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Adaptive continuation solid isotropic material with penalization for volume constrained compliance minimization. (English) Zbl 1436.74053
Summary: In this paper, the traditional decreasing tolerance continuation solid isotropic material with penalization (CSIMP) was extended by providing a way to adapt the penalty step between subproblems, decreasing the number of subproblems solved. Four linearly elastic, volume constrained, compliance minimization problems were used to test the efficacy of the penalty adaptation for different parameter settings. Three of the problems are common 2D test problems and one is 3D. The main factors affecting the efficacy of the penalty adaptation were identified. Experimental results confirmed that the penalty adaptation successfully reduces the number of finite element analysis (FEA) simulations needed to converge to the optimal solution when using the decreasing tolerance CSIMP (Dec-Tol CSIMP), with exponentially decaying tolerance. In particular, the number of FEA simulations required by Dec-Tol CSIMP was cut down by an average of $$28.8\%$$ with no more than $$4.1\%$$ increase in the objective value in the worst case. Finally, a mathematical and experimental treatment of the effect of $$x_{\min}$$ on the convergence of the SIMP algorithm was given, with recommendations for choosing a suitable value for $$x_{\min}$$.
##### MSC:
 74P05 Compliance or weight optimization in solid mechanics 74P15 Topological methods for optimization problems in solid mechanics 90C30 Nonlinear programming
##### Software:
CG_DESCENT; Ipopt; Julia; Matlab; Optim; PETSc; top.m
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