Semianalytic Hyperelement for Layered Strata

The paper presents a new numerical technique to solve dynamic wave propagation problems in layered systems. The method is based on the closed-form analytical solution in the direction parallel to the layering, and arbitrary displacement expansions in the direction perpendicular to it. Detailed information is given for the use of the theory for the particular case of a linear expansion. The main advantage of the theory is that a great reduction in the number of degrees-of-freedom necessary to model a system, as compared to conventional finite element models, can be attained. The advantage is achieved at the expense of having to solve the system in the frequency domain, and having to compute the stiffness matrix for each individual frequency. The method is, therefore, limited to linear systems. The relatively modest size of the problem allows a solution in fast memory, without having to resort to peripheral storage allocation.