二維時間域邊界元素法：內應力之求解與元素切割方式之探討

Abstract

本文主要在推導二維時間域邊界元素法求解內部點應力時，所需要的褶積基本解形式，稱之為褶積應力核心（convoluted stress - kernels）。其中，對於時間域變數分別以常數、線性與二次變化模擬之，根據這些不同階次的時間形狀函數所作的模擬，建立起五種求解系統，文中並分別詳述其褶積應力核心之形式。 文末就元素切割形式對數值解的影響，作一研究探討。

In this treatise, we devote to formulate the basis of the fundamental solutions, which will be used in the process of the calculations of interior stress by 2 - D time - domain BEM. Trough our miscellany, we name all these fundamental solutions convoluted stress - kernels. To approach the issue, we simulate the temporal variables by constant, linear and quadratic variation in turn. According to the simulation by temporal shape function with different order, we will construct five systems of the interior stress calculations. The forms of these convoluted stress - kernels appear in the five systems will be described completely in articles. Last of all, we will research the influence of the form of meshes on the solution.