Problem of design sensitivity analysis and optimization of nonlinear response of structures has become quite important in practical applications. When large displacements, rotations and strains are included in the formulation, a more accurate response of the structure is predicted. This can lead to substantially different optimal designs, as shown by optimizing small scale structural design problems. In some cases, optimum design obtained with linear structural analysis capability can be dangerous, if the structure becomes geometrically nonlinear. Catastrophic failure of the structure can occur. In other cases, the structure may be overdesigned without consideration of geometric nonlinearities because it may actually become stiffer with the inclusion of large displacement effects. Design sensitivity analysis is a necessary step towards optimization. Research to develop theory and numerical algorithms for design sensitivity analysis and optimization of nonlinear response is proposed. Full range of nonlinearities geometric as well as material will be considered. Static as well as dynamic response applications will be considered. Large displacement, rotation and strain formulations will be used. Linear and nonlinear material models will be included. Formulation of the optimal design problem with nonlinear response will be developed, i.e., particular attention will be paid to incorporate the yield conditions and nonlinear buckling load constraints. Design sensitivity analysis to include unloading of the system (history dependent respones) will be developed. Possible discontinuities in gradients will be investigated. Theory of design sensitivity analysis of nonlinear buckling load will be developed. Computational algorithms will be developed and integrated into available modern optimization methods. They will be demonstrated on a set of carefully selected structural design problems. The methods of design sensitivity analysis developed in the research can be used in the existing nonlinear analysis computer programs. Potential areas of application include: building systems, earthquake-resistant structures, automotive structures, and aircraft and aerospace structures.
