Three Dimensional Hybrid BEM-Sinc Analysis of Bonded/Bolted Composite Joints with Discrete Cracks

摘要

In this report we first illustrate a procedure for obtaining an approximate solution of the boundary integral equation form to the two- dimensional Lame' equation for a two-layer problem, based on collocation via use of Sinc approximation. The Sinc approach automatically concentrates points near corners of the boundary where the solution has singularities and yields exponential convergence. A model two-layer bi-material elasticity problem is numerically investigated here as an illustration of this novel approach. This is followed by altering our method of solving the two dimensional problem to a 'triangular form' which has resulted in decoupling of the boundary integral equation system into a sequence of subsystem equations, one over each layer. Additionally, a new method is derived for accurately approximating the 'Laplace transform' of the convolution kernel for the case of extension of the above two dimensional solution method to its three dimensional counterpart. It may be noted that non-uniqueness of solution is a frequent occurrence in layered elastic composite problems, and this phenomenon is also captured by the boundary integral equation system, demanding further modification of the method of solution of the resulting system of algebraic equations.