Analysis of thick sandwich construction by a 3,2-order theory

This study is an extension of the {1, 2}-order plate theory to a higher order 3, 2 theory. Based on the equivalent single-layer assumptions, the in-plane and transverse displacement components are expressed as cubic and quadratic expansions through the thickness of the sandwich construction. Also, the transverse stress component is assumed to vary as a cubic function through the thickness. Utilizing Reissner's definitions for kinematics of thick plates, the displacement components at any point on the plate are approximated in terms of weighted-average quantities (displacements and rotations) that are functions of the in-plane coordinates. The undetermined coefficients defining the in-plane and transverse displacement fields are then expressed in terms of the weighted-average displacements and rotations and their derivatives by directly employing Reissner's definitions and enforcing the zero transverse-shear-stress conditions on the upper and lower surfaces of the sandwich panel. The coefficients defining the transverse stress component are obtained by requiring the transverse strain component, which is expressed in terms of the unknown coefficients of the transverse stress component from a mixed constitutive relation, to be the least-squares equivalent of the kinematic definition of the transverse strain component. The resulting expressions for the unknown coefficients of the transverse stress component are related to resultant strains and curvatures defined from kinematic relations. The equations of equilibrium and boundary conditions of the sandwich plate based on the 3, 2-higher-order theory are derived by employing the principles of virtual displacements. The robustness and accuracy of this 3, 2-order plate theory are established through comparisons with exact solutions available in the literature. The finite element implementation of the present 3, 2-order plate theory is also discussed.