Comparison of Post-Buckling Behaviors of a S-S FGM Beam under Conservative and Non-Conservative Distributed Forces

2011 ◽  
Vol 250-253 ◽  
pp. 266-270
Author(s):  
Qing Lu Li ◽  
Shi Rong Li
Keyword(s):  
Deformation Theory ◽  
Shooting Method ◽  
Nonlinear Boundary ◽  
Conservative System ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Beam ◽  
Post Buckling ◽  
Fgm Beam ◽  
Distributed Forces

Based on the large deformation theory and considering the axial extension of the beam, the governing equations of post-buckling of a simply supported elastic FGM beam subjected to conservative and non-conservative distributed forces were established. In the analysis, it was assumed that the material properties of the beam vary continuously as a power function of the thickness coordinate. By using shooting method, the nonlinear boundary-value problem was solved numerically and the equilibrium paths as well as the post- buckling configurations of the deformed beam were presented. A comparison between the results of conservative system and that of non-conservative systems were given. The results shows that the features of the equilibrium paths of the the functionally graded beam under non-conservative are evidently different from those to a conservative one.

Post-Buckling Analysis of FGM Beam Subjected to Non-Conservative Forces and In-Plane Thermal Loading

2012 ◽  
Vol 152-154 ◽  
pp. 474-479
Author(s):  
Feng Qun Zhao ◽  
Zhong Min Wang ◽  
Rui Ping Zhang
Keyword(s):  
Shooting Method ◽  
Thermal Loading ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Tangential Load ◽  
Simply Supported ◽  
Runge Kutta Method ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Fgm Beam

Based on the Kirchhoff large deformation theory, the post-buckling behavior of right movable simply supported FGM beam subjected to non-conservative forces and in-plane thermal loading was analyzed in this paper. The temperature-dependent and spatially dependent material properties of the FGM beam were assumed to vary through the thickness. The nonlinear governing equations of FGM beam subjected to a uniform distributed tangential load along the central axis and in-plane thermal loading were derived. Then, a shooting method and Runge-kutta method are employed to numerically solve the resulting equations. The post-buckling equilibrium paths of the FGM beam with different parameters were plotted, and the effects of non-conservative force, temperature, gradient index of FGM on the post-buckling behavior of right movable simply supported FGM beams were analyzed.

Free Vibration Analysis the Cracked FGM Beam under Bending-Torsion Loading, Using GDQ Method

2013 ◽  
Vol 330 ◽  
pp. 942-947 ◽  
Author(s):  
Alireza Daneshmehr ◽  
D.J. Inman ◽  
A. Mohammadi Fakhar
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Algebraic Equations ◽  
Governing Equations ◽  
Functionally Graded Beam ◽  
Fg Beam ◽  
Fgm Beam

This paper presents a theoretical investigation of free vibration analysis of a functionally graded beam (FGM) under the bending-torsion loading using a classical elasticity theory. The FG beam is assumed to have an open edge crack. It is assumed that the material properties of the simply-supported cracked beam, vary along the beam thickness following a polynomial distribution in the thickness direction. This analysis is based on the linear fracture mechanics. First of all, governing equations and boundary conditions of the FG beam are derived using Hamilton's principle. The governing equations are solved using generalized differential quadrature (GDQ) method. By applying GDQ method, the governing differential equations convert to a linear system of algebraic equations. Then solving the eigenvalue problem, natural frequencies of the FG beam can be found. The results indicate that natural frequencies in the presence of a crack are affected by the crack ratio and location.

Thermal Post-Buckling Analysis of Functionally Graded Composite Plates with Nonlinear Aerodynamic Forces

2010 ◽  
Vol 123-125 ◽  
pp. 280-283
Author(s):  
Chang Yull Lee ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Composite ◽  
Post Buckling

The post-buckling of the functionally graded composite plate under thermal environment with aerodynamic loading is studied. The structural model has three layers with ceramic, FGM and metal, respectively. The outer layers of the sandwich plate are different homogeneous and isotropic material properties for ceramic and metal. Whereas the core is FGM layer, material properties vary continuously from one interface to the other in the thickness direction according to a simple power law distribution in terms of the volume fractions. Governing equations are derived by using the principle of virtual work and numerical solutions are solved through a finite element method. The first-order shear deformation theory and von-Karman strain-displacement relations are based to derive governing equations of the plate. Aerodynamic effects are dealt by adopting nonlinear third-order piston theory for structural and aerodynamic nonlinearity. The Newton-Raphson iterative method applied for solving the nonlinear equations of the thermal post-buckling analysis

