A new analytical-numerical method for calculating interacting stresses of a multi-hole problem under both remote and arb
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APPLIED MATHEMATICS AND MECHANICS (ENGLISH EDITION) https://doi.org/10.1007/s10483-020-2653-9
A new analytical-numerical method for calculating interacting stresses of a multi-hole problem under both remote and arbitrary surface stresses∗ Wei YI1 , Qiuhua RAO1,† , Wenbo MA2 , Dongliang SUN1 , Qingqing SHEN1 1. School of Civil Engineering, Central South University, Changsha 410083, China; 2. College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan 411105, Hunan Province, China (Received Mar. 29, 2020 / Revised Jun. 17, 2020)
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 (σx∞ , σy∞ ). When the maximum principal stress is aligned with the connecting line of two-hole centers and σy∞ < 0.5σx∞ , 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. Key words new analytical-numerical method, interacting stress, multi-hole problem, remote stress, arbitrary surface stress Chinese Library Classification O343.4, TU45 2010 Mathematics Subject Classification 74A10, 78B05, 74H10 ∗ 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) (2020) https://doi.org/10.1007/s10483-020-2653-9 † Corresponding author, E-mail: [email protected] 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) ©Shanghai University and Springer-Verla
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