Regularized meshless method for antiplane shear problems with multiple inclusions

Abstract

In this paper, we employ the regularized meshless method (RMM) to solve antiplane shear problem with multiple inclusions. The solution is represented by a distribution of double layer potentials. The troublesome singularity in the MFS is avoided and the diagonal terms of influence matrices are determined. The coupled problem considerably reduces to two problems. One is the exterior problem for matrix with hole subject to a far-displacement field, the other is the interior problem for inclusion. The two boundary data between matrix and inclusion satisfy the continuous conditions in the interface between the inclusion and antiplane matrix. The linear algebraic system is obtained by matching boundary conditions and continuity conditions. Finally, the numerical results demonstrate the accuracy of the solutions after compared with analytical solutions and the Laurent series expansion method. Good agreements are obtained. 本文係利用正規化無網格法求解反平面含多夾雜問題，其解是由雙層勢能表示。傳 統的基本解法是利用避開奇異行為去決定影響矩陣的對角線項，正規化無網格法是利用奇異扣除奇異的方法去正規化奇異行為及決定影響矩陣的對角線項。本問題可以拆解成兩個邊界值問題，一個是材料含空洞的外域問題受到無窮遠的位移場作用，另一個是夾雜的內域問題。而介於材料與夾雜間的接合面則須滿足連續條件。配合邊界條件與連續條件之後就可以決定線性代數系統。最後，我們將數值結果與 Laurent 級數展開法比較，驗證其正確性，我們將獲得正確的結果。