A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations

2017 ◽  
Vol 21 (6) ◽  
pp. 1906-1929 ◽  
Author(s):  
Abdelkader Mahmoudi ◽  
Samir Benyoucef ◽  
Abdelouahed Tounsi ◽  
Abdelkader Benachour ◽  
El Abbas Adda Bedia ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Deformation Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Refined Theory ◽  
Governing Equations

In this paper, a refined quasi-three-dimensional shear deformation theory for thermo-mechanical analysis of functionally graded sandwich plates resting on a two-parameter (Pasternak model) elastic foundation is developed. Unlike the other higher-order theories the number of unknowns and governing equations of the present theory is only four against six or more unknown displacement functions used in the corresponding ones. Furthermore, this theory takes into account the stretching effect due to its quasi-three-dimensional nature. The boundary conditions in the top and bottoms surfaces of the sandwich functionally graded plate are satisfied and no correction factor is required. Various types of functionally graded material sandwich plates are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Numerical examples, selected from the literature, are illustrated. A good agreement is obtained between numerical results of the refined theory and the reference solutions. A parametric study is presented to examine the effect of the material gradation and elastic foundation on the deflections and stresses of functionally graded sandwich plate resting on elastic foundation subjected to thermo-mechanical loading.

scholarly journals Higher-Order Thermo-Elastic Analysis of FG-CNTRC Cylindrical Vessels Surrounded by a Pasternak Foundation

Nanomaterials ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 79 ◽  
Author(s):  
Masoud Mohammadi ◽  
Mohammad Arefi ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Deformation Theory ◽  
Volume Fraction ◽  
Effective Properties ◽  
Shear Deformation Theory ◽  
Pressure Vessels ◽  
Functionally Graded ◽  
Elastic Response ◽  
Governing Equations ◽  
Third Order ◽  
Reinforced Composite

This study analyses the two-dimensional thermo-elastic response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) cylindrical pressure vessels, by applying the third-order shear deformation theory (TSDT). The effective properties of FG-CNTRC cylindrical pressure vessels are computed for different patterns of reinforcement, according to the rule of mixture. The governing equations of the problem are derived from the principle of virtual works and are solved as a classical eigenproblem under the assumption of clamped supported boundary conditions. A large parametric investigation aims at showing the influence of some meaningful parameters on the thermo-elastic response, such as the type of pattern, the volume fraction of CNTs, and the Pasternak coefficients related to the elastic foundation.

A NEW SIMPLE HYPERBOLIC SHEAR DEFORMATION THEORY FOR FUNCTIONALLY GRADED PLATES RESTING ON WINKLER–PASTERNAK ELASTIC FOUNDATIONS

2014 ◽  
Vol 11 (06) ◽  
pp. 1350098 ◽  
Author(s):  
ABDERRAHMANE SAID ◽  
MOHAMMED AMEUR ◽  
ABDELMOUMEN ANIS BOUSAHLA ◽  
ABDELOUAHED TOUNSI
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Governing Equations ◽  
Pasternak Elastic Foundation ◽  
Shear Deformation Theories

An improved simple hyperbolic shear deformation theory involving only four unknown functions, as against five functions in case of first or other higher-order shear deformation theories, is introduced for the analysis of functionally graded plates resting on a Winkler–Pasternak elastic foundation. The governing equations are derived by employing the principle of virtual work and the physical neutral surface concept. The accuracy of the present analysis is demonstrated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories.

scholarly journals Mode shape analysis of multiple cracked functionally graded beam-like structures by using dynamic stiffness method

2017 ◽  
Vol 39 (3) ◽  
pp. 215-228 ◽  
Author(s):  
Tran Van Lien ◽  
Ngo Trong Duc ◽  
Nguyen Tien Khiem
Keyword(s):  
Timoshenko Beam ◽  
Dynamic Stiffness ◽  
Beam Theory ◽  
Functionally Graded ◽  
Theoretical Development ◽  
Mode Shapes ◽  
Functionally Graded Beam ◽  
Stiffness Method ◽  
Dynamic Stiffness Method ◽  
Fgm Beam

Mode shapes of multiple cracked beam-like structures made of Functionally Graded Material (FGM) are analyzed by using the dynamic stiffness method. Governing equations in vibration theory of multiple cracked FGM beam are derived on the base of Timoshenko beam theory; power law variation of material; coupled spring model of crack and taking into account the actual position of neutral axis. A general solution of vibration in frequency domain is obtained and used for constructing dynamic stiffness matrix of the multiple cracked FGM Timoshenko beam element that provides an efficient method for modal analysis of multiple cracked FGM frame structures. The theoretical development is illustrated by numerical analysis of crack-induced change in mode shapes of multi-span continuous FGM beam.

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