Logarithmic Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates Under Bending

1999 ◽  
Vol 67 (1) ◽  
pp. 219-223 ◽  
Author(s):  
G. B. Sinclair
Keyword(s):  
Boundary Conditions ◽  
Classical Theory ◽  
Great Majority ◽  
Elastic Plates ◽  
Stress Singularities ◽  
Various Boundary Conditions ◽  
Logarithmic Singularities

This note considers the occurrence of pure logarithmic singularities in angular elastic plates under bending within the context of classical theory. By paralleling the development of requirements for logarithmic singularities for plates in extension, requirements for log singularities in bending are developed, both for homogeneous boundary conditions on plate edges and for inhomogeneous. Using these singularity requirements, some 50-odd configurations with log singularities are identified, the great majority being for inhomogeneous boundary conditions. [S0021-8936(00)00501-8]

The Quasi-Static Analysis for Two-Dimensional Thin Plates

2011 ◽  
Vol 255-260 ◽  
pp. 166-169
Author(s):  
Li Chen ◽  
Yang Bai
Keyword(s):  
Boundary Conditions ◽  
Eigenfunction Expansion ◽  
Solution Space ◽  
Expansion Method ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Elastic Plates ◽  
Various Boundary Conditions ◽  
Eigenfunction Expansion Method ◽  
Concentration Phenomena

The eigenfunction expansion method is introduced into the numerical calculations of elastic plates. Based on the variational method, all the fundamental solutions of the governing equations are obtained directly. Using eigenfunction expansion method, various boundary conditions can be conveniently described by the combination of the eigenfunctions due to the completeness of the solution space. The coefficients of the combination are determined by the boundary conditions. In the numerical example, the stress concentration phenomena produced by the restriction of displacement conditions is discussed in detail.

scholarly journals Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates in Extension

1952 ◽  
Vol 19 (4) ◽  
pp. 526-528
Author(s):  
M. L. Williams
Keyword(s):  
Boundary Conditions ◽  
Poisson’S Ratio ◽  
Mixed Boundary Condition ◽  
Mixed Boundary ◽  
Poisson's Ratio ◽  
Vertex Angle ◽  
Stress Singularities ◽  
Stress Concentrations ◽  
Various Boundary Conditions ◽  
Free Case

Abstract As an analog to the bending case published in an earlier paper, the stress singularities in plates subjected to extension in their plane are discussed. Three sets of boundary conditions on the radial edges are investigated: free-free, clamped-clamped, and clamped-free. Providing the vertex angle is less than 180 degrees, it is found that unbounded stresses occur at the vertex only in the case of the mixed boundary condition with the strength of the singularity being somewhat stronger than for the similar bending case. For vertex angles between 180 and 360 degrees, all the cases considered may have stress singularities. In amplification of some work of Southwell, it is shown that there are certain analogies between the characteristic equations governing the stresses in extension and bending, respectively, if ν, Poisson’s ratio, is replaced by −ν. Finally, the free-free extensional plate behaves locally at the origin exactly the same as a clamped-clamped plate in bending, independent of Poisson’s ratio. In conclusion, it is noted that the free-free case analysis may be applied to stress concentrations in V-shaped notches.

Flutter of Rectangular Plates in Three Dimensional Incompressible Flow With Various Boundary Conditions: Theory and Experiment

2012 ◽  
Author(s):  
Ivan Wang ◽  
Samuel C. Gibbs ◽  
Earl H. Dowell
Keyword(s):  
Boundary Conditions ◽  
Structural Model ◽  
Three Dimensional ◽  
Flexible Plate ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Test Bed ◽  
Trailing Edge ◽  
Various Boundary Conditions ◽  
Trailing Edge Flap

The aeroelastic stability of rectangular plates are well-documented in literature for certain sets of boundary conditions. Specifically, wing flutter, panel flutter, and divergence of a plate that is clamped on all sides are well-understood. However, the ongoing push for lighter structures and novel designs have led to a need to understand the aeroelastic behavior of elastic plates for other boundary conditions. One example is NASA’s continuous mold-line link project for reducing the noise generated by commercial transport aircraft during landing; in order to reduce the noise generated by vortex shedding from the trailing edge flap during landing, the project proposes to connect the gap between the trailing edge flap and the rest of the wing with a flexible plate. This paper summarizes the aeroelastic theory, numerical results, and experimental results of a study on the flutter and/or divergence mechanisms of a rectangular plate for different sets of structural boundary conditions. The theory combines a three-dimensional vortex lattice aerodynamic model with a plate structural model to create a high-fidelity frequency domain aeroelastic model. A modular experimental test bed is designed for this study in order to test the different boundary conditions. The test bed is also designed to test different plate thicknesses and sizes with only a small number of modifications. The well-understood boundary conditions are used as test cases to validate the analysis results, and then results of additional configurations that have not been extensively explored are presented. The results of this paper can be used to support the design efforts of projects involving plates or plate-membranes. In addition, the paper adds to the fundamental understanding of plate aeroelasticity and provides a wealth of experimental data for comparison and future validation.

Stress singularities in a biwedge under various boundary conditions

1978 ◽  
Vol 29 (1-4) ◽  
pp. 55-73 ◽  
Author(s):  
P. S. Theocaris ◽  
E. E. Gdoutos ◽  
C. G. Thireos
Keyword(s):  
Boundary Conditions ◽  
Stress Singularities ◽  
Various Boundary Conditions

On stress singularities in an anisotropic wedge for various boundary conditions

2001 ◽  
Vol 54 (1) ◽  
pp. 87-102 ◽  
Author(s):  
Ching-Hwei Chue ◽  
Chien-Hua Tseng ◽  
Chuan-I Liu
Keyword(s):  
Boundary Conditions ◽  
Stress Singularities ◽  
Various Boundary Conditions
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