Trans-accuracy elements and their application in BEM analysis of structurally multi-scale problems

When solving structurally multi-scale problems with small or slender components using BEM, different sized boundary elements are inevitably required to simulate all kinds of related geometries. In this paper, a family of trans-accuracy boundary elements are constructed based on Lagrange interpolation formulation. These elements not only can fulfil the transition between small and large elements, but also can simulate a whole or a part of end surfaces of cylinders accurately using very few nodes. Based on the constructed trans-accuracy elements, a BEM analysis method of structurally multi-scale problems (MSBEM) is proposed. Three numerical examples for media including different numbers of slender components such as fibers are given to validate the correctness and demonstrate the potential of the proposed methods.