On the curvature and internal stresses in a multilayer strip due to uniform heating, electric field, or hydration

Abstract

An appealing matrix algorithm for calculating the curvature and internal stresses in isotropic multilayer strips subjected to a uniform temperature change is presented. An explicit representation of the effective stiffness matrix is constructed for any number of layers, which is of central importance in the development of the algorithm. Detailed results are given for bi-, tri-, quadra-, quinta-, and septalayers. Closed-form expressions are deduced for multilayer strips with equal thicknesses and equal elastic moduli of all layers. The algorithm is extended to piezoelectric multilayers subjected to an electric field, and hygromorph multilayers subjected to a uniform change of relative moisture. The presented analysis complements an alternative and more general analysis within the well-known anisotropic lamination theory.