Combinatorics

Finite element method

von Mises yield criterion

Topology (electrical circuits)

Shape optimization

Mathematics

Structural engineering

Mathematical optimization

Engineering

Philosophy

Political science

Minification

Norm (philosophy)

Topology optimization

Stress (linguistics)

Geometry

Constraint (computer-aided design)

Linguistics

Structural and Multidisciplinary Optimization

This work shows that a combined shape and topology optimization method can produce optimal 2D designs with minimal stress subject to a volume constraint. The method represents the surface explicitly and discretizes the domain into a simplicial complex which adapts both structural shape and topology. By performing repeated topology and shape optimizations and adaptive mesh updates, we can minimize the maximum von Mises stress using the p-norm stress measure with p-values as high as 30, provided that the stress is calculated with sufficient accuracy.

Combined shape and topology optimization for minimization of maximal von Mises stress