Applications of regularized meshless method in engineering problems

Abstract

In this paper, we employ the regularized meshless method (RMM) to solve antiplane shear and antiplane piezoelectricity problems with a multiple inclusions and acoustic eigenproblem with multiply-connected domain. The solution is represented by a distribution of double-layer potentials. The subtracting and adding-back technique is used to regularize the singularity and hypersingularity of the kernel functions. Only boundary nodes on the real boundary are required by using the proposed technique in a different way of conventional MFS by distributing singularities on fabricated boundary. Finally, the numerical results demonstrate the accuracy of the solutions after comparing with analytical solutions and those of BEM, FEM and PM. Good agreements are obtained. 本文藉由正規化無網格法求解含多夾雜之反平面剪力及反平面壓電材問題與多連通聲場特徵值問題。以雙層勢能來表示整個場解，並配合一加一減技巧來正規化處理奇異及超奇異核函數。我們所提出的方法有別於傳統基本解法須將源點佈在虛假邊界上，可將奇異源放在真實的邊界上。最後，數值結果將與解析解，邊界元素法，有限元素法及配點法做比較，獲得一致性的結果。