Shear Buckling of Rectangular Plates with Mixed Boundary Conditions

1963 ◽  
Vol 14 (4) ◽  
pp. 349-356 ◽  
Author(s):  
I. T. Cook ◽  
K. C. Rockey
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
The Other ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Shear Buckling

SummaryThe paper presents a solution for the buckling under shear of a rectangular plate which is clamped along one edge and simply-supported along the other edges. The authors have also re-examined the case of one pair of opposite edges clamped and the other pair simply-supported.

Three-Dimensional Vibration Analysis of Rectangular Plates With Mixed Boundary Conditions

2005 ◽  
Vol 72 (2) ◽  
pp. 227-236 ◽  
Author(s):  
D. Zhou ◽  
Y. K. Cheung ◽  
S. H. Lo ◽  
F. T. K. Au
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Mixed Boundary ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Mixed Boundary Conditions ◽  
Boundary Function ◽  
Rectangular Plates ◽  
Characteristic Boundary ◽  
Fixed Boundaries

Three-dimensional vibration solutions are presented for rectangular plates with mixed boundary conditions, based on the small strain linear elasticity theory. The analysis is focused on two kinds of rectangular plates, the boundaries of which are partially fixed while the others are free. One of those studied is a rectangular plate with partially fixed boundaries symmetrically arranged around four corners and the other one is a rectangular plate with partially fixed boundaries around one corner only. A global analysis approach is developed. The Ritz method is applied to derive the governing eigenvalue equation by minimizing the energy functional of the plate. The admissible functions for all displacement components are taken as a product of a characteristic boundary function and the triplicate Chebyshev polynomial series defined in the plate domain. The characteristic boundary functions are composed of a product of four components of which each corresponds to one edge of the plate. The R-function method is applied to construct the characteristic boundary function components for the edges with mixed boundary conditions. The convergence and comparison studies demonstrate the accuracy and correctness of the present method. The influence of the length of the fixed boundaries and the plate thickness on frequency parameters of square plates has been studied in detail. Some valuable results are given in the form of tables and figures, which can serve as the benchmark for the further research.

Bending and Vibration of Plates of Variable Thickness

1976 ◽  
Vol 98 (1) ◽  
pp. 166-170 ◽  
Author(s):  
S. S. H. Chen
Keyword(s):  
Boundary Conditions ◽  
Variable Thickness ◽  
Natural Frequencies ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
The Other ◽  
Polar Coordinates ◽  
Rectangular Plates ◽  
Circular Plates ◽  
Plates Of Variable Thickness

The problem of bending and vibration of plates of variable thickness and arbitrary shapes and with mixed boundary conditions was solved by a modified energy method of the Rayleigh-Ritz type. General trial functions of deflection were obtained, one in Cartesian coordinates for rectangular plates and the other in polar coordinates for other shapes. The forced boundary conditions were satisfied approximately by introducing fixity factors which depended upon the prescribed conditions. Central deflections for circular plates subjected to static bending were within 0.2 percent of published results while they were within 1 percent for rectangular plates. The differences of natural frequencies of various rectangular plates were from 0.05 percent for simple, 2.9 percent for clamp, and up to 4.3 percent for free-free plates based on the published values.

Static Stability Behaviour of Plate Elements with Non-Uniform, in-Plane Stress Distribution

1979 ◽  
Vol 21 (5) ◽  
pp. 363-365
Author(s):  
P. K. Datta
Keyword(s):  
Stress Distribution ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Plane Stress ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Static Stability ◽  
Buckling Loads ◽  
Plate Elements ◽  
Edge Loading

The results of analytically and experimentally determined buckling loads of a rectangular plate, subjected to partial edge loading and mixed boundary conditions, are presented.

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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