洪宏基臺灣大學:土木工程學研究所劉立偉Liu, Li-WeiLi-WeiLiu2010-07-012018-07-092010-07-012018-07-092009U0001-3107200903105600http://ntur.lib.ntu.edu.tw//handle/246246/187860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。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,e 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.he 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.Contents試委員審定書 I謝 III要 IVotation convention VI Introduction 1 Dynamic optimization 4.1 Dynamic programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Variational method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Relation between dynamic programming and variational method . . . . . . . 6.4 Treatment of equality and inequality constraints . . . . . . . . . . . . . . . . 8.5 Treatment of complementarity constraints and the mathematical programsith complementarity constraints . . . . . . . . . . . . . . . . . . . . . . . . . 10 Dynamic optimization study of elastoplastic model identification 13.1 A comprehensive model of elastoplasticity . . . . . . . . . . . . . . . . . . . . 13.2 The elastoplastic models included in the comprehensive model of elastoplasticity 14.3 Optimization framework of parameter identification problems . . . . . . . . . 16.4 Necessary and sufficient conditions in identification of elastoplastic model . . 18.5 Two point boundary value problem in identification of elastoplastic model . . 22.6 The role of costate variables in identification problem . . . . . . . . . . . . . 23 Group preserving scheme in identification of elastoplastic model 26.1 The symmetry property in dynamic optimization . . . . . . . . . . . . . . . . 26.2 Discrete symplectic formulation for identification of elastoplastic model . . . 27.3 Lie group preserving scheme in ordinary differential equations . . . . . . . . . 30 Numerical method for solving two point boundary value problem in identificationf elastoplastic model 33.1 Fictitious time integration method and its modified approach . . . . . . . . . 33.2 Numerical method for solving two point boundary value problem . . . . . . . 34.3 Numerical examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36.3.1 Perfect elastoplasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . 36.3.2 Prandtl-Reuss model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3.3 Bilinear elastoplasticity . . . . . . . . . . . . . . . . . . . . . . . . . . 43.3.4 Material model consisting of bilinear elastoplasticity and linear elasticity 45.3.5 Material model consisting of Armstrong-Frederick elastoplasticity andinear elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46.3.6 Material model consisting of M perfectly elastoplastic elements in parallelnd linear elastic element . . . . . . . . . . . . . . . . . . . . . . 47 Conclusion 49eferences 51 Dynamic programming 60 Derivation from Eq.(20) to Eq.(21) 65ist of Figures Stress-strain curves of pseudo-experimental data and simulation with perfectlylastoplastic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Experiment of axial-torsional test on SS316 . . . . . . . . . . . . . . . . . . . 67 Stress-strain curves of axial-torsional test on SS316 and simulation with Prandtl-euss model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Stress-strain curves of pseudo-experimental data and simulation with bilinearlylastoplastic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Stress-strain curves of axial-torsional test on SS316 and simulation with materialodel BL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Stress-strain curves of axial-torsional test on SS316 and simulation with materialodel AF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71X Comparison between Prandtl-Reuss model, material model BL, material modelF in stress history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Stress-strain curves of axial-torsional test on SS316 and simulation with materialodel PEIP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 732129643 bytesapplication/pdfen-US彈塑性識別參數與初始狀態動態最佳化互補約束凸性辛性elastoplasticityidentificationparameters and initial statesdynamic optimizationcomplementarity constraintsconvexitysymplecticitythesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/187860/1/ntu-98-D91521017-1.pdf