A SEMI-ANALYTICAL APPROACH FOR DYNAMIC STRESS CONCENTRATION FACTOR OF HELMHOLTZ PROBLEMS WITH CIRCULAR HOLES

Abstract

In this paper, a semi-analytical approach is developed for the problem of dynamic stress concentration around circular cavities due to shear waves. To fully capture the circular geometries, separate expressions of fundamental solutions in the polar coordinate and Fourier series for boundary densities are adopted. The main gain of using degenerate kernels is free of calculating the principal values. An adaptive observer system is addressed to fully employ the property of degenerate kernels in the polar coordinate. After moving the null-field point to the boundary and matching the boundary conditions, a linear algebraic system is obtained and the unknown coefficients in the algebraic system can be easily determined. The present method is seen as a "semi-analytical" solution since error only attributes to the truncation of Fourier series. The proposed formulation is generalized to a half-plane problem with a circular cavity.本文發展一新方法來求解由 SH 波引致於圓形孔洞周圍之動應力集中因子。為 了充分利用圓形幾何外形，將基本解以分離核形式及邊界密度函數以傅立葉級數展開。使用退化核最主要可免去主值的計算。為了於極座標系統下充分使用退化核的特性，使用自適性參考座標系統。將觀察點移動至邊界並滿足邊界條件後，可獲得一個線性代數系統，且未知之傅立葉係數可輕易的被求得。誤差僅來自於所取之傅立葉級數項數的多寡。本法可廣泛應用於含圓形孔洞之全平面或半平面問題之分析。