Effect of Higher Order Element on Numerical Instability in Topological Optimization of Linear Static Loading Structure

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Abstract

This paper presents the mathematical model to solve the topological optimization problem. Effect of higher order element on the optimum topology of the isotropic structure has been studied by using 8-node elements which help in decreasing the numerical instability due to checkerboarding problem in the final topologies obtained. The algorithms are investigated on a number of two-dimensional benchmark problems. MATLAB code has been developed for different numerical two dimensional linear isotropic structure and SIMP approach is applied. Models are discretized using linear quadratic 4-node and 8-node elements and optimal criteria method is used in the numerical scheme. Checkerboarding instability in the final topology is greatly reduces when incorporated 8-node element instead of 4-node element which can be confirmed through comparing the final topologies of the structure.

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Journal of Theoretical and Applied Mechanics

The Journal of Institute of Mechanics of Bulgarian Academy of Sciences

Journal Information

CiteScore 2017: 1.14

SCImago Journal Rank (SJR) 2017: 0.217
Source Normalized Impact per Paper (SNIP) 2017: 0.583

Mathematical Citation Quotient (MCQ) 2017: 0.01

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