A numerical approach to the elastic/plastic axisymmetric buckling analysis of circular and annular plates resting on elastic foundation

2019 ◽  
Vol 233 (19-20) ◽  
pp. 7041-7061
Author(s):  
E Hasrati ◽  
R Ansari ◽  
H Rouhi
Keyword(s):  
Elastic Foundation ◽  
Constitutive Equations ◽  
Constitutive Relations ◽  
Buckling Analysis ◽  
Differential Quadrature ◽  
Elastic Plastic ◽  
Annular Plates ◽  
Theory Of Plasticity ◽  
Axisymmetric Buckling ◽  
Variational Differential Quadrature

Presented herein is the elastic/plastic axisymmetric buckling analysis of circular and annular plates resting on elastic foundation under radial loading based on a variational numerical method named as variational differential quadrature. To accomplish this aim, a first-order shear deformable plate model is developed in the context of incremental theory of plasticity (IT) (with the Prandtl-Reuss constitutive equations) and the deformation theory of plasticity (DT) (with the Hencky constitutive equations). It is considered that the material of plates exhibits strain hardening characterized by the Ramberg-Osgood relation. Also, the Winkler and Pasternak models are employed in order to formulate the elastic foundation. To implement the variational differential quadrature method, the matrix formulations of strain rates and constitutive relations are first derived. Then, based upon Hamilton's principle and using the variational differential quadrature derivative and integral operators, the discretized energy functional of the problem is directly obtained. Selected numerical results are presented to study the effects of various parameters including thickness-to-radius ratio, elastic modulus-to-nominal yield stress ratio, power of the Ramberg-Osgood relation and parameters of elastic foundation on the elastic/plastic buckling of circular and annular plates subject to different boundary conditions. Moreover, several comparisons are provided between the results of two plasticity theories, i.e. IT and DT. The effect of transverse shear deformation is also highlighted.

Axisymmetric Buckling of Elastic-Plastic Annular Plates

AIAA Journal ◽  
1974 ◽  
Vol 12 (11) ◽  
pp. 1594-1596 ◽  
Author(s):  
A. NEEDLEMAN
Keyword(s):  
Elastic Plastic ◽  
Annular Plates ◽  
Axisymmetric Buckling

Nonlinear elastic/plastic buckling analysis of thick/thin skew plates under uniaxial and biaxial loading

2014 ◽  
Vol 229 (16) ◽  
pp. 2854-2867 ◽  
Author(s):  
Mahdi Maarefdoust ◽  
Mehran Kadkhodayan
Keyword(s):  
Boundary Conditions ◽  
Buckling Analysis ◽  
Differential Quadrature ◽  
Thickness Ratio ◽  
Published Data ◽  
Plastic Behavior ◽  
Skew Angle ◽  
Plastic Buckling ◽  
Elastic Plastic ◽  
Generalized Differential

In this study, elastic/plastic buckling analysis of thick skew plates subjected to uniaxial compression or biaxial compression/tension loading using the generalized differential quadrature method is presented for the first time. The governing differential equations are derived based on the incremental and deformation theories of plasticity and first-order shear deformation theory. The elastic/plastic behavior of the plates is described by the Ramberg–Osgood model. Generalized differential quadrature discretization rules in association with an exact coordinate transformation are simultaneously used to transform and discretize the equilibrium equations and the related boundary conditions. The results are compared with the previously published data to verify the established methodology and procedures. The effect of skew angle and thickness ratio on the convergence and accuracy of the method are studied. Moreover, the effects of aspect, loading and thickness ratios, skew angle, incremental, and deformation theories and different types of boundary conditions on the buckling coefficients are presented in detail. The results show that the difference between the incremental and deformation theories becomes greater with increasing thickness ratio and constraints at boundary conditions. Furthermore, the skew angle also has an important effect on differences between those theories.

DQEM for Buckling Analysis of Nonprismatic Columns with and Without Elastic Foundation

2003 ◽  
Vol 03 (02) ◽  
pp. 183-194 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Elastic Foundation ◽  
Solution Procedure ◽  
Buckling Analysis ◽  
Numerical Results ◽  
Differential Quadrature ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Element Boundary

The differential quadrature element method is used to solve the buckling problems of nonprismatic column structures with and without elastic foundation. The extended differential quadrature is used to discretize the governing differential eigenvalue equations defined on all elements, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions. Numerical results obtained by DQEM are presented. They demonstrate the developed numerical solution procedure.

Sign in / Sign up

Export Citation Format

Share Document