A simple triangular finite element model for analysing the linear static behaviour of thick sandwich plates with equivalent material properties

Abstract

This study presents a simple triangular finite element model for analysing the linear static behaviour of thick sandwich plates. What sets this work apart is its unique combination of the deformation approach with Airy’s function and analytic integration. The triangular plate finite element (TPFE) model using the Airy function consists of three nodes, each with three degrees of freedom: one transverse displacement and two rotations. Interpolation functions for strain, displacements, and stresses are derived using equilibrium conditions. The selection of bi-harmonic polynomial functions is based on the evolution of the Airy solutions. The basic stiffness matrix is evaluated using the variational principle and analytical integration approach. Additionally, the equivalent material properties for a sandwich plate are obtained using a simple mathematical formula. The numerical results are evaluated and validated using analytical and numerical solutions. The comparison demonstrates the efficiency and accuracy of the TPFE element. Furthermore, the study presents the effects of geometrical parameters, such as thickness configurations and length-to-thickness ratios, as well as end-boundary and load conditions, on the deflection behaviour of the sandwich plates.