三維應力集中問題邊界元素法分析

Boundary Element Analysis for Three Dimensional Stress Concentration Problems

簡秋記(Chyou-Chi Chien) ； 蘇俊明(Jun-Ming Sue) ； 陳文斌(Weng-Pin Chen)

《中原學報》 24卷3期 (1996/07) Pp. 43-54

https://doi.org/10.6358/JCYU.199607.0043

摘要

本研究利用邊界元素法分析三維板挖孔應力集中之問題。文獻有關應力集中問題大多探討二維平板之情形，但涉及平面外彎矩作用或某些情況下，板厚度則影響應力集中因子甚鉅，此刻板挖孔應力集中之問題必須考慮到三維空間。針對三維板幾何外形突變之應力集中問題，以數值分析方法進行分析，頗為方便且迅速，尤其以邊界元素法數值模擬分析，只需處理表面邊界之幾何量或物理量即可，不似有限元素法需使用到實體元素之困擾。本文邊界元素法擬採用八點二階平面邊界元素分析數個三維板挖孔應力集中之算例，進行模擬分析所得之數值解將與二維板解析解作比較。

關鍵字

邊界元素法 ； 應力集中 ； 三維板

並列摘要

In this research, the analysis of stress concentration problems using the boundary element method in three-dimensional plate with a hole is presented. Literature’s concerning the stress concentration problems most put emphasis on the study of two-dimensional plane cases. However, the thickness of plate affects the stress concentration factor in certain cases, for example, due to the application of out-of-plane bending and hence three-dimensional case should be considered here. It is straightforward and convenient to solve the three-dimensional stress concentration problems using computational techniques. The boundary element analysis is a powerful numerical approach since only the geometrical and physical variables on the surface of solid are involved. For another numerical approach, the finite element method must complicatedly deal with solid element modeling. To demonstrate the accuracy and efficiency of the proposed boundary element method, some benchmark problems with eight-noded isoparametric quadrilateral boundary elements are presented. For numerical results, comparisons are made with analytical solutions or other existing numerical results.

並列關鍵字

Boundary Element Method ； Stress Concentration ； Three-Dimensional Plate