動態網格之應用

Abstract

本文主要在討論利用動態網格的方式，進行電腦輔助分析時模型網格的修正，以滿足模型變化的情形。首先介紹有限單元的方法，針對拉格蘭公式化、歐勒公式化以及隨意式拉格蘭-歐勒公式化間的差異做說明，接著介紹接觸問題，討論點接觸分析與線接觸分析，最後以幾個簡單工程問題的例子做為動態網格應用的說明，這裡包括兩個應力分析中的接觸問題與流力分析中平板擠壓流的問題，希望文中提出的修正程序與概念，能提供工程分析人員處理相關動態網格修正時的參考。

For path-dependent problems, such as crack propagation and two-body contact, moving meshes we needed to keep track of the crack growth and contact surface development. In this paper we propose a new approach for the solution of two-body contact problem which utilized the merit of moving mesh in adapting to changing geometries. We developed a procedure for updating the contact length. We found that it is necessary to break the process into a series of small steps in order not to lose the accuracy of the numerical computation. For the squeezed flow problem, we propose a new moving mesh that simultaneously avoids the deficiency of both the conventional Eulerian formulation and the Lagrangian formulation.