The fast multipole boundary element method for anisotropic material problems under centrifugal loads

This paper presents a two-dimensional fast multipole boundary element method designed for the efficient analysis of large-scale anisotropic elastic problems subjected to centrifugal loads. The expansions and fast multipole operations employed in this study bear resemblances to those utilized in existing formulations of the fast multipole boundary element method, previously proposed for addressing potential and isotropic elastostatic problems. The anisotropic fundamental solutions adopted here are rooted in the Leknitskii formalism and have been suitably expanded to facilitate the implementation of fast multipole operations. The treatment of problems involving centrifugal loads are taken into account by the utilization of the modified boundary condition method. This approach entails augmenting the boundary condition with a specific solution tailored to the problem. Following the solution of the linear system, the particular solution is subsequently subtracted from both displacements and tractions. Importantly, this procedural step obviates the need for generating additional vectors or matrices within the integral equation. To evaluate the accuracy and efficiency of the proposed method, numerical solutions are juxtaposed against analytical solutions and benchmarked against the conventional boundary element method. The formulated approach exhibits quasi-linear computational complexity, rendering it particularly well-suited for tackling large-scale problems. The key inference drawn from this work is that the proposed formulation outperforms the conventional BEM in terms of effectiveness. It offers reduced computational time and memory utilization, thereby enabling the analysis of larger problems within shorter time.