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The nonlinear free and forced bending vibration of sandwich plates with incompressible viscoelastic core is investigated under the effects of different source of nonlinearities. For the core constrained between stiffer layers, the transverse shear strains, as well as the rotations are assumed to be moderate. The linear and quadratic displacement fields are also adopted for the in-plane and out-of-plane displacements of the core, respectively. The assumption of moderate transverse strains requires a nonlinear constitutive equation which is obtained from a single-integral nonlinear viscoelastic model using the assumed order of magnitudes for linear strains and rotations. The 5th-order method... 

In this paper, the three-dimensional (3D) stress analysis of plate-type structures in instability conditions is presented. The displacement-based and hybrid-mixed four-node quadrilateral elements are developed taking the advantages of the sampling surfaces (SaS) method. The SaS formulation is based on considering inside the plate N not equally spaced SaS parallel to the middle surface to specify the displacements of these surfaces as primary plate unknowns. The displacements, strains and stresses are assumed to be distributed through the thickness using Lagrange polynomials of degree N–1 that lead to a well-set higher-order plate theory. The locations of SaS are based on the use of Chebyshev... 

The finite deformation displacement-based and hybrid-mixed four-node quadrilateral elements using the sampling surfaces (SaS) technique are developed. The SaS formulation is based on choosing inside the plate N not equally spaced SaS parallel to the middle surface to introduce the displacements of these surfaces as basic plate unknowns. Such choice of unknowns with the consequent use of Lagrange polynomials of degree N–1 in the thickness direction permits the presentation of the plate formulation in a very compact form. The SaS are located at only Chebyshev polynomial nodes that allows one to minimize uniformly the error due to the Lagrange interpolation. To circumvent shear locking and have...