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.

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.

Higher-Order Terms for the Mode-III Stationary Crack-Tip Fields in a Functionally Graded Material

2010 ◽  
Vol 78 (1) ◽  
Author(s):  
Linhui Zhang ◽  
Jeong-Ho Kim
Keyword(s):  
Functionally Graded Material ◽  
Crack Tip ◽  
Functionally Graded ◽  
Mode Iii ◽  
Stationary Crack ◽  
Crack Tip Field ◽  
Homogeneous Solutions ◽  
Variable Approach ◽  
Graded Material ◽  
Plane Displacement

This paper provides full asymptotic crack-tip field solutions for an antiplane (mode-III) stationary crack in a functionally graded material. We use the complex variable approach and an asymptotic scaling factor to provide an efficient procedure for solving standard and perturbed Laplace equations associated with antiplane fracture in a graded material. We present the out-of-plane displacement and the shear stress solutions for a crack in exponentially and linearly graded materials by considering the gradation of the shear modulus either parallel or perpendicular to the crack. We discuss the characteristics of the asymptotic solutions for a graded material in comparison with the homogeneous solutions. We address the effects of the mode-III stress intensity factor and the antiplane T-stress onto crack-tip field solutions. Finally, engineering significance of the present work is discussed.

A tangent stiffness–based approach to study free vibration of shear-deformable functionally graded material rotating beam through a geometrically non-linear analysis

2017 ◽  
Vol 52 (5) ◽  
pp. 310-332 ◽  
Author(s):  
Suman Pal ◽  
Debabrata Das
Keyword(s):  
Free Vibration ◽  
Functionally Graded Material ◽  
Thermal Loading ◽  
Linear Analysis ◽  
Functionally Graded ◽  
Rotating Beam ◽  
Governing Equations ◽  
Tangent Stiffness ◽  
Non Linear ◽  
Graded Material

An improved mathematical model to study the free vibration behavior of rotating functionally graded material beam is presented, considering non-linearity up to second order for the normal and transverse shear strains. The study is carried out considering thermal loading due to uniform temperature rise and using temperature-dependent material properties. Power law variation is assumed for through-thickness symmetric functional gradation of ceramic–metal functionally graded beam. The effects of shear deformation and rotary inertia are considered in the frame-work of Timoshenko beam theory. First, the rotating beam configuration under time-invariant centrifugal loading and thermal loading is obtained through a geometrically non-linear analysis, employing minimum total potential energy principle. Then, the free vibration analysis of the deformed beam is performed using the tangent stiffness of the deformed beam configuration, and employing Hamilton’s principle. The Coriolis effect is considered in the free vibration problem, and the governing equations are transformed to the state-space to obtain the eigenvalue problem. The solution of the governing equations is obtained following Ritz method. The validation is performed with the available results, and also with finite element software ANSYS. The analysis is carried out for clamped-free beam and for clamped–clamped beam with immovably clamped ends. The results for the first two modes of chord-wise and flap-wise vibration in non-dimensional speed-frequency plane are presented for different functionally graded material compositions, material profile parameters, root offset parameters and operating temperatures.

The Nonlinear Dynamic Response of Functionally Graded Material Flat Spherical Shells Subjected to Thermal Loading

2012 ◽  
Vol 549 ◽  
pp. 580-583
Author(s):  
Yao Dai ◽  
Xiao Chong ◽  
Lei Zhang ◽  
Hong Qian Chen
Keyword(s):  
Functionally Graded Material ◽  
Thermal Loading ◽  
Method Of Lines ◽  
Functionally Graded ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Spherical Shells ◽  
Nonlinear Dynamic Response ◽  
The Method Of Lines ◽  
Graded Material

The response of functionally graded material flat spherical shells subjected to thermal loading is studied using the method of lines. Based on the Kirchhoff straight normal hypothesis and Von Karman's geometrically nonlinear theory, the governing equations are obtained. A semi-analytical numerical method, viz. the method of lines is introduced. Then, the partial differential equations are transformed into ordinary differential ones. The numerical results of flat spherical shells are given and compared with ones of the finite element method. The effects of the material gradient parameters on the responses are discussed in details.

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