Topology optimization of material nonlinear continuum structures under stress constraints

This paper proposes a methodology to extend the bi-directional evolutionary structural optimization (BESO) method for compliance minimization (stiffness maximization) design of material nonlinear continuum structures subject to both constraints on volume fraction and maximum von Mises stress. BESO method based on discrete variables can effectively avoid the well-known stress singularity problem in density-based methods with low density elements. The aggregated p-norm global stress measure is adopted to approximate the maximum von Mises stress. The conventional compliance design objective is augmented with p-norm stress measures by introducing one Lagrange multiplier. The Lagrange multiplier is employed to yield compromised designs of compliance and the p-norm stress. A scheme is developed for the determination of the Lagrange multiplier so that the maximum von Mises stress could be effectively constrained. The update of the binary topological design variables lies in the sensitivity numbers derived using the adjoint method. As for the highly nonlinear stress behavior, both topological variables and sensitivity numbers are filtered to stabilize the optimization procedure. The filtered sensitivity numbers are further stabilized with their historical information. A series of comparison studies has been conducted to validate the effectiveness of the method on several benchmark design problems.