Research On Fast Algorithm Of Large Scale Finite Element Analysis And Topology Optimization Based On Assembly-free Technology

With the increasing application of finite element analysis(FEA)and topology optimization technologies,the computing scale is getting larger,therefore,the computing speed becomes a challenging factor.The acceleration of large scale FEA can extend its applicability in engineering so as to improve design efficiency and to reduce design cost.This research,on the basis of iterative algorithm,reducing the memory footprint and access as the starting point,improves as well as combines the technologies of assembly-free,deflation,parallel computing,voxelization model,so that a complete assembly-free FEA system is constructed to provide fast calculation of sparse matrix-vector multiplication(Sp MV).The paper carries out study on the fast algorithm around statics analysis,modal analysis,linear bulking analysis,and topology optimization,as a result,a set of assembly-free FEA software and method is formulated with engineering application value.It improves the speed of large scale FEA and topology optimization and can be applied to analysis and optimization design of vehicle parts to solve the practical engineering problems more efficiently.The main contents and results are as followings:(1)Establishment of an efficient assembly-free FEA system.The system is based on the voxelization model,which can reduce the memory footprint by utilize congruency of voxels,and the accuracy is improved without increasing the computing complexity by using Wilson elements;accelerates the convergency of iterative algorithm by deflated processing;reduces the memory footprint in FEA solution and provides the basis of parallel computation on element level by handling the stiffness and deflation matrix in an assembly-free way;avoids race condition by assigning nodes to threads as well as reduces memory footprint by congruency and achieves highly efficient parallel calculation of Sp MV on graphics processing unit.The system is used to improve conjugate gradient algorithm,so that the assembly-free conjugate gradient method is developed to implement high-speed linear equations solution.Consequently,the calculation of large-scale static problem speeds up.In addition,for the low precision of local stress caused by voxelization model,the mesh is fitted to the geometric model through adjusting the node coordinates,only a small number of different elements are generated during this process,so that only a few stiffness matrix are calculated and saved as templates,which reduces the memory footprint.As a result,the assembly-free FEA based on non-conforming elements is obtained with higher accuracy of local stress.(2)The assembly-free deflated subspace Rayleigh-Ritz conjugate gradient method is proposed for fast large-scale modal analysis.The method obtains a better convergency by improving the subspace Rayleigh-Ritz conjugate gradient algorithm through deflation.After that,the primary computational cost is Sp MV and the solution of linear equations,which can be effectively accomplished by assembly-free FEA system.The complete algorithm flow is displayed and implemented by C.What's more,the numerical example of gearbox modal analysis is used to prove the validity and effectiveness of the method.(3)On the issue of the Pareto-tracing Topology Optimization(Pare TO)needs lots of FEA during the optimization,the assembly-free FEA is adopted for Pare TO,so that an efficient assembly-free 3D Pare TO method is proposed and implemented by C to achieve fast 3D continuum topology optimization.Then,its effectiveness is verified by classic examples.By adding multi-condition model and processing constraint,the algorithm is more suitable for practical engineering applications.Moreover,the effectiveness of the algorithm is proved by comparing with Hyper Works through the multi-condition topology optimization of suspension control arm.(4)A fast linear buckling analysis method based on assembly-free FEA is proposed.Due to the particularity of the stress stiffness matrix in linear buckling analysis,the congruency cannot be utilized,so the inverse iteration is used to solve the general eigenvalue problem.Meanwhile,the assembly-free FEA is utilized to fast solve linear equations in inverse iteration,which reduces the numerical error and increases the convergence speed.The method is implemented by C and testified to be correct and effective compared with commercial software by several numerical examples.(5)A fast 3D continuum buckling topology optimization algorithm is presented.Firstly,the model of 2D buckling optimization is formulated,while the critical buckling load maximization is considered as the objective function,and implemented by Matlab to contrast the optimization results and time generated from different buckling sensitivity.The proposed assembly-free 3D buckling analysis method is used in the buckling topology optimization,a topology optimization model is built,while the objective is minimizing the compliance,and buckling constraint is introduced by weighting functions,and then a fast buckling topology optimization method for 3D continuum structure is implemented by C.Some numerical examples of the buckling analysis and topology optimization of the vehicle parts are presented to demonstrate the feasibility and effectiveness of the algorithm.(6)Overall conceptual design of vehicle frame is conducted by 3D topology optimization software based on assembly-free FEA programmed by C.The large-scale FEA model with million-DOF is built.First,the single objective topology optimization is conducted from two typical working conditions: overall bending and torsion working condition.From the material distribution of optimized topology,the impact to bending and torsion stiffness of each part on vehicle frame can be realized.Then,the multi-condition topology optimization is carried out under the combined conditions of bending and torsion to improve the overall stiffness of vehicle frame,which provides particular reference and theoretical basis for Lightweight vehicle frame.Compared with Hyper Works,the advantage of computing speed for large-scale problem of topology optimization method based on assembly-free FEA is verified.