There are different finite element models in place for predicting the bending behavior of shear deformable beams and plates. Mostly, the literature abounds with traditional equi-spaced Langrange based low order finite element approximations using displacement formulations. However, the finite element models of Timoshenko beams and Mindlin plates with linear interpolation of all generalized disp...

In this paper, layerwise theory (LT) along with the first, second and third-order shear deformation theories (FSDT, SSDT and TSDT) are used to determine the stress distribution in a simply supported square sandwich plate subjected to a uniformly distributed load. Two functionally graded (FG) face sheets encapsulate an elastomeric core while two epoxy adhesive layers adhere the core to the face ...

geometrically nonlinear governing equations for a plate with linear viscoelastic material are derived. the material model is of boltzmann superposi¬tion principle type. a third-order displacement field is used to model the shear deformation effects. for the solution of the nonlinear governing equations the dynamic relaxation (dr) iterative method together with the finite difference discretizati...

in the present work, study of the vibration of a functionally graded (fg) cylindrical shell made up of stainless steel, zirconia, and nickel is presented. free vibration analysis is presented for fg cylindrical shells with simply supported-simply supported and clamped–clamped boundary condition based on temperature independent material properties. the equations of motion are derived by hamilton...

this paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. the characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal mindlin plate. this theory is considering both the small length scale effects and transverse shear deformation ef...

A 5th order shear deformation theory considering transverse shear deformation effect as well as transverse normal strain deformation effect is presented for static flexure   analysis of simply supported isotropic plate. The assumed displacement field accounts for non-linear variation of in-plane displacements as well as transverse displacement through the plate thickness. The condition of zero ...

For a plate subject to stress boundary condition, the deformation determined by the Reissner–Mindlin plate bending model could be bending dominated, transverse shear dominated, or neither (intermediate), depending on the load. We show that the Reissner–Mindlin model has a wider range of applicability than the Kirchhoff–Love model, but it does not always converge to the elasticity theory. In the...

In this study, free vibration of functionally graded rectangular plates for various types of boundary conditions has been presented . The properties of the plate are assumed as power- law form along the thickness direction , while poisson's ratio is kept constant. the linear vibration equations of functionally graded rectangular plates are derived based on first order shear deformation theory b...

This paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. The characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal Mindlin plate. This theory is considering both the small length scale effects and transverse shear deformation ef...

This paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. The characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal Mindlin plate. This theory is considering both the small length scale effects and transverse shear deformation ef...