High-precision stress determination in photoelasticity

doi:10.1007/s10483-022-2830-9

Abstract

Abstract: Stress separation is usually achieved by solving differential equations of equilibrium after parameter determination from isochromatics and isoclinics. The numerical error resulting from the stress determination is a main concern as it is always a function of parameters in discretization. To improve the accuracy of stress calculation, a novel meshless barycentric rational interpolation collocation method (BRICM) is proposed. The derivatives of the shear stress on the calculation path are determined by using the differential matrix which converts the differential form of the equations of equilibrium into a series of algebraic equations. The advantage of the proposed method is that the auxiliary lines, grids, and error accumulation which are commonly used in traditional shear difference methods (SDMs) are not required. Simulation and experimental results indicate that the proposed meshless method is able to provide high computational accuracy in the full-field stress determination.

Key words: photoelasticity, stress determination, barycentric rational interpolation, collocation method, differential matrix

2010 MSC Number:

74-05

Zikang XU, Yongsheng HAN, Hongliang SHAO, Zhilong SU, Ge HE, Dongsheng ZHANG. High-precision stress determination in photoelasticity. Applied Mathematics and Mechanics (English Edition), 2022, 43(4): 557-570.

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