A new multi-p-norm formulation approach for stress-based topology optimization design

Published Date
15 November 2016, Vol.156:10–19, doi:10.1016/j.compstruct.2016.05.058
70th Anniversary of Professor J. N. Reddy

Author 

C.Y. Kiyono ^a,b,,,

S.L. Vatanabe ^a

E.C.N. Silva ^a

J.N. Reddy ^b

aDepartment of Mechatronics and Mechanical Systems Engineering, Politechnique School of University of São Paulo, Avenida Professor Mello Moraes, 2231, 05508-900 São Paulo, SP, Brazil

bDepartment of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, USA

Received 1 January 2016. Revised 15 May 2016. Accepted 18 May 2016. Available online 20 May 2016.

Abstract

Although the stress-based topology optimization problem has been extensively studied for continuum structures, it is still an open problem and there is still room for improvements. This work proposes a comprehensive approach for dealing with stresses in topology optimization problems. The SIMP method is used to distribute material along the domain. For limiting the stress, a multi-p-norm formulation is proposed to deal with the local nature of stress and to avoid stress concentration. This function considers many values of p coefficients at the same time while other formulations adopt a specific value for p defined for subregions. As a consequence this formulation can avoid the stress concentrations without being necessary to define sub-regions. In addition, the proposed formulation is load independent because the multi-p-norm is used as the objective function. A SIMP-like formulation is used to address the stress singularity phenomenon and the heaviside projection is used to avoid mesh dependency, checkerboarding, and to control the minimum length-scale. A proper continuation scheme is proposed to all penalization coefficients in order to achieve black-and-white solutions. The optimization problem is solved by using GCMMA. Numerical examples for homogeneous and composite structures are presented to illustrate the proposed formulation.

Keywords

Topology optimization

Stress limit

Composite structures

Multi-p-norm

SIMP

Load independent

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  Corresponding author at: Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, USA.

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