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

9713481戈迪斯，这项提议的目标有两个。(1)用于大型结构局部非线性有限元模型暂态结构综合的高效、通用和精确的积分方程组的理论和数值解的发展；(2)其在大型结构系统非线性暂态响应优化中的应用。这项研究将涉及到非线性暂态综合公式的理论和数值发展。已经(由PI)开发了线性公式，目前正在进行非线性公式的初步开发。对非线性积分方程组进行了完整的理论发展，包括局部非线性结构修改、子结构与非线性关联耦合、通过非线性元件激励基础和半主动控制情况下解的存在唯一性的形式证明。随后，将进一步发展一种综合公式，作为涉及非线性暂态响应约束(或目标函数)的结构优化中的重新分析方法。优化发展将集中在被动和半主动隔震在结构地震反应和机械冲击方面的应用问题。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. ***