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Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (4): 557-570.doi: https://doi.org/10.1007/s10483-022-2830-9

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High-precision stress determination in photoelasticity

Zikang XU1, Yongsheng HAN2, Hongliang SHAO3, Zhilong SU1, Ge HE1, Dongsheng ZHANG1   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200444, China;
    2. Shandong Water Conservancy Vocational College, Rizhao 276826, Shandong Province, China;
    3. Shanghai Institute of Space Craft Equipment, Shanghai 200240, China
  • 收稿日期:2022-01-05 修回日期:2022-02-23 发布日期:2022-03-30
  • 通讯作者: Dongsheng ZHANG, E-mail:donzhang@stafi.shu.edu.cn
  • 基金资助:
    the National Key R&D Program of China (No.2018YFF01014200), the National Natural Science Foundation of China (Nos.11727804, 11872240, 12072184, 12002197, and 51732008), and the China Postdoctoral Science Foundation (Nos.2020M671070 and 2021M692025)

High-precision stress determination in photoelasticity

Zikang XU1, Yongsheng HAN2, Hongliang SHAO3, Zhilong SU1, Ge HE1, Dongsheng ZHANG1   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200444, China;
    2. Shandong Water Conservancy Vocational College, Rizhao 276826, Shandong Province, China;
    3. Shanghai Institute of Space Craft Equipment, Shanghai 200240, China
  • Received:2022-01-05 Revised:2022-02-23 Published:2022-03-30
  • Contact: Dongsheng ZHANG, E-mail:donzhang@stafi.shu.edu.cn
  • Supported by:
    the National Key R&D Program of China (No.2018YFF01014200), the National Natural Science Foundation of China (Nos.11727804, 11872240, 12072184, 12002197, and 51732008), and the China Postdoctoral Science Foundation (Nos.2020M671070 and 2021M692025)

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摘要： 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.

关键词: photoelasticity, stress determination, barycentric rational interpolation, collocation method, differential matrix

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

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