정적파손과 피로파손을 고려한 위상최적설계 기법

Abstract

In this dissertation, we present novel topology optimization (TO) methods that consider local static failure and dynamic fatigue failure, which have been regarded as difficult TO problems for decades. We developed the first TO method to consider the static failure of ductile or brittle material. The non-differentiable failure constraints of ductile and brittle materials are considered for a solid isotropic material with penalization (SIMP) by using differentiable operators that accurately approximate the criterion into differentiable form. The second method uses a new interpolation scheme called separable stress interpolation (SSI) for stress-based TO of multiple materials. If conventional SIMP is used to evaluate the stress of multiple materials, it provides layouts that are physically infeasible. SSI makes a physically feasible layout by interpolating the stresses of stacked elements separately. To prevent dynamic fatigue failure, we developed a TO method for static failure and dynamic fatigue constraints under constant and proportional loading. The local mode and non-differentiable fatigue criteria are addressed first. By resolving the inherited and newly found issues, the dynamic fatigue criteria under constant and proportional loads can be considered. Also, fatigue failure induced by variable-amplitude loads is considered. Due to the difficulties with sensitivity analysis for fatigue constraints that are calculated from multi-axial cycle counting, it is rarely considered in TO. To cope with this difficulty, we used pseudo-sensitivities calculated by applying equivalent static loads (ESL). We verified the validity and usefulness of the developed methods by applying them to not only simple 2D design problems but also practical 3D design problems through the use of a finite element software package.