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.

The Nonlinear Dynamic Response of Functionally Graded Material Flat Spherical Shells

2012 ◽  
Vol 479-481 ◽  
pp. 1399-1402 ◽  
Author(s):  
Yao Dai ◽  
Xiao Hong ◽  
Jun Feng Liu ◽  
Lei Zhang
Keyword(s):  
Functionally Graded Material ◽  
Method Of Lines ◽  
Functionally Graded ◽  
Geometrically Nonlinear ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Spherical Shells ◽  
Nonlinear Dynamic Response ◽  
The Method Of Lines ◽  
Graded Material

The response of functionally graded material (FGM) flat spherical shell under mechanical 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 of the response of FGM flat spherical shells are obtained. A semi-analytical numerical method, i.e. the method of lines was introduced, and then the partial differential equations were transformed into ordinary differential ones. The effects of the material gradient parameters on the responses are discussed in details. The numerical results of flat spherical shells are given and compared with the finite element method ones.

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.

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.

Geometrically nonlinear dynamic response and vibration of shear deformable eccentrically stiffened functionally graded material cylindrical panels subjected to thermal, mechanical, and blast loads

2018 ◽  
Vol 22 (3) ◽  
pp. 658-688 ◽  
Author(s):  
Nguyen Dinh Duc ◽  
Ngo Duc Tuan ◽  
Pham Hong Cong ◽  
Ngo Dinh Dat ◽  
Nguyen Dinh Khoa
Keyword(s):  
Dynamic Response ◽  
Functionally Graded Material ◽  
Material Properties ◽  
Nonlinear Dynamic ◽  
Functionally Graded ◽  
Blast Loads ◽  
Temperature Dependent ◽  
Nonlinear Dynamic Response ◽  
Cylindrical Panels ◽  
Graded Material

Based on the first order shear deformation shell theory, this paper presents an analysis of the nonlinear dynamic response and vibration of imperfect eccentrically stiffened functionally graded material (ES-FGM) cylindrical panels subjected to mechanical, thermal, and blast loads resting on elastic foundations. The material properties are assumed to be temperature-dependent and graded in the thickness direction according to simple power-law distribution in terms of the volume fractions of the constituents. Both functionally graded material cylindrical panels and stiffeners having temperature-dependent properties are deformed under temperature, simultaneously. Numerical results for the dynamic response of the imperfect ES-FGM cylindrical panels with two cases of boundary conditions are obtained by the Galerkin method and fourth-order Runge–Kutta method. The results show the effects of geometrical parameters, material properties, imperfections, mechanical and blast loads, temperature, elastic foundations and boundary conditions on the nonlinear dynamic response of the imperfect ES-FGM cylindrical panels. The obtained numerical results are validated by comparing with other results reported in the open literature.

scholarly journals Nonlinear vibration of functionally graded material sandwich doubly curved shallow shells reinforced by FGM stiffeners. Part 1: Governing equations

2017 ◽  
Vol 39 (3) ◽  
pp. 245-257
Author(s):  
Dang Thuy Dong ◽  
Dao Van Dung
Keyword(s):  
Nonlinear Vibration ◽  
Thermal Loading ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Nonlinear Frequency ◽  
Governing Equations ◽  
Shallow Shells ◽  
Geometrical Imperfection ◽  
Graded Material ◽  
Doubly Curved

Nonlinear vibration of FGM sandwich doubly curved shallow shells reinforced by FGM stiffeners subjected to mechanical and thermal loading are investigated based on the first-order shear deformation theory (FSDT) with von Karman type nonlinearity, taking into account initial geometrical imperfection and smeared stiffener technique. Four material models of the FGM sandwich shells are presented. Explicit expressions for natural frequencies, nonlinear frequency-amplitude relation, and time-deflection curves of the FGM sandwich shallow shells are derived using Galerkin method.

scholarly journals Extended finite element method for simulating the mechanical behavior of multiple random holes and inclusions in functionally graded material

2017 ◽  
Vol 20 (K2) ◽  
pp. 141-147
Author(s):  
Bang Kim Tran ◽  
Huy The Tran ◽  
Tinh Quoc Bui ◽  
Thien Tich Truong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mechanical Behavior ◽  
Functionally Graded Material ◽  
Extended Finite Element Method ◽  
Functionally Graded ◽  
The Finite Element Method ◽  
Extended Finite Element ◽  
Graded Material ◽  
Element Method

Analysis of mechanical behavior of a structure containing defects such as holes and inclusions is essential in many engineering applications. In many structures, the discontinuities may have a significant influence on the reduction of the structural stiffness. In this work, we consider the effect of multiple random holes and inclusions in functionally graded material (FGM) plate and apply the extended finite element method with enrichment functions to simulate the mechanical behavior of those discontinuous interfaces. The inclusions also have FGM properties. Numerical examples are considered and their obtained results are compared with the COMSOL, the finite element method software.

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