The general solution of the classical problem of the response of an infinite plate with an elastic foundation and damping

1971 ◽  
Vol 1 (1) ◽  
pp. 37-49 ◽  
Author(s):  
Wolfram Stadler
Keyword(s):  
General Solution ◽  
Elastic Foundation ◽  
Infinite Plate ◽  
Classical Problem

The Effect of Transverse Shear Deformation on the Bending of Elastic Plates

1945 ◽  
Vol 12 (2) ◽  
pp. A69-A77 ◽  
Author(s):  
Eric Reissner
Keyword(s):  
General Solution ◽  
Rectangular Plate ◽  
Transverse Shear ◽  
Plate Theory ◽  
Infinite Plate ◽  
Present Theory ◽  
System Of Equations ◽  
Elastic Plates ◽  
Classical Plate Theory

Abstract A system of equations is developed for the theory of bending of thin elastic plates which takes into account the transverse shear deformability of the plate. This system of equations is of such nature that three boundary conditions can and must be prescribed along the edge of the plate. The general solution of the system of equations is obtained in terms of two plane harmonic functions and one function which is the general solution of the equation Δψ − (10/h2)ψ = 0. The general results of the paper are applied (a) to the problem of torsion of a rectangular plate, (b) to the problems of plain bending and pure twisting of an infinite plate with a circular hole. In these two problems important differences are noted between the results of the present theory and the results obtained by means of the classical plate theory. It is indicated that the present theory may be applied to other problems where the deviations from the results of classical plate theory are of interest. Among these other problems is the determination of the reactions along the edges of a simply supported rectangular plate, where the classical theory leads to concentrated reactions at the corners of the plate. These concentrated reactions will not occur in the solution of the foregoing problem by means of the theory given in the present paper.

Bearing Capacity of a Coulomb Plate on Elastic Foundation

1975 ◽  
Vol 42 (1) ◽  
pp. 121-126 ◽  
Author(s):  
M. M. Mohaghegh ◽  
M. D. Coon
Keyword(s):  
Bearing Capacity ◽  
Elastic Foundation ◽  
Yield Criterion ◽  
Infinite Plate ◽  
Ice Sheets ◽  
Plate Material ◽  
Rigid Plastic ◽  
Plastic Bending ◽  
Coulomb Criterion ◽  
Plate On Elastic Foundation

The bearing capacity of an infinite plate resting on elastic foundation is determined assuming that the plate material is rigid-plastic satisfying the Coulomb yield criterion. The sandwich idealization of the plate is utilized and the Coulomb criterion is developed for this plate. The bearing capacity is determined using the method of limit analysis. The analysis shows that the plastic bending of the Coulomb plate is associated with the development of compressive forces which increase the limit moment and therefore the bearing capacity. An example of applying the analysis results is given by determining the bearing capacity of floating ice sheets.

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