Post-Buckling of Rectangular Plates with Various Boundary Conditions

1970 ◽  
Vol 21 (2) ◽  
pp. 163-181 ◽  
Author(s):  
K. R. Rushton
Keyword(s):  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Relaxation Method ◽  
Rectangular Plates ◽  
Dynamic Relaxation ◽  
Various Boundary Conditions ◽  
Post Buckling ◽  
Dynamic Relaxation Method ◽  
Theoretical Results

SummaryThe Dynamic Relaxation method is used to analyse the post-buckling of flat rectangular plates. Extensive results are obtained for two types of problem in which the transverse edges are unloaded; in one case the transverse edges remain straight, in the other they are free to wave. Comparisons are made with alternative experimental and theoretical results. The potentiality of this approach to post-buckling problems is demonstrated by considering a variable thickness plate with mixed boundary conditions.

Large deflection of plates with unsupported edges

1972 ◽  
Vol 7 (1) ◽  
pp. 44-53 ◽  
Author(s):  
K R Rushton
Keyword(s):  
Large Deflection ◽  
Relaxation Method ◽  
Lateral Loading ◽  
Edge Condition ◽  
Rectangular Plates ◽  
Dynamic Relaxation ◽  
Finite Difference Technique ◽  
Small Deflection ◽  
Post Buckling ◽  
Dynamic Relaxation Method

A method of including the unsupported edge condition in the large deflection of rectangular plates is proposed. Solutions are obtained which use a finite-difference technique based on the dynamic-relaxation method. Comparisons are made with certain theoretical small-deflection solutions. Two particular problems are considered in detail, the lateral loading of plates supported at the corners and the post-buckling of a plate with one unsupported edge.

Vibration of Orthotropic Rectangular Plates With Variable Thickness

1989 ◽  
Vol 111 (1) ◽  
pp. 101-103 ◽  
Author(s):  
Wei-Cheun Liu ◽  
Stanley S. H. Chen
Keyword(s):  
Boundary Conditions ◽  
Computer Program ◽  
Variable Thickness ◽  
Energy Method ◽  
Natural Frequencies ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Orthotropic Properties

The problem vibration of rectangular orthotropic plates with variable thickness and mixed boundary conditions are solved by a modified energy method. A general expression is written for the deflection of the plate without aiming at any particular combination of boundary conditions. Boundary conditions are satisfied approximately by adjusting a set of so-called fixity factors. A computer program has been developed to solve for natural frequencies of plates with variable thicknesses and having different orthotropic properties.

Hencky Bar-Net Model for Vibration of Rectangular Plates with Mixed Boundary Conditions and Point Supports

2018 ◽  
Vol 18 (03) ◽  
pp. 1850046 ◽  
Author(s):  
H. Zhang ◽  
Y. P. Zhang ◽  
C. M. Wang
Keyword(s):  
Boundary Conditions ◽  
Total Mass ◽  
Mixed Boundary ◽  
Grid Cell ◽  
Mixed Boundary Conditions ◽  
Rectangular Plates ◽  
Lumped Mass ◽  
Spring System ◽  
Vibration Problems ◽  
Continuous Boundary

This paper is concerned with the development of the Hencky bar-net model (HBM) for free vibration analyses of rectangular plates with mixed boundary conditions and point supports. The HBM is a two-dimensional discrete net system composed of rigid segments connected by frictionless hinges and rotational springs. In the model, bending is accommodated by rotational springs at each joint while the twisting by a diagonal spring system in each grid cell. The total mass of the plate is distributed as lumped mass at each joint and the continuous boundary stiffness of plate is simulated by springs located at the edge joints. Owing to the discrete property of HBM, it is able to readily handle any boundary conditions of plates including mixed boundary conditions and point supports. The HBM is herein used to solve some vibration problems of rectangular plates with mixed boundary conditions and point supports to demonstrate its accuracy and convenience for plate analyses.

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