Scale-span stress-constrained topology optimization for continuum structures integrating truss-like microstructures and solid material

Abstract

This paper proposes a stress-constrained topology optimization method for structures integrating truss-like microstructures and a solid material. By utilizing the representative volume element (RVE) method, the truss-like microstructures are equivalent to homogeneous materials. Then, a power-law material interpolation scheme for bi-material, including the solid material and the equivalent material, is constructed. Based on the mechanical analysis, a yield index g is introduced to indicate the yielding situation of the truss-like microstructures. In addition, the yielding of truss-like microstructures is controlled implicitly by constraining the von Mises stress of the equivalent materials. By means of two p-norm clustered stress measures, the stress of the solid material and the equivalent material are constrained. Finally, based on the adjoint method, the sensitivity of stress and displacement constraints is obtained and the optimization can be solved by a gradient-based optimization algorithm. Two numerical examples are presented to demonstrate the validity and effectiveness of the proposed methodology.