結構最佳化之準二次移動漸近線近似法

Abstract

本文根據移動漸近線近似法，提出一個新型結構最佳化近似方法，稱為準二次移動漸近線近似法。在此方法中，藉由在近似函數當中加入一個準二次項來提升近似函數的保守度，並利用前一設計點的靈敏度值將近似函數中的待定係數求出。在此近似函數當中，被視為變數虛擬上下界的兩個待定參數，加以調整後可提升近似函數的凸度，並增加近似函數的準確性。經由此近似法，可將結構之行為函數，諸如應力、位移、共振頻率等，轉化為設計變數的顯函數。如此一來，結構最佳化問題即可使用傳統數值方法加以求解。另外，本文整合最佳化理論、電腦輔助繪圖軟體、有限元素分析軟體及程式設計軟體，發展一套結構最佳化之整合程式，藉以求解結構最佳化問題。結果顯示在一般結構最佳化問題中，利用準二次移動漸近線近似法可準確而快速地找出最佳解，同時驗證此近似法在結構最佳化的效率及實用性。

This thesis presents a new approximation method for structural optimization called quasi-quadratic method of moving asymptotes approximation (QMMA), which is derived from method of moving asymptotes approximation (MMA). By adding a nonspherical second order term, the approximate function can be constructed with respect to the function value of current design point and sensitivities of two successive design points. With the use of this new approximation method, the structural behavior functions, such as stress, natural frequency or displacement functions, can be converted to explicit functions of design variables. Therefore, structural optimization problem can be solved efficiently by applying conventional optimization techniques. Moreover, a new computer program is developed by integrating CAD software, FEM analysis software and optimization theorem to solve structural optimization problems. The result indicates that the proposed approximation method can quickly find the convergence and accurate solutions for some typical structural optimization problems, and it also verified that this new method is practical and efficient in structural optimization.