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.

A Mixed Boundary-Value Problem of Elasticity With Parabolic Boundary

1957 ◽  
Vol 24 (1) ◽  
pp. 122-124
Author(s):  
Gunadhar Paria
Keyword(s):  
Stress Distribution ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Complex Variable ◽  
Hilbert Problem ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Mixed Boundary Value Problem ◽  
Parabolic Boundary

Abstract The problem of finding the stress distribution in a two-dimensional elastic body with parabolic boundary, subject to mixed boundary conditions, has been reduced to the solution of the nonhomogeneous Hilbert problem following the method of complex variable. The result has been compared with that for a straight boundary.

Series Solution and Stress Analysis of Rectangular Plate With Mixed Boundary Conditions

2005 ◽  
Author(s):  
Jiemin Liu ◽  
Jintang Liu ◽  
Toshiyuki Sawa
Keyword(s):  
Stress Concentration ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Size Factor ◽  
Singular Stress ◽  
Feature Size ◽  
Concentrated Force ◽  
Displacement Boundary

Stress functions expressed from Fourier series, suitable for arbitrary stress boundary conditions, were derived using method of variable separation. General displacement expressions containing the displacement of rigid body were also derived. A method of solving mixed boundary problems (in which external forces acting at a part of the whole boundaries are known and displacements at the rest boundaries are known) was presented. As an example, a rectangular plate, one side of which was fixed and objective side was subjected to a concentrated force, was analyzed. In addition, characteristics of stress distributions in the regions of stress concentration were questioned. It was found from the presented results of calculation that describing stress concentration with the singular stress at a point was unworkable. Describing stress concentration with the average stress in the feature size instead of the singular stress at a point was operative and reflected objectively practical stress and displacement boundary conditions. The concept of feature-size-factor was introduced.

Relaxation Methods Applied to Two Problems of Two-Dimensional Stress Distribution Involving Mixed Boundary Conditions

1948 ◽  
Vol 1 (2) ◽  
pp. 135
Author(s):  
WH Wittrick ◽  
W Howard
Keyword(s):  
Stress Distribution ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Stress Distributions ◽  
Relaxation Methods

Relaxation methods have been used to determine the stress distributions in both a rectangular and a highly tapered plate under tension when the load is applied through absolutely rigid clamps. Both problems require the treatment of boundary conditions involving the values of both stresses and displacements. The solutions were obtained in terms of displacements and the stresses were subsequently determined from them.

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.

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.

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