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 specifica- tions. The unknown State S2 has the desired structural response and locally optimum topology. First, the gen- eral 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 elem- ent analyses, based on the initial State S1 and the spe- cifications for State S2. The solution algorithm is based on an incremental predictor-corrector method. The op- timization problems formulated in both the predictor and corrector phases are solved using commercial non- linear 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 perturba- tion equation is improved by static mode compensation thus reducing errors significantly. The moduli of elastic- ity of solid elements are used as redesign variables. The LEAP and optimization solvers are implemented in code RESTRUCT (REdesign of STRUCTures) which postpro- cesses finite element analyses results of MSC-NASTRAN. Several topology redesign problems are solved success- fully 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