Dynamic Instability of Functionally Graded Shells Using Higher-Order Theory

2010 ◽  
Vol 136 (5) ◽  
pp. 551-561 ◽  
Author(s):  
S. Pradyumna ◽  
J. N. Bandyopadhyay
Keyword(s):  
Dynamic Instability ◽  
Order Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Higher Order Theory

Linear Thermoelastic Higher-Order Theory for Periodic Multiphase Materials

2001 ◽  
Vol 68 (5) ◽  
pp. 697-707 ◽  
Author(s):  
J. Aboudi ◽  
M.-J. Pindera ◽  
S. M. Arnold
Keyword(s):  
Finite Element ◽  
Predictive Accuracy ◽  
Local Stress ◽  
Computer Code ◽  
Order Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Infinite Matrix ◽  
Homogenization Technique ◽  
Higher Order Theory

A new micromechanics model is presented which is capable of accurately estimating both the effective elastic constants of a periodic multiphase composite and the local stress and strain fields in the individual phases. The model is presently limited to materials characterized by constituent phases that are continuous in one direction, but arbitrarily distributed within the repeating unit cell which characterizes the material’s periodic microstructure. The model’s analytical framework is based on the homogenization technique for periodic media, but the method of solution for the local displacement and stress fields borrows concepts previously employed by the authors in constructing the higher-order theory for functionally graded materials, in contrast with the standard finite element solution method typically used in conjunction with the homogenization technique. The present approach produces a closed-form macroscopic constitutive equation for a periodic multiphase material valid for both uniaxial and multiaxial loading which, in turn, can be incorporated into a structural analysis computer code. The model’s predictive accuracy is demonstrated by comparison with reported results of detailed finite element analyses of periodic composites as well as with the classical elasticity solution for an inclusion in an infinite matrix.

Nonlinear Vibration Analysis of Shear Deformable Functionally Graded Ceramic-Metal Plates Using an Improved Higher Order Theory

2010 ◽  
Author(s):  
Mohammad Talha ◽  
B. N. Singh
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Order Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Normal Strain ◽  
Higher Order Terms ◽  
Higher Order Theory ◽  
Shear Deformable

In the present study, an improved higher order theory in conjunction with finite element method (FEM) is presented and is applied to study the nonlinear vibration analysis of shear deformable functionally graded material (FGMs) plates. The present structural model kinematics assumes the cubically varying in-plane displacement over the entire thickness, while the transverse displacement varies quadratically to achieve the accountability of normal strain and its derivative in calculation of transverse shear strains. The theory also satisfies zero transverse strains conditions at the top and bottom faces of the plate, and the geometric nonlinearity is based on Green-Lagrange assumptions. All higher order terms appearing from nonlinear strain displacement relations are incorporated in the formulation. The material properties of the plates are assumed to vary smoothly and continuously throughout the thickness of the plate by a simple power-law distribution in terms of the volume fractions of the constituents. A C0 continuous isoparametric nonlinear FEM with 13 degrees of freedom per node is proposed for the accomplishment of the improved elastic continuum. Numerical results with different system parameters and boundary conditions are accomplished, to show the importance and necessity of the higher order terms in the nonlinear formulations.

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