Topological derivative-based topology optimization of structures subject to Drucker–Prager stress constraints

• Published in: Computer methods in applied mechanics and engineering Vol. 233-236; pp. 123 - 136
• Main Authors: Amstutz, S., Novotny, A.A., de Souza Neto, E.A.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 01.08.2012; Elsevier
• Subjects: Differential geometry; Drucker–Prager criterion; Exact sciences and technology; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Geometry; Inelasticity (thermoplasticity, viscoplasticity...); Local stress constraint; Mathematics; Physics; Sciences and techniques of general use; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Topological derivative; Topological sensitivity; Topology optimization; Topology optimization; Drucker–Prager criterion; Topological derivative; Local stress constraint; Topological sensitivity; Geometrical shape; Biaxial stress; Yield criterion; Rupture; Algorithmics; Contour line; Mechanical properties; Compressive strength; Topology; Optimization; Tensile strength; Asymmetry; Domain structure; Drucker-Prager criterion; Yield strength; Structural analysis; Symmetry
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2012.04.004

An algorithm for topology optimization of elastic structures under plane stress subject to the Drucker–Prager stress constraint is presented. The algorithm is based on the use of the topological derivative of the associated objective functional in conjunction with a level-set representation of the structure domain. In this context, a penalty functional is proposed to enforce the point-wise stress constraint and a closed formula for its topological derivative is derived. The resulting algorithm is of remarkably simple computational implementation. It does not require post-processing procedures of any kind and features only a minimal number of user-defined algorithmic parameters. This is in sharp contrast with current procedures for topological structural optimization with local stress constraints. The effectiveness and efficiency of the algorithm presented here are demonstrated by means of numerical examples. The examples show, in particular, that it can easily handle structural optimization problems with underlying materials featuring strong asymmetry in their tensile and compressive yield strengths.