scholarly journals Non-linear dynamical analysis of imperfect functionally graded material shallow shells

2010 ◽  
Vol 32 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Dao Huy Bich ◽  
Vu Do Long
Keyword(s):  
Functionally Graded Material ◽  
Linear Equations ◽  
Functionally Graded ◽  
Dynamical Analysis ◽  
Power Law Distribution ◽  
Shallow Shells ◽  
Dynamical Behaviors ◽  
Non Linear ◽  
Graded Material ◽  
Geometrical Imperfections

Dynamical behaviors of functionally graded material shallow shells with geometrical imperfections are studied in this paper. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. The motion, stability and compatibility equations of these structures are derived using the classical shell theory. The non-linear equations are solved by the Newmark's numerical integration method. The non-linear transient responses of cylindrical and doubly-curved shallow shells subjected to excited external forces are obtained and the dynamic critical buckling loads are evaluated based on the displacement responses using the criterion suggested by Budiansky and Roth. Obtained results show the essential influence of characteristics of functionally graded materials on the dynamical behaviors of shells.

A third-order shear deformation theory for nonlinear vibration analysis of stiffened functionally graded material sandwich doubly curved shallow shells with four material models

2017 ◽  
Vol 21 (4) ◽  
pp. 1316-1356 ◽  
Author(s):  
Dang T Dong ◽  
Dao Van Dung
Keyword(s):  
Functionally Graded Material ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Shallow Shells ◽  
Graded Material ◽  
Doubly Curved

This study presents a nonlinear vibration analysis of function graded sandwich doubly curved shallow shells, which reinforced by functionally graded material stiffeners and rested on the Pasternak foundation. The shells are subjected to the combination of mechanical, thermal, and damping loading. Four models of the sandwich shells with general sigmoid and power laws distribution are considered. The governing equations are established based on the third-order shear deformation theory. Von Kármán-type nonlinearity and smeared stiffener technique are taken into account. The explicit expressions for determining natural frequencies, nonlinear frequency–amplitude relation, and time–deflection curves are obtained by employing the Galerkin method. Finally, the fourth-order Runge–Kutta method is applied to investigate the influences of functionally graded material stiffeners, the boundary conditions, the models of the shells, thermal environment, foundation and geometrical parameters on the natural frequencies and dynamic nonlinear responses of the sandwich shells.

BI-STABLE ANALYSES OF LAMINATED FGM SHELLS

2012 ◽  
Vol 12 (02) ◽  
pp. 311-335 ◽  
Author(s):  
X. Q. HE ◽  
L. LI ◽  
S. KITIPORNCHAI ◽  
C. M. WANG ◽  
H. P. ZHU
Keyword(s):  
Power Law ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Optimum Combination ◽  
Thickness Direction ◽  
Power Law Distribution ◽  
Deployable Structures ◽  
Graded Material ◽  
Two Parameter

Based on an inextensional two-parameter analytical model for cylindrical shells, bi-stable analyses were carried out on laminated functionally graded material (FGM) shells with various layups of fibers. Properties of FGM shells are functionally graded in the thickness direction according to a volume fraction power law distribution. The effects of constituent volume fractions of FGM matrix are examined on the curvature and twist of laminated FGM shells. The results reveal that the optimum combination of constituents of FGM matrix can be obtained for the maximum twist of FGM shells with antisymmetric layups, which helps the design of deployable structures. The effects of Young's modulus of fibers and the symmetry of layups on bi-stable behaviors are also discussed in detail.

scholarly journals Numerical solution of thermal elastic-plastic functionally graded thin rotating disk with exponentially variable thickness and variable density

2019 ◽  
Vol 23 (1) ◽  
pp. 125-136 ◽  
Author(s):  
Sanjeev Sharma ◽  
Sanehlata Yadav
Keyword(s):  
Strain Hardening ◽  
Functionally Graded Material ◽  
Circumferential Stress ◽  
Rotating Disk ◽  
Functionally Graded ◽  
Linear Strain ◽  
Annular Disk ◽  
Elastic Plastic ◽  
Non Linear ◽  
Graded Material

Thermal elastic-plastic stresses and strains have been obtained for rotating annular disk by using finite difference method with Von-Mises? yield criterion and non-linear strain hardening measure. The compressibility of the disk is assumed to be varying in the radial direction. From the numerical results, we can conclude that thermal rotating disk made of functionally graded material whose thickness decreases exponentially and density increases exponentially with non-linear strain hardening measure (m = 0.2) is on the safe side of the design as compared to disk made of homogenous material. This is because of the reason that circumferential stress is less for functionally graded disk as compared to homogenous disk. Also, plastic strains are high for functionally graded disk as compared to homogenous disk. It means that disk made of functionally graded material reduces the possibility of fracture at the bore as compared to the disk made of homogeneous material which leads to the idea of stress saving.

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.

Buckling and free vibration analysis of functionally graded sandwich plates and shallow shells by the Ritz method and the R-functions theory

2020 ◽  
pp. 095440622093630
Author(s):  
LV Kurpa ◽  
TV Shmatko
Keyword(s):  
Power Law ◽  
Functionally Graded Material ◽  
Complex Shape ◽  
Ritz Method ◽  
Mathematical Formulation ◽  
Functionally Graded ◽  
Buckling Load ◽  
Shallow Shells ◽  
Graded Material ◽  
R Functions

The purpose of the paper is to study stability and free vibrations of laminated plates and shallow shells composed of functionally graded materials. The approach proposed incorporates the Ritz method and the R-functions theory. It is assumed that the shell consists of three layers and is loaded in the middle plane. The both cases of uniform as well as non-uniform load are possible. The power-law distribution in terms of volume fractions is applied to get effective material properties for the layers. These properties are calculated for different arrangements and thicknesses of the layers by the analytical formulae obtained in the paper. The mathematical formulation is carried out in framework of the first-order shear deformation theory. The proposed approach consists of two steps. The first step is to define the pre-buckling state by solving the respective elasticity problem. The critical buckling load and frequencies of functionally graded material shallow shells are determined in the second step. The highlight of the method proposed is that it can be used for vibration and buckling analysis of plates and shallow shells of complex shape. The numerical results for frequencies and buckling load of plates and shallow shells of complex shape and different curvatures are presented to demonstrate the potential of the method developed. Different functionally graded material plates and shallow shells composed of a mixture of metal and ceramics are studied. The effects of the power law index, boundary conditions, thickness of the core, and face sheet layers on the fundamental frequencies and critical loads are discussed in this paper. The main advantage of the method is that it provides an analytical representation of the unknown solution, which is important when solving nonlinear problems.

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