Exact 3D solutions and finite element 2D models for free vibration analysis of plates and cylinders

Abstract

The paper proposes a comparison between classical two-dimensional (2D) finite elements (FEs) and an exact three-dimensional (3D) solution for the free vibration analysis of one-layered and multilayered isotropic, composite and sandwich plates and cylinders. Low and high order frequencies are analyzed for thick and thin simply supported structures. Vibration modes are investigated to make a comparison between results obtained via the finite element method and those obtained by means of the exact three-dimensional solution. The 3D exact solution is based on the differential equations of equilibrium written in general orthogonal curvilinear coordinates. This exact method is based on a layer-wise approach, the continuity of displacements and transverse shear/normal stresses is imposed at the interfaces between the layers of the structure. The geometry for shells is considered without any simplifications. The 2D finite element results are obtained by means of a well-known commercial FE code. The differences between 2D FE solutions and 3D exact solutions depend on the considered mode, the order of frequency, the thickness ratio of the structure, the geometry, the embedded material and the lamination sequence.

Dynamic analysis of thick and thin elliptic shell structures made of laminated composite materials

“…Another two comparisons are reported in Tables 2, 3 considering the work by Brischetto and Torre [69]. The first assessment reported in Table 2 50 kg/m ).…”

On the radially symmetric vibrations of circular sandwich plates with polar orthotropic facings and isotropic core of quadratically varying thickness by harmonic differential quadrature method

“…A strong formulation finite element method (SFEM) based on radial basis functions (RBF) and generalized differential quadrature (GDQ) techniques has been used by Fantuzzi et al [32] for the static and dynamic analyses of multi-layered plates of airbitraty shape with discontinuities. Brischetto and Torre [33] have made a comparison between classical twodimensional (2D) finite elements (FEs) and an exact three-dimensional (3D) solution for the free vibration analysis of one-layered and multilayered isotropic, composite and sandwich plates and cylinders. Tornabene et al [34] computed displacement and the recovery of through-the-thickness transverse normal and shear strains and stresses in statically deformed functionally graded (FG) doubly-curved sandwich shell structures and shells of revolution using generalized differential quadrature method.…”

A new approach for treating concentrated loads in doubly-curved composite deep shells with variable radii of curvature

“…Theories on shells have been developed a lot through the years. In particular, the physical three-dimensional (3D) problem [32][33][34][35] can be simplified using different approximations which can lead to two-dimensional (2D) models. As a function of the hypothesis of the theory under study the solutions can closely fit the original 3D shell or plate.…”