A Linear Superposition Method for Pressurized Holes/Cracks in 2D Anisotropic Elastic Solids

In this paper, we present a linear superposition method (LSM) for solving problems of multiple pressurized elliptical holes/cracks in a two-dimensional anisotropic elastic solid. The method is developed based on the analytical solutions for a single elliptical hole subjected to internal pressure and/or far-field stress at infinity. By this approach, the solutions of each material point can be found by summing the local displacements and stresses contributed by all holes within the anisotropic elastic plate. By letting one of the dimensions of the elliptical hole be zero, the derived solution method can also be applied to the crack problems. The solutions here are established in the general context where the plate is generally an anisotropic elastic material; the holes/cracks can be different and placed anywhere inside the body, and each hole can be subjected to different individual pressurized loads. To demonstrate the correctness and applicability of the derived solutions, we perform a rigorous verification process, comparing our results with those obtained by the previous solutions in the literature. It is found that the present LSM can provide accurate results for the case of a single hole or crack and is valid for the case of multiple holes/cracks with acceptable errors when the distance between the holes is about four times greater than its major dimensions, e.g., [Formula: see text]. With the benefits such as being gridless and in closed-form solutions, the LSM can be used as a fast and effective method for solving pressurized holes/cracks problem in composite plates. Through the numerical results, parametric studies are also performed to investigate influences of anisotropy of materials, loading conditions and geometries of holes/cracks on the displacement and stress field around the holes/cracks.