Meshfree analysis of non-rectangular sandwich plates based on refined C0 higher order shear deformation theories

Abstract

In the present work, bending and free vibration characteristics of non-rectangular laminated composite and sandwich plates are investigated using C0 meshfree formulation based on element free Galerkin (EFG) method with moving kriging (MK) shape function and newly proposed higher-order shear deformation theories. The five new refined higher-order theories with non-polynomial transverse shear stress functions are proposed, which automatically satisfy traction free conditions on top and the bottom surfaces of the plate. The governing differential equations of motion for the continuum system are derived through the minimization of Lagrange functional and are discretized into the algebraic form using MK based meshfree method. The accuracy and applicability of the proposed models are examined first for benchmark problems on the bending and vibration analysis of thin and thick laminated composite and sandwich square plates. Thereafter, several new results on the flexural and free vibration behaviour of sandwich skew, trapezoidal and L-shaped plates, hitherto not found in the literature, are presented for various geometrical parameters and boundary conditions. The presented results for the sandwich plates may serve as the benchmark solutions for the other numerical methods employed for structural analysis of complicated geometry.