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High-precision stress determination in photoelasticity

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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.

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Funding

Project 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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Authors and Affiliations

  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

    Zikang Xu, Zhilong Su, Ge He & Dongsheng Zhang

  2. Shandong Water Conservancy Vocational College, Rizhao, Shandong Province, 276826, China

    Yongsheng Han

  3. Shanghai Institute of Space Craft Equipment, Shanghai, 200240, China

    Hongliang Shao

Authors
  1. Zikang Xu
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  2. Yongsheng Han
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  3. Hongliang Shao
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  4. Zhilong Su
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  5. Ge He
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  6. Dongsheng Zhang
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Corresponding author

Correspondence to Dongsheng Zhang.

Additional information

Citation: XU, Z. K., HAN, Y. S., SHAO, H. L., SU, Z. L., HE, G., and ZHANG, D. S. High-precision Stress Determination in Photoelasticity. Applied Mathematics and Mechanics (English Edition), 43(4), 557–570 (2022) https://doi.org/10.1007/s10483-022-2830-9

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Xu, Z., Han, Y., Shao, H. et al. High-precision stress determination in photoelasticity. Appl. Math. Mech.-Engl. Ed. 43, 557–570 (2022). https://doi.org/10.1007/s10483-022-2830-9

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  • DOI: https://doi.org/10.1007/s10483-022-2830-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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