A Finite Element Formulation for Kirchhoff Plates in Strain-gradient Elasticity

Abstract

The current contribution is centered on bending of rectangular plates using the finite element method in the strain-gradient elasticity. To this aim, following introducing stresses and strains for a plate based on the Kirchhoff hypothesis, the principle of the virtual work is adopted to derive the weak form. Building upon Hermite polynomials and by deeming convergence requirements, four rectangular elements for the static analysis of strain-gradient plates are presented. To explore the performance of the proposed elements, particularly in small scales, some problems are solved and the results are compared with analytical solutions.