A study of free terms for plate problems in the dual BEM

Abstract

In this paper, we review the free terms of Lapalce and Navier equations for 2-D and 3-D problems and extend to biharmonic equation for plate problem. We derive the free terms of the dual BEM with a smooth boundary by means of the bump-contour technique surrounding the singularity. After using the limiting approach, the free terms and boundary terms for the sixteen improper integrals in the dual formulation for the plate problems are derived. The improper integrals due to the sixteen kernels with singularity or hypersingularity are interpreted as the finite part. 本文針對二維及三維的勢能及彈力問題的自由項做回顧並推廣至四階雙諧和函數的板問題。藉由繞過平滑邊界上奇異點的半圓弧路徑積分的技巧，並以極限方法求得十六個核函數邊界積分的自由項與跳躍項。最後，此十六個核函數的主值問題所屬的奇異性或超強奇異性均可以有限部分觀念予以詮釋。