Reanalysis Accelerated Topology Optimization For 0-1 Discrete Variables

In recent decades,structural topology optimization has got many progresses under the framework of solid isotropic material penalty method,level-set method,moving morphable components method and other methods.In recent years,researchers continue to exploretopology optimization of 0-1 discrete variables.In the proposed canonical relaxation algorithm,it was pointed out that the sensitivity calculation of 0-1 discrete variables requires two approximations and there are problems with the addition of elements.In order to solve the above problems,this paper proposes a canonical relaxation algorithm with reanalysis acceleration.Firstly,this article introduces the 0-1 discrete variable topology optimization method and the canonical relaxation algorithm.The two-step approximation is needed to calculate the sensitivity of discrete variables and the results diverge when adding elements are analyzed with examples.Then four reanalysis methods,including combined approximation method,conjugate gradient method,preconditioned conjugate gradient method,and SMW exact reanalysis method,are used to verify the adaptability of the reanalysis method in the structurally topology modification problem,and the modification format of SMW method is presented for topology modification.The number of algebraic operations of the four reanalysis methods are compared,and the combined approximation method and SMW reanalysis method are verified through calculation examples,which can efficiently solve the topology modification problem.Then,due to the high efficiency of SMW method in modifying a small number of elements,the sensitivity of 0-1 discrete variables is derived and simplified by using SMW reanalysis method.Combining it with the canonical relaxation algorithm,reanalysis accelerated regular relaxation algorithm is obtained on the premise that the accuracy is consistent with the exact calculation.Finally,the MATLAB code is written.The numerical example verifies the accuracy of the reanalysis sensitivity,and also verifies that the canonical relaxation algorithm can obtain the topological configuration without intermediate density.It shows the correctness of introducing the reanalysis into the canonical relaxation algorithm.Finally,analyze the two pre-settings the influence of parameters on the canonical relaxation algorithm illustrates the generality of the reanalysis accelerated canonical relaxation algorithm.Under the premise that the accuracy is consistent with the exact solution,the results show that the proposed method can realize the accelerated canonical relaxation algorithm.