Fundamental Solutions of Transversely Isotropic Immaterial Due to Point Forces via Cylindrical System of Vector Functions

摘要

Many physical systems can be modeled as layered structures, such as pavements, piezoelectric and piezomagnetic composites. Thus, response of these systems due to different types of loading and boundary conditions is important. One of the fundamental issues is associated with the response in trimaterials due to point forces. These trimaterials could have many practical applications in composite laminates and thin films coating on substrates. In this paper, we present the static solution of the trimaterial subjected to a point force. The transversely isotropic trimaterial is made of a plate bonded by two half spaces on its top and bottom. The cylindrical system of vector functions is adopted to derive the Green's functions in the transformed domain. Then, a fast and efficient mathematical methodology is developed to solve the equations for the displacements and stresses at any field point within the trimaterial domain. Numerical examples are carried out to verify the present formulation. It is obvious that if the properties of all the three materials are identical, then our solution is reduced to the corresponding full space case. By selecting the material properties properly, our solution can be also reduced to the corresponding half space and bimaterial cases.