Post-buckling analysis of Timoshenko beams made of functionally graded material under thermal loading

2012 ◽  
Vol 41 (6) ◽  
pp. 775-789 ◽  
Author(s):  
Turgut Kocaturk ◽  
Seref Doguscan Akbas
Keyword(s):  
Functionally Graded Material ◽  
Thermal Loading ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Timoshenko Beams ◽  
Graded Material ◽  
Post Buckling

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

Buckling and post-buckling behaviour of semicircular functionally graded material arches: a theoretical study

2011 ◽  
Vol 226 (3) ◽  
pp. 607-614 ◽  
Author(s):  
A A Atai ◽  
A Nikranjbar ◽  
R Kasiri
Keyword(s):  
Functionally Graded Material ◽  
Thermal Loading ◽  
Slenderness Ratio ◽  
Boundary Value ◽  
Functionally Graded ◽  
Graded Material ◽  
Post Buckling ◽  
Support Conditions ◽  
Semicircular Arch ◽  
Study Behaviour

In this study, behaviour of a thin semicircular arch made of functionally graded material subjected to radial and tangential follower forces, as well as thermal loading, based on the theory of large deformation of the arches and critical buckling load and post-buckling of structures is investigated. Assuming thin arch, governing equations of the arch behaviour are derived using kinematics and static equilibrium. Resulting equations including different support conditions form a set of highly coupled and non-linear boundary value differential equations. To solve the problem, the well-known numerical boundary value problems of shooting method are employed. By gradual increase of loading, the buckling and post-buckling behaviour is closely monitored. Several examples corresponding to different combinations of support conditions/loadings/non-homogeneity/slenderness ratio to illustrate the performance of the proposed algorithm are presented.

Thermomechanically induced post-buckling analysis of functionally graded material plates with circular cut-outs resting on elastic foundations

2020 ◽  
pp. 089270572090410 ◽  
Author(s):  
Rajesh Kumar
Keyword(s):  
Functionally Graded Material ◽  
Material Properties ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Free Expansion ◽  
Elastic Foundations ◽  
Aspect Ratios ◽  
Present Solution ◽  
Graded Material ◽  
Post Buckling

Post-buckling analysis of functionally graded material (FGM) plates resting on Winkler and Pasternak elastic foundations subjected to thermomechanical loadings with circular cut-outs at centre and random material properties is presented. The material properties of each constituent’s materials, volume fraction index, thermal expansion coefficients, foundation stiffness parameters and thermal conductivities are taken as independent basic random input variables. The basic formulation is based on applying Reddy’s higher order shear deformation theory, which requires C1 continuous element approximation. A modified form C0 continuity is applied in the present investigation. A serum-free expansion medium with mean-centred first-order regular perturbation technique for composite plates is extended for FGM plates to solve the random eigenvalue problem. Typical numerical results are presented to examine the second-order statistics for effect of the volume fractions index, plate length-to-thickness ratios, plate aspect ratios, types of loadings, amplitude ratios, support conditions and various shape and size of holes with random thermomechanical properties. The results obtained by the present solution approach are validated with published papers and the robust method of simulation. It is found that the laminates with round cuts (FGM plates resting on Winkler and Pasternak elastic foundations) have a significant influence on the post-buckling response under Thermomechanical loading conditions. Present investigations are useful for the applications and further research.

Delamination of Compressively Stressed Orthotropic Functionally Graded Material Coatings Under Thermal Loading

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
Bora Yıldırım ◽  
Suphi Yılmaz ◽  
Suat Kadıoğlu
Keyword(s):  
Functionally Graded Material ◽  
Bond Coat ◽  
Thermal Loading ◽  
Layer Structure ◽  
Crack Problem ◽  
Functionally Graded ◽  
Internal Crack ◽  
Correlation Technique ◽  
Fracture Parameters ◽  
Graded Material

The objective of this study is to investigate a particular type of crack problem in a layered structure consisting of a substrate, a bond coat, and an orthotropic functionally graded material coating. There is an internal crack in the orthotropic coating layer. It is parallel to the coating bond-coat interface and perpendicular to the material gradation of the coating. The position of the crack inside the coating is kept as a variable. Hence, the case of interface crack is also addressed. The top and bottom surfaces of the three layer structure are subjected to different temperatures and a two-dimensional steady-state temperature distribution develops. The case of compressively stressed coating is considered. Under this condition, buckling can occur, the crack can propagate, and the coating is prone to delamination. To predict the onset of delamination, one needs to know the fracture mechanics parameters, namely, Mode I and Mode II stress intensity factors and energy release rates. Hence, temperature distributions and fracture parameters are calculated by using finite element method and displacement correlation technique. Results of this study present the effects of boundary conditions, geometric parameters (crack length and crack position), and the type of gradation on fracture parameters.

A refined sinusoidal model for functionally graded plates subjected to thermomechanical loading

2018 ◽  
Vol 53 (14) ◽  
pp. 1883-1896
Author(s):  
Ren Xiaohui ◽  
Wu Zhen
Keyword(s):  
Functionally Graded Material ◽  
Thermal Loading ◽  
Functionally Graded ◽  
Normal Strain ◽  
Sinusoidal Model ◽  
Proposed Model ◽  
Graded Material ◽  
Plane Displacement ◽  
Stress Free Boundary ◽  
Transverse Normal Strain

A refined sinusoidal model considering transverse normal strain has been developed for thermoelastic analysis of functionally graded material plate. Although transverse normal strain has been considered, the additional displacement parameters are not increased as transverse normal strain only includes the thermal expansion coefficient and thermal loading. Moreover, the merit of the previous sinusoidal model satisfying tangential stress-free boundary conditions on the surfaces can be maintained. It is important that the effects of transverse normal thermal deformation are incorporated in the in-plane displacement field, which can actively influence the accuracy of in-plane stresses. To assess the performance of the proposed model, the thermoelastic behaviors of functionally graded material plates with various configurations have been analyzed. Without increase of displacement variables, accuracy of the proposed model can be significantly improved by comparing to the previous sinusoidal model. Agreement between the present results and quasi-dimensional solutions are very good, and the proposed model only includes the five displacement variables which can illustrate the accuracy and effectiveness of the present model. In addition, new results using several models considered in this paper have been presented, which can serve as a reference for future investigations.

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.

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