9713481 Gordis The objective of this proposal is two-fold. (1) The theoretical and numerical-solution development of a high efficient, general and exact integral equation formulation for transient structural synthesis for large structural FE models with localized nonlinearities and (2), its implementation in the optimization of nonlinear transient response of large structural systems. This research will involve the theoretical and numerical development of the nonlinear transient synthesis formulation. The linear formulation has been developed (by the PI) and initial development of the nonlinear formulation is currently under way. A full theoretical development of the nonlinear integral equation formulation will be carried out to include formal proofs of solution existence and uniqueness for the cases of localized nonlinear structural modifications, substructure coupling with nonlinear interconnections, base excitation through nonlinear elements, and semi-active control. Subsequently a synthesis formulation will be further specifically developed as a re-analysis methodology in structural optimization involving nonlinear transient response constraints (or objective function). The optimization development will focus on the application problems of passive and semi-active isolation for seismic structural response and mechanical shock. Design issues will also be addressed. ***
