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TECHNICAL PAPERS

A Useful Solution for Estimating Contact Pressure Between a Plate and Foundation

[+] Author and Article Information
L. B. Shulkin, D. A. Mendelsohn, G. L. Kinzel, T. Altan

Ohio State University, Columbus, OH 43210-1181

J. Manuf. Sci. Eng 122(4), 781-789 (Oct 01, 1999) (9 pages) doi:10.1115/1.1286167 History: Received January 01, 1997; Revised October 01, 1999
Copyright © 2000 by ASME
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References

Poulos, H. G., and Davis, E. H., 1974, Elastic Solutions for Soil and Rock Mechanics, Wiley, New York, NY.
Li,  H., and Dempsey,  J. P., 1990, “Axisymmetric Contact of an Elastic Layer Underlain by Rigid Base,” Int. J. Numer. Methods Eng., 29, pp. 57–72.
Dempsey,  J. P., Zhao,  Z. G., and Li,  H., 1991, “Axisymmetric Indentation of an Elastic Layer Supported by a Winkler Foundation,” Int. J. Solids Struct., 27, No. 1, pp. 73–87.
Hetenyi, M., 1946, Beams on Elastic Foundation; Theory with Applications in the Fields of Civil and Mechanical Engineering, University of Michigan Press, Ann Arbor, MI.
Westergaard,  H. M., 1926, “Stress in Concrete Pavements Computed by Theoretical Analysis,” Public Roads, 7, pp. 25–35.
Terzaghi,  K., 1955, “Evaluation of Coefficient of Subgrade Reaction,” Geotechnique, 5, pp. 297–326.
Iyengar, K. T. S. R., and Ramu, S. A., 1979, Design Tables for Beams on Elastic Foundations and Related Problems, Elsevier Applied Science, London, England.
Sneddon, I. N., 1972, The Use of Integral Transforms, McGraw-Hill, New York, NY.
Vlasov, V. Z., and Leont’ev, N. N., 1966, Beams, Plates, and Shells on Elastic Foundations, Translated from Russian. NASA TT F-357, Washington, DC.
Timoshenko, S., and Goodier, J. N., 1951, Theory of Elasticity, 2nd ed., McGraw-Hill, New York, NY.
Vesic, A. B., 1961, “Beams on Elastic Subgrade and the Winkler’s Hypothesis,” Proceedings, 5th International Conference on Soil Mechanics and Foundation Engineering, Paris, France, pp. 845–850.
Abramowitz, M., and Stegun, I. A., 1964, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, 5th printing, U.S. Government Printing Office.
Fullerton, W., 1977, Function BESJ0(X), Developed in Los Alamos National Labs, NIST Guide to Available Math Software, retrieved from the internet cite: http://www.public.iastate.edu/∼math/cmlib/fnlib/besj0.

Figures

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Comparison of FEM and analytical pressure curves: between the layer and the foundation a) h=0.0127 m,b) h=0.0254 m,c) h=0.0508 m, and d) between the cylinder and the layer, h=0.0127 m
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Parametric study: force on the cylinder P
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Parametric study: layer material properties
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Parametric study: radius of the cylinder c
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Axisymmetric load on an infinite layer supported by a Winkler foundation. Origin of the (r,z) coordinate system is at the center of the loading circle of radius c.
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Possible contact pressure distributions on the boundary of an elastic half-space: a) uniform pressure, b) uniform displacement [see Eqs. (9) and (11) for expressions for p(r)]
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Evaluation of the integral function σzz(r,z): integration strategy
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Validation of analytical solution: test loading case of a) elastic half-space and b) infinite elastic layer supported by a Winkler foundation
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Validation of analytical solution: σzz stress comparison
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Axisymmetric FEM model to study the contact pressure distribution
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Parametric study: foundation stiffness k
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Parametric study: thickness of the layer h
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Parametric study: comparison of pressure between the cylinder and the layer p(r) for the uniform pressure and rigid indenter cases

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