RMVT-based finite cylindrical prism methods for multilayered functionally graded circular hollow cylinders with various boundary conditions

2013 ◽  
Vol 100 ◽  
pp. 592-608 ◽  
Author(s):  
Chih-Ping Wu ◽  
Hao-Yuan Li
Keyword(s):  
Boundary Conditions ◽  
Functionally Graded ◽  
Various Boundary Conditions ◽  
Hollow Cylinders

Static Analysis of Moderately Thick Functionally Graded Plates With Various Boundary Conditions

2010 ◽  
Author(s):  
Nastaran Shahmansouri ◽  
Mohammad Mohammadi Aghdam ◽  
Kasra Bigdeli
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Various Boundary Conditions ◽  
Fg Plates ◽  
Ode Systems

The present study investigates static analyses of moderately thick FG plates. Using the First Order Shear Deformation Theory (FSDT), functionally graded plates subjected to transversely distributed loading with various boundary conditions are studied. Effective mechanical properties which vary from one surface of the plate to the other assumed to be defined by a power law form of distribution. Different ceramic-metal sets of materials are studied. Solution of the governing equations, including five equilibrium and eight constitutive equations, is obtained by the Extended Kantorovich Method (EKM). The system of thirteen Partial Differential Equations (PDEs) in terms of displacements, rotations, force and moment resultants are considered as multiplications of separable function of independent variables x and y. Then by successful utilization of the EKM these equations are converted to a double set of ODE systems in terms of x and y. The obtained ODE systems are then solved iteratively until final convergence is achieved. Closed form solution is presented for these ODE sets. It is shown that the method is very stable and provides fast convergence and highly accurate predictions for both thin and moderately thick plates. Comparison of the normal stresses at various points of rectangular plates and deflection of mid-point of the plate are presented and compared with available data in the literature. The effects of the volume fraction exponent n on the behavior of the normalized deflection, moment resultants and stresses of FG plates are also studied. To validate data for analysis fully clamped FG plates, another analysis was carried out using finite element code ANSYS. Close agreement is observed between predictions of the EKM and ANSYS.

scholarly journals Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point Method

2016 ◽  
Vol 2016 ◽  
pp. 1-23 ◽  
Author(s):  
Peng Liu ◽  
Kun Lin ◽  
Hongjun Liu ◽  
Rong Qin
Keyword(s):  
Boundary Conditions ◽  
Transverse Vibration ◽  
Spline Interpolation ◽  
Computational Cost ◽  
Functionally Graded ◽  
Point Method ◽  
Finite Point ◽  
Various Boundary Conditions ◽  
Finite Point Method ◽  
Free Transverse Vibration

A new model for the free transverse vibration of axially functionally graded (FG) tapered Euler-Bernoulli beams is developed through the spline finite point method (SFPM) by investigating the effects of the variation of cross-sectional and material properties along the longitudinal directions. In the proposed method, the beam is discretized with a set of uniformly scattered spline nodes along the beam axis instead of meshes, and the displacement field is approximated by the particularly constructed cubic B-spline interpolation functions with good adaptability for various boundary conditions. Unlike traditional discretization and modeling methods, the global structural stiffness and mass matrices for beams of the proposed model are directly generated after spline discretization without needing element meshes, generation, and assembling. The proposed method shows the distinguished features of high modeling efficiency, low computational cost, and convenience for boundary condition treatment. The performance of the proposed method is verified through numerical examples available in the published literature. All results demonstrate that the proposed method can analyze the free vibration of axially FG tapered Euler-Bernoulli beams with various boundary conditions. Moreover, high accuracy and efficiency can be achieved.

NONLINEAR MECHANICAL BENDING OF FUNCTIONALLY GRADED MATERIAL PLATES UNDER TRANSVERSE LOADS WITH VARIOUS BOUNDARY CONDITIONS

2011 ◽  
Vol 02 (02) ◽  
pp. 237-258 ◽  
Author(s):  
MOHAMMAD TALHA ◽  
B. N. SINGH
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Nonlinear Strain ◽  
Various Boundary Conditions ◽  
Transverse Loads ◽  
Nonlinear Mechanical ◽  
Graded Material ◽  
Mechanical Bending

Nonlinear mechanical bending of functionally graded material (FGM) plates under transverse loads with various boundary conditions are presented. The material properties of the FGM plates are graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The theoretical nonlinear finite element formulations are based on the higher-order shear deformation theory, with a special modification in the transverse displacement in order to estimate the parabolic distribution of transverse shear strains through the plate thickness. The Green–Lagrange nonlinear strain–displacement relation with all higher-order nonlinear strain terms is included to account for the large deflection response of the plate. The fundamental equations for FGM plates with traction-free boundary conditions on the top and bottom faces of the plate are accomplished using variational approach. Results have been achieved using a C0 continuous isoparametric Lagrangian finite element with 13 degrees of freedom per node. Convergence and comparison studies have been performed to ascertain the effectiveness of the present model. Numerical results are highlighted for different thickness ratios, aspect ratios, and role played by the constituent volume fraction index with different boundary conditions.

A modified couple stress theory for buckling analysis of higher order inhomogeneous microbeams with porosities

2018 ◽  
Vol 233 (8) ◽  
pp. 2855-2866 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Fateme Mahmoodi
Keyword(s):  
Boundary Conditions ◽  
Power Law ◽  
Couple Stress ◽  
Volume Fraction ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Stress Theory ◽  
Various Boundary Conditions ◽  
Modified Couple Stress

In this paper, buckling behavior of a higher order functionally graded microbeam with porosities is investigated based on the modified couple stress theory and the exact position of the neutral axis. Porosities are evenly and unevenly distributed inside the functionally graded microbeam. Material properties of the functionally graded microbeam are assumed to vary in the thickness direction through a modified form of power-law distribution in which the volume fraction of porosities is considered. The governing equations are derived by using Hamilton's principle and an analytical method is employed to solve these equations for various boundary conditions. The present formulation and numerical results demonstrate a good agreement with some available cases in the literature. Influences of several important parameters such as power-law exponent, porosity distributions, porosity volume fraction, slenderness ratio, and various boundary conditions on buckling loads of porous functionally graded microbeams are investigated and discussed in detail.

Exact Solution for Free Vibration and Buckling of Sandwich S-FGM Plates on Pasternak Elastic Foundation with Various Boundary Conditions

2019 ◽  
Vol 19 (03) ◽  
pp. 1950028 ◽  
Author(s):  
S. J. Singh ◽  
S. P. Harsha
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Load Parameter ◽  
Various Boundary Conditions ◽  
Pasternak Elastic Foundation ◽  
Parametric Studies

In the present study, free vibration and buckling characteristics of a sandwich functionally graded material (FGM) plate resting on the Pasternak elastic foundation have been investigated. The formulation is based on non-polynomial higher-order shear deformation theory with inverse hyperbolic shape function. A new modified sigmoid law is presented to compute the effective material properties of sandwich FGM plate. The governing equilibrium equations have been derived using Hamilton’s principle. Non-dimensional frequencies and critical buckling loads are evaluated by considering different boundary conditions based on admissible functions satisfying the desired primary and secondary variables. Comprehensive parametric studies have been performed to analyze the influence of geometric configuration, volume fraction exponent, elastic medium parameter, and non-dimensional load parameter on the non-dimensional frequency and critical buckling load. These parametric studies have been done for various boundary conditions and different configurations of the sandwich plate. The computed results can be used as a benchmark for future comparison of sandwich S-FGM plates.

Sign in / Sign up

Export Citation Format

Share Document