On the Equivalence of Displacement-Based Third-Order Shear Deformation Plate Theories

Abstract

Based on a literature review of the assumed kinematics in the so-called higher-order displacement-based shear-deformation theories, a generalization of this kinematics is first proposed and used to formulate variationally consistent field equations and boundary conditions for the bending and vibration of a flat plate of a rectangular platform. Second, attention is focused on displacement-based polynomial shear-deformation plate theories. It is shown that all the kinematics of polynomial third-order theories ({3,0}-order polynomial) proposed in the open literature are special cases of the present theory. Furthermore, it is concluded that the {3,0}-order polynomial kinematics of all the theories is the same when the maximum transverse shear strain is used as generalized displacement coordinates. A deep analysis of the static and dynamic behavior of simply supported rectangular plates in cylindrical bending is performed in order to substantiate the general conclusion that all the {3,0}-order polynomial displacement-based shear-deformation theories give the same numerical results, i.e., they are kinematically equivalent, although not all are statically equivalent.