彈塑性力學參數識別最佳化架構

Abstract

本論文旨在研究彈塑性模式的識別問題,並且提出一致的方法來估測模式參數與初始狀態。本文特別注意實際收到的材料、既存的結構物，其內變數事實上不能假設初值為零。首先,提出一個廣泛的彈塑性模式。根據此模式,建立其彈塑性識別的動態最佳化架構。對於這個包含等式約束、不等式約束與互補約束的最佳化問題，本文獲得其正確的最佳化條件。文中所得結果之特色在於呈現凸與辛之特性。 鑒於現代實驗資料擷取朝向離散數位化之趨勢，本文除了處理識別之連續時間最佳化問題外,也考慮識別之離散時間最佳化問題,所得離散解條件也保有辛群之特性。依據實務的狀況，本文提出一個估測模式參數與初始狀態的演算法並且實際以實驗資料來識別模式之參數與初始狀態。

The identification problem of elastoplastic models are addressed and a unified way to estimate the optimal values of model parameters and initial states is proposed. Special attention is drawn to materials as received and structures as existing for which initial values of internal state variables could no longer be assumed to vanish. A comprehensive model of elastoplasticity is formulated first and then a dynamic optimization framework for the identification problem of the elastoplastic model is established. A correct optimality condition of the dynamic optimization problem subjected to constraints in the forms of equalities, inequalities, and complementarity constraints is obtained. The important feature of our results is that they are convex and symplectic. In view of modern trends of digital data acquisition in experiments, we further consider the discrete-time version in addition to the continuous-time optimization problem, and obtain discrete conditions of solution which are proved to preserve the structure of a symplectic group. The algorithm of finding the optimal values of parameters and initial states is proposed. Experimental data were used to identify them in several testing and real cases.