scholarly journals Discussion: “Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates in Extension” (Williams, M. L., 1952, ASME J. Appl. Mech., 19, pp. 526–528)

1953 ◽  
Vol 20 (4) ◽  
pp. 590
Author(s):  
M. L. Williams
Keyword(s):  
Boundary Conditions ◽  
Stress Singularities ◽  
Various Boundary Conditions

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.

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

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]

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

Upon Impact Numerical Modeling of Foam Materials

2017 ◽  
Vol 54 (2) ◽  
pp. 195-202
Author(s):  
Vasile Nastasescu ◽  
Silvia Marzavan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Modeling ◽  
Numerical Analysis ◽  
Numerical Methods ◽  
Boundary Conditions ◽  
General Character ◽  
Foam Material ◽  
Various Boundary Conditions ◽  
Specific Behaviour

The paper presents some theoretical and practical issues, particularly useful to users of numerical methods, especially finite element method for the behaviour modelling of the foam materials. Given the characteristics of specific behaviour of the foam materials, the requirement which has to be taken into consideration is the compression, inclusive impact with bodies more rigid then a foam material, when this is used alone or in combination with other materials in the form of composite laminated with various boundary conditions. The results and conclusions presented in this paper are the results of our investigations in the field and relates to the use of LS-Dyna program, but many observations, findings and conclusions, have a general character, valid for use of any numerical analysis by FEM programs.

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