On asymmetric bending of functionally graded solid circular plates

2018 ◽  
Vol 39 (6) ◽  
pp. 767-782
Author(s):  
Yingwu Yang ◽  
Ying Zhang ◽  
Weiqiu Chen ◽  
Bo Yang
Keyword(s):  
Functionally Graded ◽  
Circular Plates ◽  
Asymmetric Bending

NONLINEAR ANALYSIS OF FUNCTIONALLY GRADED CIRCULAR PLATES UNDER DIFFERENT LOADS AND BOUNDARY CONDITIONS

2008 ◽  
Vol 08 (01) ◽  
pp. 131-159 ◽  
Author(s):  
RECEP GUNES ◽  
J. N. REDDY
Keyword(s):  
Nonlinear Analysis ◽  
Strain Tensor ◽  
Homogenization Method ◽  
Functionally Graded ◽  
Gradient Material ◽  
Graphical Form ◽  
Circular Plates ◽  
Geometrically Nonlinear Analysis ◽  
Steady State Heat Transfer ◽  
Lagrange Strain

Geometrically nonlinear analysis of functionally graded circular plates subjected to mechanical and thermal loads is carried out in this paper. The Green–Lagrange strain tensor in its entirety is used in the analysis. The locally effective material properties are evaluated using homogenization method which is based on the Mori–Tanaka scheme. In the case of thermally loaded plates, the temperature variation through the thickness is determined by solving a steady-state heat transfer (i.e. energy) equation. As an example, a functionally gradient material circular plate composed of zirconium and aluminum is used and results are presented in graphical form.

A Unified Modeling Method for Dynamic Analyses of FGP Annular and Circular Plates with General Boundary Conditions

2021 ◽  
Author(s):  
J. Lu ◽  
X. Hua ◽  
C. Chiu ◽  
X. Zhang ◽  
S. Li ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation Theory ◽  
Modeling Method ◽  
Functionally Graded ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Circular Plates ◽  
Unified Modeling ◽  
Dynamic Analyses ◽  
Vibration Responses

The porous material is an emerging lightweight material, which is able to reduce structural weight and also keeps the superiority of the structure. Therefore, this work is devoted to the investigation of the functionally graded porous (FGP) annular and circular plates with general boundary conditions. The unified modeling method is proposed by combining the first-order shear deformation theory, the virtual spring technology, the multi-segment partition method, and the semi-analysis Rayleigh–Ritz approach. Afterwards, the convergency and correctness of the proposed method are verified, respectively. The frequency parameters, modal shapes, and forced vibration responses are uniformly calculated based on the proposed method. Finally, the dynamic analyses of the FGP annular and circular plates with different parameters, such as the porosity distribution types, porosity ratios, boundary condition types, geometry parameters, and load types, are conducted in detail. It is found that the reasonable porous design is able to keep the dynamic stability of the structure under different parameter variations.

A closed form solution for bending/stretching analysis of functionally graded circular plates under asymmetric loading using the Green function

2010 ◽  
Vol 224 (6) ◽  
pp. 1153-1163 ◽  
Author(s):  
A R Saidi ◽  
A Naderi ◽  
E Jomehzadeh
Keyword(s):  
Green Function ◽  
Closed Form ◽  
Volume Fraction ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Form Solution ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Circular Plates ◽  
Equilibrium Equations

In this article, a closed-form solution for bending/stretching analysis of functionally graded (FG) circular plates under asymmetric loads is presented. It is assumed that the material properties of the FG plate are described by a power function of the thickness variable. The equilibrium equations are derived according to the classical plate theory using the principle of total potential energy. Two new functions are introduced to decouple the governing equilibrium equations. The three highly coupled partial differential equations are then converted into an independent equation in terms of transverse displacement. A closed-form solution for deflection of FG circular plates under arbitrary lateral eccentric concentrated force is obtained by defining a new coordinate system. This solution can be used as a Green function to obtain the closed-form solution of the FG plate under arbitrary loadings. Also, the solution is employed to solve some different asymmetric problems. Finally, the stress and displacement components are obtained exactly for each problem and the effect of volume fraction is also studied.

Exact Relationships between Eigenvalues of FGM Circular Plates Based on RPT and those of Isotropic Homogeneous Circular Plates Based on CPT

2007 ◽  
Vol 353-358 ◽  
pp. 3002-3005
Author(s):  
Lian Sheng Ma ◽  
Lei Wu
Keyword(s):  
Eigenvalue Problem ◽  
Plate Theory ◽  
Functionally Graded ◽  
Classical Solutions ◽  
Transverse Shear Deformation ◽  
Axisymmetric Vibration ◽  
Circular Plates ◽  
Third Order ◽  
Classical Plate Theory ◽  
Graded Material

Based on the mathematical similarity of the eigenvalue problem of the Reddy’s third-order plate theory (RPT) and the classical plate theory (CPT), relationships between the solutions of axisymmetric vibration or buckling of functionally graded material (FGM) circular plates based on RPT and those of isotropic homogeneous circular plates based on CPT are presented, from which one can easily obtain the RPT solutions of axisymmetric vibration or buckling of FGM circular plates expressed in terms of the well-known CPT solutions of isotropic circular plates without much tedious mathematics. Effects of rotary inertia are not considered in the present analysis. The relationships obtained from the present analysis may be used to check the validity, convergence and accuracy of numerical results of FGM plates based on RPT, and also show clearly the intrinsic features of the effect of transverse shear deformation on the classical solutions.

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