A Numerical Method for Shape Design Sensitivity Analysis and Optimization of Built-up Structures

Abstract

A general purpose design sensitivity analysis and optimization method for built-up structures is proposed and software implementation of the method is considered. Both conventional (sizing) and shape design variables for components of built-up structures are studied. For conventional design sensitivity analysis, distributed parameter structural design sensitivity analysis theory is used. For shape design sensitivity analysis, the material derivative concept of continuum mechanics is employed. A domain method of shape design sensitivity analysis is presented as the foundation of a design component method that leads to systematic organization of computations for design sensitivity analysis, which can be implemented with existing finite element codes. A sparse matrix symbolic factorization technique for iterative structural optimization is used for efficient repeated solution of matrix finite element equilibrium and eigenvalue equations. For optimization, Pshenichny’s linearization method is employed. Feasibility of the proposed method is demonstrated through design optimization of a truss-beam-plate built-up structure.