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A new analytical-numerical method for calculating interacting stresses of a multi-hole problem under both remote and arbitrary surface stresses

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Abstract

Based on the elementary solutions and new integral equations, a new analytical-numerical method is proposed to calculate the interacting stresses of multiple circular holes in an infinite elastic plate under both remote stresses and arbitrarily distributed stresses applied to the circular boundaries. The validity of this new analytical-numerical method is verified by the analytical solution of the bi-harmonic stress function method, the numerical solution of the finite element method, and the analytical-numerical solutions of the series expansion and Laurent series methods. Some numerical examples are presented to investigate the effects of the hole geometry parameters (radii and relative positions) and loading conditions (remote stresses and surface stresses) on the interacting tangential stresses and interacting stress concentration factors. The results show that whether the interference effect is shielding (k < 1) or amplifying (k > 1) depends on the relative orientation of holes (α) and remote stresses (<∞x , <∞y ). When the maximum principal stress is aligned with the connecting line of two-hole centers and <∞y < 0.05<∞x , the plate containing two circular holes has greater stability than that containing one circular hole, and the smaller circular hole has greater stability than the bigger one. This new method not only has a simple formulation and high accuracy, but also has advantage of wide applications over common analytical methods and analytical-numerical methods in calculating the interacting stresses of a multi-hole problem under both remote and arbitrary surface stresses.

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Authors and Affiliations

  1. School of Civil Engineering, Central South University, Changsha, 410083, China

    Wei Yi, Qiuhua Rao, Dongliang Sun & Qingqing Shen

  2. College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan, Hunan Province, 411105, China

    Wenbo Ma

Authors
  1. Wei Yi
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  2. Qiuhua Rao
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  3. Wenbo Ma
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  4. Dongliang Sun
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  5. Qingqing Shen
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Correspondence to Qiuhua Rao.

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Citation: YI, W., RAO, Q.H., MA,W.B., SUN, D. L., and SHEN, Q. Q. A new analytical-numerical method for calculating interacting stresses of a multi-hole problem under both remote and arbitrary surface stresses. Applied Mathematics and Mechanics (English Edition) 41(10), 1539—1560 (2020) https://doi.org/10.1007/s10483-020-2653-9

Project supported by the National Natural Science Foundation of China (Nos. 51474251, 51874351, and 11502226), the Natural Science Foundation of Hunan Province of China (No. 2019JJ50625), and the Key Research and Development Plan of Hunan Province of China (No. 2017WK2032)

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Yi, W., Rao, Q., Ma, W. et al. A new analytical-numerical method for calculating interacting stresses of a multi-hole problem under both remote and arbitrary surface stresses. Appl. Math. Mech.-Engl. Ed. 41, 1539–1560 (2020). https://doi.org/10.1007/s10483-020-2653-9

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  • DOI: https://doi.org/10.1007/s10483-020-2653-9

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