Design sensitivity analysis and optimization of nonlinear structures--a unified approach

The present work describes a unified variational theory of design sensitivity analysis of linear and nonlinear structures for shape, nonshape and material selection problems. The concepts of reference volume and adjoint structure are used to develop the unified view point. A general formula for design sensitivity analysis is derived. Several analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use. Adjoint state fields are interpreted as sensitivities for the functional related to the primary structure. The sensitivity formula is also derived for the field problem of elastic torsion.;A Lagrangian continuum approach is also used to derive the sensitivity formula. In this approach, the adjoint displacement is interpreted as a Lagrange multiplier vector and the equilibrium equation for the adjoint structure is interpreted as the Euler-Lagrange equation of the Lagrangian functional.;The finite element method is used for discretization of the derived general sensitivity equation and equivalence is shown between continuum and discrete models of sensitivity analysis. The isoparametric concept of the finite element formulation is related to the concept of reference volume. The concept of design element is used for the design modelling of the structure and to generate the analysis model from the design model. Several design elements are formulated and implemented into the commercial computer program ADINA. An imbedded sensitivity analysis strategy is used to transmit the information from the analysis phase to the optimization phase. The general purpose codes, ADINA and IDESIGN for analysis and optimization, respectively, are combined to create an optimal design capability. Several examples of design sensitivity analysis and design optimization are presented.