Topology and performance redesign of complex structures by large admissible perturbations

Abstract

A methodology for topology redesign of com- plex structures by LargE Admissible Perturbations (LEAP) is developed. LEAP theory is extended to solve topology redesign problems using 8-node solid elements. The corresponding solution algorithm is developed as well. The redesign problem is defined as a two-state problem. State S1 has undesirable characteristics and/or performance not satisfying certain designer specifications. The unknown State S2 has the desired structural response and locally optimum topology. First, the general nonlinear perturbation equations relating specific response of States S1 and S2 are derived. Next, a LEAP algorithm is developed which solves successfully two-state problems for large structural changes (on the order of 100–300%) of State S2, without repetitive finite element analyses, based on the initial State S1 and the specifications for State S2. The solution algorithm is based on an incremental predictor-corrector method. The optimization problems formulated in both the predictor and corrector phases are solved using commercial nonlinear optimization solvers. Minimum change is used as the optimality criterion. The designer specifications are imposed as constraints on modal dynamic and/or static displacement. The static displacement general perturbation equation is improved by static mode compensation thus reducing errors significantly. The moduli of elasticity of solid elements are used as redesign variables. The LEAP and optimization solvers are implemented in code RESTRUCT (REdesign of STRUCTures) which postprocesses finite element analyses results of MSC-NASTRAN. Several topology redesign problems are solved successfully by code RESTRUCT to illustrate the methodology and study its accuracy. Performance changes on the order of 3300% with high accuracy are achieved with only 3–5 intermediate finite element analyses (iterations) to arrest the error. Numerical applications show significant topological differences for varying redesign constraints.