Efficient Nonlinear Transient Dynamic Analysis for Structural Optimization Using an Exact Integral Equation Formulation

9713481 Gordis这个提议的目的是双重的。(1)针对具有局部非线性的大型结构有限元模型，建立了一种高效、通用、精确的瞬态结构综合积分方程的理论和数值解；(2)在大型结构系统非线性瞬态响应优化中的实现。这项研究将涉及非线性瞬态综合公式的理论和数值发展。线性公式已经开发（由PI），非线性公式的初步开发目前正在进行中。将对非线性积分方程公式进行全面的理论发展，包括局部非线性结构修改、子结构与非线性互连耦合、通过非线性元素的基础激励和半主动控制的解的存在性和唯一性的形式化证明。随后，综合公式将进一步具体发展为涉及非线性瞬态响应约束（或目标函数）的结构优化的再分析方法。优化的发展将集中在被动和半主动隔震在地震结构反应和机械冲击中的应用问题。设计问题也将得到解决。＊＊＊

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. ***