect of the M-SHCA algorithm based on the SIED* function (i.e. M-SHCA#2) is further discussed here. The total cost of 34 parts and the performance improvement percentage under side collisions before and after optimization as listed in Table 8, in which the optimal solution obtained by the M-SHCA algorithm has achieved a cost reduction effect of 14.72%, while d1(Mat), d2(Mat), v1(Mat) and v2(Mat) have reduced by 15.00%, 12.07%, 10.54%, and 7.26%, respectively. The proposed algorithm not only reduces the total cost of body frame to a large extent, but also significantly improves the safety of vehicle under side collisions.
The material distributions of the optimization solution and the initial body frame are compared in TABLE 9, in which the material of the optimal solution have been distributed more reasonably compared with the initial design; with the optimal material distribution for body frame, the side collision safety performance of body frame can be improved while the total cost of body frame can be greatly reduced. In other words, the multi-material body frame has a stronger potential to improve its crash safety and reduce its total cost than initial body frame with a small amount of materials.
From
From the discussion mentioned above, it is concluded that the M-SHCA algorithm based on the SIED* function have a higher efficiency of global searching than that based on the HIED* function for solving the large scale nonlinear dynamic responses structural optimization problems with many discrete design variables, So the M-SHCA algorithm based on the SIED* function can be employed to effectively solve the optimization problems including the intrusion amounts and the intrusion velocity constraints, specially the nonlinear dynamic structural optimization problems with large scale discrete design variables.
The described embodiment is a preferred embodiment of the present invention, but the present invention is not limited to the aforementioned embodiment. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essential content of the present invention shall fall within the protection scope of the present invention.
Number | Date | Country | Kind |
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202110238581.2 | Mar 2021 | CN | national |
This application is the national phase entry of International Application No. PCT/CN2021/082325, filed on Mar. 23, 2021, which is based upon and claims priority to Chinese Patent Application No. 202110238581.2, filed on Mar. 4, 2021, the entire contents of which are incorporated herein by reference.
Filing Document | Filing Date | Country | Kind |
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PCT/CN2021/082325 | 3/23/2021 | WO |