Applied Composite Materials 3: 277-300, 1996. 277 @ 1996 Kluwer Academic Publishers. Printed in the Netherlands. Layerwise Fundamental Solutions and Three-Dimensional Model for Layered Media F. T. KOKKINOS* and J. N. REDDY** Department of Mechanical Engineering Texas A & M University College Station, Texas 77843-3123, U.S.A. Abstract. A hybrid method is presented for the analysis of layers, plates, and multilayered systems consisting of isotropic and linear elastic materials. The problem is formulated for the general case of a multilayered system using a total potential energy formulation and employing the layerwise laminate theory of Reddy. The developed boundary integral equation model is two-dimensional, displacement based and assumes piecewise continuous distribution of the displacement components through the system's thickness. A one-dimensional finite element model is used for the analysis of the multilayered system through its thickness, and integral Fourier transforms are used to obtain the exact solution for the in-plane problem. Explicit expressions are obtained for the fundamental solution of a typical infinite layer (element), which can be applied in a two-dimensional boundary integral equation model to analyze layered structures. This model describes the three-dimensional displacement field at arbitrary points either in the domain of the layered medium or on its boundary. The proposed method provides a simple, efficient, and versatile model for a three-dimensional analysis of thick plates or multilayered systems. Key words: layered media, layerwise theory, sandwich plates, laminated plates, fundamental solu- tions, boundary integral equations, finite element models, boundary element models, BEM and FEM coupling. 1. Introduction In recent years the boundary element method (BEM) has become an established method for analyzing structures, and it is widely used to solve elastostatic and elastodynamic problems [1, 2]. The formulation of boundary integral equations (BIE) via the direct method requires a fundamental solution that satisfies the governing differential equations and the free-field conditions at infinity. In a number of papers, different boundary integral formulations have been shown to be useful for different classes of boundary value problems. The main difference among them is the fundamental solution, which is dependent on the geometry of the problem. The problems of a single infinite layer or the multilayered half-space have received extensive attention because of their relevance to the theory of plates, foundations, geomechanics, micro-mechanics, and composite materials. For these problems it is rather cumbersome to evaluate the exact state of stress and dis- * Visiting Assistant Professor ** Oscar S. Wyatt, Jr. Chair