Generality and Special Cases of Dual Integral Equations of Elasticity

Abstract

In this paper the generality if the theory of dual integral equations derived earlier is explored. It is found that many integral equations and potential methods can be deduced from the dual equations and regarded as special cases of the theory. Some useful new formulations are also invented therefrom. These two equations are independent and totally have four kernel functions, which make it possible an unified theory encompassing different schemes and various derivations and interpretations.本文導出彈性體的對偶邊界積分方程式，指出這一對式子可視為彈性力學邊界值問題的通用列式，足以解析各種二維與三維的彈性力學與彈性破裂力學問題。積分方程式組可以傳統勢位理論來解釋，含有單層勢位、單層勢位導數、雙層勢位、與雙層勢位導數; 對應四個核函數。文中重點在於對此積分方程式組的廣義性加以闡述，發現許多現有方法均為其特例，並且推展出數種新的方法。