A level set solution to the stress-based structural shape and topology optimization

• Published in: Computers & structures Vol. 90-91; pp. 55 - 64
• Main Authors: Xia, Qi, Shi, Tielin, Liu, Shiyuan, Wang, Michael Yu
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.01.2012; Elsevier
• Subjects: Exact sciences and technology; Finite element method; Fundamental areas of phenomenology (including applications); Level set method; Mathematical analysis; Mathematical models; Optimization; Physics; Shape and topology optimization; Solid mechanics; Static elasticity (thermoelasticity...); Stress; Stresses; Structural and continuum mechanics; Structural shapes; Topology optimization; Voids; Shape and topology optimization; Level set method; Stress; Finite element method; Geometrical shape; Cavity; Contour line; Topology; Modeling; Optimization; Structural analysis
• ISSN: 0045-7949; 1879-2243
• DOI: 10.1016/j.compstruc.2011.10.009

► We present a level set solution to stress-based shape and topology optimization. ► A novel global measure of stress is proposed. ► Shape sensitivity analysis is performed via the material derivative method. ► Artificial weak material usually used in level set method to mimic void is avoided. ► Peak stress can be effectively controlled. We present a level set solution to the stress-based structural shape and topology optimization. First, a novel global measure of stress is proposed, and the optimization problem is formulated to minimize the global measure of stress subject to a constraint of material volume. In order to solve this optimization problem, the level set method is employed. The finite element analysis is accomplished by modifying a fixed background mesh, and the artificial weak material that is conventionally used in the level set method to mimic void is avoided in the present work.