The scaled flexibility matrix method for the efficient solution of boundary value problems in 2D and 3D layered elastic media Original Research Article

We present a method that extends the flexibility matrix method for multilayer elasticity problems to include problems with very thin layers. This method is particularly important for solving problems in which one or a number of very thin layers are juxtaposed with very thick layers. The standard flexibility matrix method suffers from round-off errors and poor scaling of the flexibility equations which occur when one of the layers in the multilayered medium becomes much smaller than the others. The method proposed in this paper makes use of power series expansions of the various components of the flexibility matrix in order to arrive at a system of equations that is appropriately scaled. The effectiveness of the scaled flexibility matrix method is demonstrated on a number of test problems.