K�rm�n-type equations for a higher-order shear deformation plate theory and its use in the thermal postbuckling analysis

1997 ◽  
Vol 18 (12) ◽  
pp. 1137-1152 ◽  
Author(s):  
Shen Huishen
Keyword(s):  
Shear Deformation ◽  
Plate Theory ◽  
Higher Order ◽  
Shear Deformation Plate Theory ◽  
Thermal Postbuckling

Nonlinear thermo-mechanical buckling of higher-order shear deformable porous functionally graded material plates reinforced by orthogonal and/or oblique stiffeners

2019 ◽  
Vol 233 (17) ◽  
pp. 6177-6196 ◽  
Author(s):  
Vu Hoai Nam ◽  
Nguyen Thi Phuong ◽  
Dang Thuy Dong ◽  
Nguyen Thoi Trung ◽  
Nguyen Van Tue
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Functionally Graded Material ◽  
Thermal Environment ◽  
Plate Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Shear Deformation Plate Theory ◽  
Graded Material ◽  
Post Buckling

In this paper, an analytical approach for nonlinear buckling and post-buckling behavior of stiffened porous functionally graded plate rested on Pasternak's elastic foundation under mechanical load in thermal environment is presented. The orthogonal and/or oblique stiffeners are attached to the surface of plate and are included in the calculation by improving the Lekhnitskii's smeared stiffener technique in the framework of higher-order shear deformation plate theory. The complex equilibrium and stability equations are established based on the Reddy's higher-order shear deformation plate theory and taken into account the geometrical nonlinearity of von Kármán. The solution forms of displacements satisfying the different boundary conditions are chosen, the stress function method and the Galerkin procedure are used to solve the problem. The good agreements of the present analytical solution are validated by making the comparisons of the present results with other results. In addition, the effects of porosity distribution, stiffener, volume fraction index, thermal environment, elastic foundation… on the critical buckling load and post-buckling response of porous functionally graded material plates are numerically investigated.

Applying isogeometric approach for free vibration, mechanical, and thermal buckling analyses of functionally graded variable-thickness blades

2020 ◽  
Vol 26 (23-24) ◽  
pp. 2193-2209
Author(s):  
Ehsan Ansari ◽  
AliReza Setoodeh
Keyword(s):  
Aspect Ratio ◽  
Free Vibration ◽  
Shear Deformation ◽  
Variable Thickness ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Numerical Predictions ◽  
Shear Deformation Plate Theory

This article presents free vibration and buckling analyses of functionally graded blades with variable thickness subjected to mechanical and thermal loading using isogeometric analysis as a powerful numerical method. The proposed method is based on deployment of Hamilton’s principle to the two-dimensional kinematics of blades. The governing equations are derived in the context of a modified form of higher order shear deformation plate theory that merely needs C0-continuity (C0-higher order shear deformation plate theory). Without the necessity of defining a shear correction factor, the theory can accurately predict the solution for different thickness-to-length ratios. The numerical predictions for the buckling loads and natural frequencies are successfully compared with the available solutions in the published articles and in the lack of relevant results, finite element analysis using ANSYS is used for verification of the model. The effects of variable thickness and aspect ratio on the natural frequencies and mode shapes known as the frequencies loci veering phenomena are assessed for the first time, which is an important design factor for the blades. The proposed method uses non-uniform rational B-spline element, which is able to approximate linear and nonlinear thickness distribution and the couple modes with an excellent numerical consistency. The influences of aspect ratio, thickness variation, taper ratio, volume fraction exponent, and boundary conditions on the free vibration and buckling of variable-thickness functionally graded blades are also examined.

A simple higher-order non-linear shear deformation plate theory

1989 ◽  
Vol 24 (2) ◽  
pp. 127-137 ◽  
Author(s):  
K.H. Lee ◽  
N.R. Senthilnathan ◽  
S.P. Lim ◽  
S.T. Chow
Keyword(s):  
Shear Deformation ◽  
Plate Theory ◽  
Higher Order ◽  
Shear Deformation Plate Theory ◽  
Non Linear ◽  
Linear Shear
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