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

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 (SCFs). 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 (σ_x^∞, σ_y^∞). When the maximum principal stress is aligned with the connecting line of two-hole centers and σ_y^∞ <0.5σ_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 an 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.