Integrated topology and performance redesign of complex structures by large admissible perturbations

The first major contribution of this dissertation is the development of a LEAP algorithm implementing static mode compensation. The second is the development of a methodology for topology redesign of complex structures by LargE Admissible Perturbation (LEAP). 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 performance characteristics not satisfying the designer specifications. The unknown State S2 has the desired structural response constraints 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 two-state problems for large structural changes (on the order of 100%–300%), without repetitive finite element analyses, and uses 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 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 3–6 intermediate finite element analyses (iterations) to keep the error within bounds. Numerical applications show optimal topologies for static, dynamic, and combined static/dynamic redesign constraints.