Linear Vibration Analysis of Shells Using a Seven-Parameter Spectral/hp Finite Element Model

Abstract

In this paper, a seven-parameter spectral/hp finite element model to obtain natural frequencies in shell type structures is presented. This model accounts for constant and variable thickness of shell structures. The finite element model is based on a Higher-order Shear Deformation Theory, and the equations of motion are obtained by means of Hamilton’s principle. Analysis is performed for isotropic linear elastic shells. A validation of the formulation is made by comparing the present results with those reported in the literature and with simulations in the commercial code ANSYS. Finally, results for shell like structures with variable thickness are presented, and their behavior for different ratios r/h and L/r is studied.

A Seven-Parameter Spectral/hp Finite Element Model for the Linear Vibration Analysis of Functionally Graded Shells with Nonuniform Thickness

“…Since the present work is an extension of the finite element model presented in [49], the most relevant aspects related to the formulation are given below, and a more detailed explanation can be found in the previously mentioned work. In Figure 1, the three-dimensional (3D) geometry of the shell element Φ and the discretization of the mid-surface Ω are shown; the main idea to model the 3D domain is to represent it by means of its mid-surface.…”

“…The main aim of this work is to extend the finite element analysis previously presented in [49] for the modeling of shell-type structures made of FGMs; that is, to take into account the FGM behavior in the seven-parameter finite element formulation in order to determine the natural frequencies and vibration modes of arbitrary FG shell structures with uniform and nonuniform thicknesses. Moreover, due to the few results available in the literature for FG shell-like structures with variable thickness, a user-defined routine to model these type of structures by means of the commercial code ANSYS mechanical APDL is developed and used to compare the results of the present finite element model.…”

Third-Order Theory for the Bending Analysis of Laminated Thin and Thick Plates Including the Strain Gradient Effect

“…The displacement field that characterizes the Third-order Shear Deformation Theory (TSDT), for instance, determines a quadratic profile of shear strains and stresses along the thickness [ 7 , 8 ], due to its cubic expansion in the thickness coordinate. Consequently, there is no need for the shear correction factor [ 9 , 10 , 11 , 12 ]. The importance of these cubic terms in the analysis of laminates has been recently highlighted in the paper by Petrolo and Carrera [ 13 ], in which the best theory diagrams for multilayered structures have been widely discussed.…”