Fail-Safe Topology Optimization of Continuum Structures with Multiple Constraints Based on ICM Method

Abstract

Traditional topology optimization methods may lead to a great reduction in the redundancy of the optimized structure due to unexpected material removal at the critical components. The local failure in critical components can instantly cause the overall failure in the structure. More and more scholars have taken the fail-safe design into consideration when conducting topology optimization. A lot of good designs have been obtained in their research, though limited regarding minimizing structural compliance (maximizing stiffness) with given amount of material. In terms of practical engineering applications considering fail-safe design, it is more meaningful to seek for the lightweight structure with enough stiffness to resist various component failures and/or to meet multiple design requirements, than the stiffest structure only. Thus, this paper presents a fail-safe topology optimization model for minimizing structural weight with respect to stress and displacement constraints. The optimization problem is solved by utilizing the independent continuous mapping (ICM) method combined with the dual sequence quadratic programming (DSQP) algorithm. Special treatments are applied to the constraints, including converting local stress constraints into a global structural strain energy constraint and expressing the displacement constraint explicitly with approximations. All of the constraints are nondimensionalized to avoid numerical instability caused by great differences in constraint magnitudes. The optimized results exhibit more complex topological configurations and higher redundancy to resist local failures than the traditional optimization designs. This paper also shows how to find the worst failure region, which can be a good reference for designers in engineering.