Accurate stresses in the thin-layer method

A method is described by means of which accurate strains and stresses can be obtained for problems of wave motion in laminated media modelled with the thin layer method (TLM), a semi-discrete procedure that combines the power of finite elements with that of analytical solutions. It is shown that when the displacements in the TLM are combined with the consistent stresses at the layer interfaces, strains and stresses anywhere in the medium can be obtained with the same level of accuracy as the displacements. The proposed method thus circumvents the intrinsic problem that arises when strains are obtained via differentiation. As a bonus, it also renders the stresses continuous across layer interfaces, which is not the case when stresses are obtained via differentiation of the primary interpolation field