Analysis of two-dimensional thin structures (from micro- to nano-scales) using the boundary element method

摘要: In this paper, the boundary element method (BEM) based on elasticity theory is developed for two-dimensional (2-D) thin structures with thickness to length ratio in micro (10−6) or nano (10−9) scales. An efficient analytical deal nearly-singular integrals integral equation (BIE) 2-D structures. The integrals, which are line problems and arise when two curves close each other, transformed into function evaluations at end points of integration. addition, a new nonlinear coordinate transformation nearly weakly-singular further increase numerical accuracy. For test studied, very promising results obtained orders 10−6 10−9, sufficient modeling most micro- nano-scales. can be applied readily model layered coatings, films other analyze contact stresses, interfacial cracks, thermal effects deformations.