Stress-constrained concurrent two-scale topology optimization of functionally graded cellular structures using level set-based trimmed quadrilateral meshes

This paper presents a novel method for stress-constrained concurrent two-scale topology optimization of functional-graded cellular structures using level set-based trimmed quadrilateral meshes. During the optimization process, trimmed quadrilateral meshes are created by cutting macro- and micro-background quadrilateral meshes with the zero-isolines of macro- and micro-level set functions. Micro-cellular structures are defined by a basic level set function and a macro-height function. A continuous field of the macro-height function over a macro-background mesh guarantees a perfect connection between adjacent micro-cellular structures. Based on the fact that hard materials are required where the stress level is high, the macro-height function is determined by the maximum von-Mises stresses in micro-cellular structures. The maximum von-Mises stresses in micro-cellular structures are taken as the representative stresses of macro-elements and are then aggregated into a p -norm stress measure. Numerical examples of stress-constrained concurrent two-scale topology optimization of functionally graded cellular structures are provided to show the effectiveness and efficiency of the present method.