scholarly journals Reply to the comments of M.E. Golmakani and J. Rezatalab, Comment on “Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates” (by R. Aghababaei and J.N. Reddy, Journal of Sound and Vibration 326 (2009) 277–289), Journal of Sound Vibration, 333 (2014) 3831–3835

2014 ◽  
Vol 333 (21) ◽  
pp. 5654-5656 ◽  
Author(s):  
Noël Challamel ◽  
J.N. Reddy
Keyword(s):  
Shear Deformation ◽  
Plate Theory ◽  
Third Order ◽  
Shear Deformation Plate Theory ◽  
Sound Vibration

Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory

2017 ◽  
Vol 119 ◽  
pp. 687-699 ◽  
Author(s):  
Thom Van Do ◽  
Dinh Kien Nguyen ◽  
Nguyen Dinh Duc ◽  
Duc Hong Doan ◽  
Tinh Quoc Bui
Keyword(s):  
Shear Deformation ◽  
Plate Theory ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Third Order ◽  
Shear Deformation Plate Theory

On the Singularity Induced by Boundary Conditions in a Third-Order Thick Plate Theory

2002 ◽  
Vol 69 (6) ◽  
pp. 800-810 ◽  
Author(s):  
C. S. Huang
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Thick Plate ◽  
Plate Theory ◽  
Vertex Angle ◽  
Singular Behavior ◽  
Third Order ◽  
Characteristic Equations ◽  
Shear Deformation Plate Theory ◽  
Comparison Results

This paper thoroughly examines the singularity of stress resultants of the form r−ξFθ for 0<ξ⩽1 as r→0 (Williams-type singularity) at the vertex of an isotropic thick plate; the singularity is caused by homogeneous boundary conditions around the vertex. An eigenfunction expansion is applied to derive the first known asymptotic solution for displacement components, from the equilibrium equations of Reddy’s third-order shear deformation plate theory. The characteristic equations for determining the singularities of stress resultants are presented for ten sets of boundary conditions. These characteristic equations are independent of the thickness of the plate, Young’s modulus, and shear modulus, but some do depend on Poisson’s ratio. The singularity orders of stress resultants for various boundary conditions are expressed in graphic form as a function of the vertex angle. The characteristic equations obtained herein are compared with those from classic plate theory and first-order shear deformation plate theory. Comparison results indicate that different plate theories yield different singular behavior for stress resultants. Only the vertex with simply supported radial edges (S(I)_S(I) boundary condition) exhibits the same singular behavior according to all these three plate theories.

Nonlinear Vibration of the Cantilever FGM Plate Based on the Third-order Shear Deformation Plate Theory

2010 ◽  
Author(s):  
Y. X. Hao ◽  
W. Zhang ◽  
Jane W. Z. Lu ◽  
Andrew Y. T. Leung ◽  
Vai Pan Iu ◽  
...  
Keyword(s):  
Nonlinear Vibration ◽  
Shear Deformation ◽  
Plate Theory ◽  
Third Order ◽  
The Third ◽  
Shear Deformation Plate Theory

scholarly journals Static Bending Analysis of Auxetic Plate by FEM and a New Third-Order Shear Deformation Plate Theory

2020 ◽  
Vol 36 (1) ◽  
Author(s):  
Pham Hong Cong ◽  
Pham Minh Phuc ◽  
Hoang Thi Thiem ◽  
Duong Tuan Manh ◽  
Nguyen Dinh Duc
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Poisson’S Ratio ◽  
Plate Theory ◽  
Poisson's Ratio ◽  
Element Formulation ◽  
Negative Poisson’S Ratio ◽  
Third Order ◽  
Shear Deformation Plate Theory ◽  
Negative Poisson's Ratio

In this paper, a finite element method (FEM) and a new third-order shear deformation plate theory are proposed to investigate a static bending model of auxetic plates with negative Poisson’s ratio. The three – layer sandwich plate is consisted of auxetic honeycombs core layer with negative Poisson’s ratio integrated, isotropic homogeneous materials at the top and bottom of surfaces. A displacement-based finite element formulation associated with a novel third-order shear deformation plate theory without any requirement of shear correction factors is thus developed. The results show the effects of geometrical parameters, boundary conditions, uniform transverse pressure on the static bending of auxetic plates with negative Poisson’s ratio. Numerical examples are solved, then compared with the published literatures to validate the feasibility and accuracy of proposed analysis method. Keywords: Static bending; New third-order shear deformation plate theory; Auxetic material.

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