整合數位光彈及有限元素分析於孔之結構設計

Integration of Digital Photoelasticity and Finite Element Analysis for Structural Design of Holes

在機械結構中，孔之位置常設計於主軸應力相等處（等應力點）之所在。本文利用新近發展之最小─最大掃描（min-max scan）分析法，經由光彈實驗獲得之全場主應力角分佈，搭配運用電腦自動尋找等應力點之位置；然後使用有限元素分析比較：(1)在等應力點或其附近不同位置鑽孔時，及(2)於等應力點上，鑽以不同大小之孔時，孔周圍之von-Mises 應力之分佈情形，以探討於等應力點處鑽孔之適當性。研究中以一圓盤三點受力為例。由結果歸納出，在等應力點位置上鑽孔，其孔周圍之最大von-Mises 應力值較附近其他位置者為小；若鑽孔之孔徑越小，其孔周圍最大von-Mises 應力值亦越小。因此光彈實驗獲得等應力點之位置，可有效作為孔之最佳化結構設計之用。

In mechanical structures, the holes are frequently designed at the isotropicpoints where the principal stresses are equal. In this paper, a newlydeveloped min-max scanning method is applied to determine the wholefield principal stress direction of a photoelastic model by experiment, andthe isotropic points on the model are further extracted automatically by aself-designed program. The von-Mises stress distributions around holes: (1)drilled at the determined isotropic point and near-by locations, and (2)having various sizes drilled at the determined isotropic point location areobtained and compared by finite element analysis. The suitability of drillinga hole at the determined isotropic point is investigated. Test resultsfrom a three-point loaded disk show that the maximum von-Mises stressaround the hole drilled at the determined isotropic point is less than that around the near-by locations. As the size of the hole drilled at the determinedisotropic point is decreased, the maximum von-Mises stress aroundthe hole is also decreased. Therefore the isotropic point location determinedby using the digital photoelastic approach can be effectively utilizedfor optimal design of holes in structures.