邊界積分法於鍍膜半空間之應用

Abstract

本文目的為探討一鍍膜半空間，即為一半無窮平面上完美接合一有限厚度的層板，受到線差排或均佈線力作用產生的情形。本研究是以雙層異向性材料(bimaterials)的格林函數解建構鍍膜半空間含均佈線力或線差排的非奇異邊界積分方程式。該方程式之基本變數為鍍膜表面的位移梯度，因相關積分不具奇異性，故可使用高斯積分法求得數值解。由表面位移梯度即可計算出任意位置所產生的應力場。與文獻中已有的算例結果比較顯示，本文所提之方法具有極高的準確性。

The objective of this thesis is to discuss the stress distribution of a line dislocation or a line force in a coated half-spaces. A coated half-space is a half-space perfectly coated with a layer with finite thickness. The Green’s function for anisotropic biomaterials is used to construct a nonsingular boundary integration for coated half-spaces with a line force or a line dislocation. The basic unknown in the integral equation is the gradient of the surface displacement, which can be calculated numerically using Gaussian quadrature as the related integral is non-singular. The stress fields at any point in the coated half-space can be computed once the gradient of the surface displacement is determined. Comparison with the existing results show that the proposed method is highly accurate.