The transverse flexure of thin elastic plates supported at several points

1957 ◽  
Vol 53 (3) ◽  
pp. 728-743 ◽  
Author(s):  
W. A. Bassali
Keyword(s):  
Exact Solutions ◽  
Circular Plate ◽  
Half Plane ◽  
Plane Elasticity ◽  
Infinite Plane ◽  
Elastic Plates ◽  
Thin Circular Plate ◽  
Boundary Points ◽  
Explicit Formulae ◽  
Thin Elastic Plates

ABSTRACTThis paper depends upon the method developed by Kolossoff and Muskhelishvili for problems of plane elasticity and later extended to plate problems by Lechnitzky. Exact solutions in closed forms are obtained for the problem of a thin circular plate supported at several interior or boundary points and normally loaded over the area of an eccentric circle, the load being symmetrical with respect to the centre of the circle and the boundary of the plate being free. Explicit formulae for the deflexion, the bending and twisting moments and shearing stresses are given at any point of the plate. As limiting cases plates in the form of the infinite plane and half plane are also considered.

The transverse flexure of thin perforated elastic plates supported at several points

1957 ◽  
Vol 53 (3) ◽  
pp. 744-754 ◽  
Author(s):  
W. A. Bassali
Keyword(s):  
Exact Solutions ◽  
Outer Edge ◽  
Elastic Plates ◽  
Large Plate ◽  
Circular Boundary ◽  
Boundary Points

ABSTRACTFollowing the method outlined in a previous paper, exact solutions in finite terms are obtained for the problem of an infinitely large plate with outer edge free and an inner free circular boundary, the plate being supported at any number of interior or boundary points and normally loaded over a circle. The load considered is symmetrical with respect to the centre of the circle.

Problems concerning the bending of isotropic thin elastic plates subject to various distributions of normal pressures

1958 ◽  
Vol 54 (2) ◽  
pp. 265-287 ◽  
Author(s):  
W. A. Bassali ◽  
H. P. F. Swinnerton-Dyer
Keyword(s):  
Circular Plate ◽  
Plate Theory ◽  
Normal System ◽  
Free Boundaries ◽  
Elastic Plates ◽  
Normal Loading ◽  
Complex Variable Methods ◽  
Concentrated Forces ◽  
Special Case ◽  
Thin Elastic Plates

ABSTRACTWithin the limitations of the small-deflexion plate theory, complex variable methods are used in this paper to obtain an exact solution for the problem of a thin circular plate supported at several interior or boundary points, and subjected to a certain normal loading spread over the area of an eccentric circle, the boundary of the plate being free. The load considered includes as a special case a linearly varying load over the circle and, as the radius of the loaded circle tends to zero, this load can be made to tend to a couple nucleus at its centre. As limiting cases the procedure adopted provides us with solutions appropriate to a circular plate, an infinitely large plate and a half-plane having free boundaries and acted upon by any normal system of concentrated forces and concentrated couples in equilibrium. Formulae for the moments, shears and deflexions relating to special examples are worked out in detail.

The analysis of singularly loaded and rigidly clamped thin elastic slabs with curvilinear boundaries. I

1959 ◽  
Vol 55 (1) ◽  
pp. 121-136 ◽  
Author(s):  
W. A. Bassali
Keyword(s):  
Exact Solutions ◽  
Complex Variable ◽  
Elastic Plates ◽  
Complex Variable Methods ◽  
Isotropic Plates ◽  
Special Cases ◽  
Concentrated Forces ◽  
Quartic Curves ◽  
Thin Elastic Plates

ABSTRACTIn this paper complex variable methods are used to derive exact solutions in closed forms for the small deflexions of certain thin elastic plates due to transverse concentrated forces or couples applied at arbitrary or specified points. The isotropic plates considered are bounded by curvilinear edges of certain types along which the plates are rigidly clamped. Plates bounded by quartic curves having the forms of the inverses of an ellipse with respect to its centre or its focus are included as special cases.

A thin circular plate normally and uniformly loaded over a concentric elliptic patch

1959 ◽  
Vol 55 (1) ◽  
pp. 101-109 ◽  
Author(s):  
W. A. Bassali ◽  
M. Nassif
Keyword(s):  
Circular Plate ◽  
Normal Pressure ◽  
Complex Potentials ◽  
Thin Plates ◽  
Transverse Displacement ◽  
Thin Circular Plate ◽  
Circular Boundary ◽  
Explicit Formulae ◽  
Elastically Restrained

ABSTRACTThis paper is concerned with the small transverse displacement of a thin circular plate elastically restrained along the circular boundary and subject to uniform normal pressure distributed over the area of an ellipse concentric with the plate. The method of complex potentials is used and the general assumptions relating to the small deflexion theory of thin plates are adopted. Explicit formulae for the bending and twisting moments and shearing forces are given at any point on the boundary and at the centre of the plate.

scholarly journals Self-dual singularity through lasing and antilasing in thin elastic plates

2021 ◽  
Vol 103 (13) ◽  
Author(s):  
M. Farhat ◽  
P.-Y. Chen ◽  
S. Guenneau ◽  
Y. Wu
Keyword(s):  
Elastic Plates ◽  
Thin Elastic Plates

scholarly journals Spacetime modulation in floating thin elastic plates

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
Mohamed Farhat ◽  
Sebastien Guenneau ◽  
Pai-Yen Chen ◽  
Ying Wu
Keyword(s):  
Elastic Plates ◽  
Thin Elastic Plates

Mixed Mode Interface Cracks in a Bi-Material Half Plane and a Bi-Material Strip

1999 ◽  
Author(s):  
Haiying Huang ◽  
George A. Kadomateas ◽  
Valeria La Saponara
Keyword(s):  
Stress Intensity ◽  
Free Boundary ◽  
Half Plane ◽  
Stress Intensity Factors ◽  
Mixed Mode ◽  
Infinite Strip ◽  
Infinite Plane ◽  
Intensity Factors ◽  
Interface Cracks ◽  
Mode Stress

Abstract This paper presents a method for determining the dislocation solution in a bi-material half plane and a bi-material infinite strip, which is subsequently used to obtain the mixed-mode stress intensity factors for a corresponding bi-material interface crack. First, the dislocation solution in a bi-material infinite plane is summarized. An array of surface dislocations is then distributed along the free boundary of the half plane and the infinite strip. The dislocation densities of the aforementioned surface dislocations are determined by satisfying the traction-free boundary conditions. After the dislocation solution in the finite domain is achieved, the mixed-mode stress intensity factors for interface cracks are calculated based on the continuous dislocation technique. Results are compared with analytical solution for homogeneous anisotropic media.

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