A new multi-p-norm formulation approach for stress-based topology optimization design. (15th November 2016)

• Record Type: Journal Article
• Authors: Kiyono, C.Y.; Vatanabe, S.L.; Silva, E.C.N.; Reddy, J.N.
• Is Part Of: Composite structures. Volume 156(2016)
• Page Start: 10
• Page End: 19
• Publication Date: 2016-11-15
• Subjects: Topology optimization -- Stress limit -- Composite structures -- Multi-p-norm -- SIMP -- Load independent; Composite construction -- Periodicals; Composites -- Périodiques; 624.18
• DOI: 10.1016/j.compstruct.2016.05.058
• Languages: English
• ISSNs: 0263-8223

Abstract

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.