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.

Rigid-plastic analysis of floating ice sheets under impact loads

1981 ◽  
Vol 8 (4) ◽  
pp. 409-415
Author(s):  
John B. Kennedy ◽  
K. J. Iyengar
Keyword(s):  
Impact Load ◽  
Design Method ◽  
Yield Criterion ◽  
Ice Sheets ◽  
Contact Radius ◽  
Impact Loads ◽  
Rigid Plastic ◽  
Deformation Response ◽  
Safe Thickness ◽  
The Impact

The deformation response of floating ice sheets under high intensity, short duration loads is examined. Using a rigid-plastic theory, together with a Tresca yield criterion, expressions are derived for the total time of response and the final deformed configuration of floating ice sheets. The influence of the magnitude of the impact load and the load-contact radius on the various design quantities such as deflection profile and stress distribution is discussed. Based on the results derived, a design method is presented to find the safe thickness of a floating ice sheet to sustain a given impact load. The method is illustrated with a numerical example.

DEFLECTIONS OF AN INFINITE PLATE

1950 ◽  
Vol 28a (3) ◽  
pp. 293-302 ◽  
Author(s):  
Max Wyman
Keyword(s):  
Elastic Foundation ◽  
Maximum Stress ◽  
Infinite Plate ◽  
Ice Sheets ◽  
Uniform Load ◽  
Circular Area ◽  
Concentrated Load ◽  
Loaded Plate ◽  
Simplifying Assumptions ◽  
Domain Of Validity

Problems associated with the thickness of ice sheets on Canadian lakes led the author to investigate mathematically the deflection of a loaded plate resting upon an elastic foundation. Certain simplifying assumptions, which appear to be not unreasonable, permit the solutions obtained to be applied to the strength of a floating ice sheet. Relations for maximum stress and maximum deflections in terms of known functions are derived, both for a concentrated load and a uniform load distributed over a circular area. The resulting expressions should be tested experimentally to determine their domain of validity. Owing to similarity of conditions, these results may also be applied to the design of concrete roadways and airport runways.

scholarly journals Finite Pure Plane Strain Bending of Inhomogeneous Anisotropic Sheets

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 145
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Yeong-Maw Hwang
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Large Strains ◽  
Rigid Plastic ◽  
Plastic Properties ◽  
Elastic Plastic ◽  
Starting Point ◽  
The Difference ◽  
Inside Radius ◽  
Elastic Unloading

The present paper concerns the general solution for finite plane strain pure bending of incompressible, orthotropic sheets. In contrast to available solutions, the new solution is valid for inhomogeneous distributions of plastic properties. The solution is semi-analytic. A numerical treatment is only necessary for solving transcendent equations and evaluating ordinary integrals. The solution’s starting point is a transformation between Eulerian and Lagrangian coordinates that is valid for a wide class of constitutive equations. The symmetric distribution relative to the center line of the sheet is separately treated where it is advantageous. It is shown that this type of symmetry simplifies the solution. Hill’s quadratic yield criterion is adopted. Both elastic/plastic and rigid/plastic solutions are derived. Elastic unloading is also considered, and it is shown that reverse plastic yielding occurs at a relatively large inside radius. An illustrative example uses real experimental data. The distribution of plastic properties is symmetric in this example. It is shown that the difference between the elastic/plastic and rigid/plastic solutions is negligible, except at the very beginning of the process. However, the rigid/plastic solution is much simpler and, therefore, can be recommended for practical use at large strains, including calculating the residual stresses.

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