Boundary Conditions in 2D Numerical and 3D Exact Models for Cylindrical Bending Analysis of Functionally Graded Structures

Abstract

The cylindrical bending condition for structural models is very common in the literature because it allows an incisive and simple verification of the proposed plate and shell models. In the present paper, 2D numerical approaches (the Generalized Differential Quadrature (GDQ) and the finite element (FE) methods) are compared with an exact 3D shell solution in the case of free vibrations of functionally graded material (FGM) plates and shells. The first 18 vibration modes carried out through the 3D exact model are compared with the frequencies obtained via the 2D numerical models. All the 18 frequencies obtained via the 3D exact model are computed when the structures have simply supported boundary conditions for all the edges. If the same boundary conditions are used in the 2D numerical models, some modes are missed. Some of these missed modes can be obtained modifying the boundary conditions imposing free edges through the direction perpendicular to the direction of cylindrical bending. However, some modes cannot be calculated via the 2D numerical models even when the boundary conditions are modified because the cylindrical bending requirements cannot be imposed for numerical solutions in the curvilinear edges by definition. These features are investigated in the present paper for different geometries (plates, cylinders, and cylindrical shells), types of FGM law, lamination sequences, and thickness ratios.

Thermally induced large deflection analysis of shear deformable FGM shallow curved tubes using perturbation method

“…Properties of the FGM media are obtained according to the simple rule of mixtures, same as Equation . Here , and is the temperature rise from reference temperature T 0 at room temperature (300K).…”

“…In this study, except for Poisson's ratio which is assumed to be constant, the other temperature-dependent functionally graded material properties are assumed to be nonlinear functions of temperature and may be expressed by the following function [35,36] ( ) = 0 ( . [37][38][39][40][41][42][43][44][45][46][47][48][49][50] Here = 0 + Δ , and Δ is the temperature rise from reference temperature 0 at room temperature (300K). Also, ( = 0, ±1, 2, 3) are temperature-dependent coefficients of the FG material properties given by Table. 1.…”

Non-Linear Stability of the Step-Variable In-Plane Functionally Graded Plates Subjected to Linear Approaches of the Edges

“…Owing to that fact, many analytical, numerical, and experimental studies of FGM structures have been conducted to better understand their behaviour with respect to nonlinear stability and limitations of carrying-load capacity in references [6][7][8]. The analysis of vibrations of FGM structures was performed in references [9,10], among others. In works [11,12], constitutive relations referred to neutral physical surface for functionally graded materials based on nonlinear six-parameter shell theory.…”

Free Vibration Analysis of Triclinic Nanobeams Based on the Differential Quadrature Method

“…Based on the literature, it is well known that many analytical solutions based on the Navier approximations cannot satisfy the governing equations of the problem, such that numerical approaches are usually required. In this context, the differential quadrature method (DQM) has been increasingly applied in several works and demanding applications as a powerful and efficient numerical method [7][8][9][10][11][12], due to its beneficial properties. This method, indeed, is user-friendly for different engineering problems and it features a high accuracy even with few grid points and a reduced computational effort, (see [7][8][9][10][11]).…”