The Elastic Field of an Elliptic Cylindrical Inclusion in a Laminate With Multiple Isotropic Layers

Abstract

An elliptic cylindrical inclusion with an eigenstrain in an infinite laminate composed of multiple isotropic layers is analyzed. The problem is formulated by using the classical laminated plate theory in which displacement fields in the laminated plate are expressed in terms of in-plane displacements on the main plane and transverse displacement. Employing a method based on influence functions, an integral type solution to the equilibrium equation is expressed in terms of the eigenstrain. Closed-Form solutions for the elastic fields are obtained by evaluating the integrals explicitly for interior points and exterior points of the ellipse. The elastic fields caused by an elliptic cylindrical inhomogeneity with an eigenstrain in the infinite laminate are determined by the equivalent eigenstrain method. Solutions for a finite laminate with an eigenstrain in a circular cylindrical inhomogeneity are also obtained in terms of material and geometric parameters for each layer composing the laminate.