彈塑性結構載重空間崩塌面探討

A study of collapse surfaces in load space for elastoplastic structures

郭建呈(Chien-Cheng Kuo)

指導教授 ： 洪宏基

國立臺灣大學/工學院/土木工程學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.01991

摘要

本文考慮材料為片段線性多降伏平面模型，藉由最大塑性耗散率原理，加入適當的約束條件，提出處理彈塑性問題的最佳化命題，
並且推導出最佳化問題的 KKT(Karush-Kuhn-Tucker) 條件。
視極限分析為漸近(asymptotically)的彈塑性問題，額外加入符合極限狀態的約束條件，並且給定比例載重的限制，重新定義極限分析的最佳化問題，
藉由極限分析的最佳化條件，找出等價的最佳化命題，定義求取崩塌載重的最佳化問題為等價的下限法問題。

由於比例載重的限制，極限分析需要最大化單一載重因子，形成單目標最佳化問題。
將等價的下限法問題中比例載重的限制去除，建立高維度的載重空間，定義出崩塌點、崩塌面與角點的觀念，定義極限分析的多目標最佳化問題。
求解線性多目標最佳化問題，可以利用加權方法配合交互式線性多目標流程得出角點，建構出安全載重區域。

關鍵字

極限分析 ； KKT條件 ； 下限法 ； 多目標最佳化 ； 加權方法 ； 交互式線性多目標流程

並列摘要

This paper consider the piecewise linear model in the following
issues. We introduce the optimal proposition of plasticity problems
by using the principle of maximum plastic dissipation which
satisfied appropriate constraints. According to the optimization
problem about plasticity derive the KKT conditons. As the limit
analysis is the plasticity problem asymptotically. We redefine
optimization problem of limit analysis including the additional
constraints which the structure reach the limit state, and given the
restriction of proportional loading. Hence a set optimal conditons
including complementarity constraints via limit analysis, we can
find out a group of optimal problems equivalently. Choosing the
optimal problem is considered the maximization of a load factor, and
we define the problem is equivalent to static approach.

According to the restriction of proportional loading, the problem of
limit analysis form a single optimization problem. We loose the
restriction from the problem of static appraach, constructing the
load space in high dimensions. And we introduce the ideas of
collapse points, collapse surfaces and critical points in the load
space. Hence we refine the problem of limit analysis is a
multiobjective optimization problem. For solving linear
multiobjective optimization problem, we can use weighted sum method
which coordinate with interactive multiple objective linear
programming procedure getting critical points. So constructing the
safe region that the engineer can regard as a critical threshold in
engineering analysis.

並列關鍵字

limit analysis ； KKT conditions ； static approach ； multiobjective optimization ； weighted sum method ； interactive multiple objective linear programming procedure

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