Homogenization of Plates with Microstructure and Application to Corrugated Core Sandwich Panels

Abstract

Current thermal protection systems (TPS) in hypersonic vehicles do not carry significant loads. One potential method of saving weight is to have a load-bearing TPS that performs some structural functions. One such concept, the Integrated Thermal Protection System (ITPS), uses a corrugated-core sandwich structure. Design-optimization of an ITPS requires thousands of three-dimensional high-fidelity simulations, which is very expensive. In this paper we develop a finite element based homogenization procedure for predicting the equivalent stiffness and strength properties of the ITPS. Micromechanical analysis is possible due to the presence of a repeating unit-cell. The unit cell is discretized with plate finite elements, and periodic boundary conditions are imposed between opposite end-faces of the unit cell. The derivation of the periodic boundary conditions is presented. The equivalent stiffness properties, the extensional stiffness matrix [A], coupling stiffness matrix [B], bending stiffness [D], and the transverse shear stiffness terms A44 and A55 are obtained using the micromechanics procedures. The plate deflection under uniform pressure compares well with that from the three-dimensional finite element analysis. The efficacy of the procedures is demonstrated by studying the effects of web angle on the plate stiffness and deflection.