Thermal post-buckling of Functionally Graded Material Timoshenko beams

2006 ◽  
Vol 27 (6) ◽  
pp. 803-810 ◽  
Author(s):  
Shi-rong Li ◽  
Jing-hua Zhang ◽  
Yong-gang Zhao
Keyword(s):  
Functionally Graded Material ◽  
Functionally Graded ◽  
Timoshenko Beams ◽  
Graded Material ◽  
Post Buckling

Stability of the Size-Dependent and Functionally Graded Curvilinear Timoshenko Beams

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
J. Awrejcewicz ◽  
A. V. Krysko ◽  
S. P. Pavlov ◽  
M. V. Zhigalov ◽  
V. A. Krysko
Keyword(s):  
Differential Equations ◽  
Functionally Graded Material ◽  
Timoshenko Beam ◽  
Stability Loss ◽  
Functionally Graded ◽  
Beam Deflection ◽  
Timoshenko Beams ◽  
Size Dependent ◽  
Rigid Layer ◽  
Graded Material

The size-dependent model is studied based on the modified couple stress theory for the geometrically nonlinear curvilinear Timoshenko beam made from a functionally graded material having its properties changed along the beam thickness. The influence of the size-dependent coefficient and the material grading on the stability of the curvilinear beams is investigated with the use of the setup method. The second-order accuracy finite difference method is used to solve the problem of nonlinear partial differential equations (PDEs) by reducing it to the Cauchy problem. The obtained set of nonlinear ordinary differential equations (ODEs) is then solved by the fourth-order Runge–Kutta method. The relaxation method is employed to solve numerous static problems based on the dynamic approach. Eight different combinations of size-dependent coefficients and the functionally graded material coefficient are used to study the stress-strain responses of Timoshenko beams. Stability loss of the curvilinear Timoshenko beams is investigated using the Lyapunov criterion based on the estimation of the Lyapunov exponents. Beams with/without the size-dependent behavior, homogeneous beams, and functionally graded beams having the same stiffness are investigated. It is shown that in straight-line beams, the size-dependent effect decreases the beam deflection. The same is observed if the most rigid layer is located on the top of the beam. In the curvilinear Timoshenko beam, such a location of the most rigid layer essentially improves the beam strength against stability loss. The observed transition of the largest Lyapunov exponent from a negative to positive value corresponds to the transition from a precritical to postcritical beam state.

Nonlinear thermo-mechanical buckling of higher-order shear deformable porous functionally graded material plates reinforced by orthogonal and/or oblique stiffeners

2019 ◽  
Vol 233 (17) ◽  
pp. 6177-6196 ◽  
Author(s):  
Vu Hoai Nam ◽  
Nguyen Thi Phuong ◽  
Dang Thuy Dong ◽  
Nguyen Thoi Trung ◽  
Nguyen Van Tue
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Functionally Graded Material ◽  
Thermal Environment ◽  
Plate Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Shear Deformation Plate Theory ◽  
Graded Material ◽  
Post Buckling

In this paper, an analytical approach for nonlinear buckling and post-buckling behavior of stiffened porous functionally graded plate rested on Pasternak's elastic foundation under mechanical load in thermal environment is presented. The orthogonal and/or oblique stiffeners are attached to the surface of plate and are included in the calculation by improving the Lekhnitskii's smeared stiffener technique in the framework of higher-order shear deformation plate theory. The complex equilibrium and stability equations are established based on the Reddy's higher-order shear deformation plate theory and taken into account the geometrical nonlinearity of von Kármán. The solution forms of displacements satisfying the different boundary conditions are chosen, the stress function method and the Galerkin procedure are used to solve the problem. The good agreements of the present analytical solution are validated by making the comparisons of the present results with other results. In addition, the effects of porosity distribution, stiffener, volume fraction index, thermal environment, elastic foundation… on the critical buckling load and post-buckling response of porous functionally graded material plates are numerically investigated.

Thermal post-buckling analysis of uniform slender functionally graded material beams

2010 ◽  
Vol 36 (5) ◽  
pp. 545-560 ◽  
Author(s):  
K. Sanjay Anandrao ◽  
R.K. Gupta ◽  
P. Ramchandran ◽  
G. Venkateswara Rao
Keyword(s):  
Functionally Graded Material ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Graded Material ◽  
Post Buckling

scholarly journals The Study of Buckling and Post-Buckling of a Step-Variable FGM Box

Materials ◽  
2019 ◽  
Vol 12 (6) ◽  
pp. 918 ◽  
Author(s):  
Leszek Czechowski ◽  
Zbigniew Kołakowski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Functionally Graded Material ◽  
Asymptotic Theory ◽  
Functionally Graded ◽  
Pure Alumina ◽  
Mixed Case ◽  
Graded Material ◽  
Post Buckling ◽  
Thin Walled

This work concerns the analysis of a thin-walled box made of ceramic and step-variable functionally graded material (FGM) subjected to compression. The components of the box taken into account were pure alumina and aluminium-alumina graded material. The problem was solved on the basis of a finite element method and Koiter’s asymptotic theory using a semi-analytical method (SAM). It analysed both the buckling state and the post-buckling state of the box. In addition, three conditions were considered: The presence of alumina outside or inside of the box and a mixed case. The obtained results were presented and discussed.

scholarly journals Geometrically Nonlinear Static Analysis of Edge Cracked Timoshenko Beams Composed of Functionally Graded Material

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Şeref Doğuşcan Akbaş
Keyword(s):  
Finite Element ◽  
Static Analysis ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Nonlinear Static Analysis ◽  
Geometrically Nonlinear ◽  
Timoshenko Beams ◽  
Graded Material ◽  
Nonlinear Static ◽  
Fgm Beam

Geometrically nonlinear static analysis of edge cracked cantilever Timoshenko beams composed of functionally graded material (FGM) subjected to a nonfollower transversal point load at the free end of the beam is studied with large displacements and large rotations. Material properties of the beam change in the height direction according to exponential distributions. The cracked beam is modeled as an assembly of two subbeams connected through a massless elastic rotational spring. In the study, the finite element of the beam is constructed by using the total Lagrangian Timoshenko beam element approximation. The nonlinear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The convergence study is performed for various numbers of finite elements. In the study, the effects of the location of crack, the depth of the crack, and various material distributions on the nonlinear static response of the FGM beam are investigated in detail. Also, the difference between the geometrically linear and nonlinear analysis of edge cracked FGM beam is investigated in detail.

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