This paper concerns the plastic collapse of an elastic/perfectly plastic medium with randomly variable yield strength under a fixed load. The yield strength is represented by a Gaussian random field of known statistical properties. Using the theorems of limit analysis and the methods of reliability theory, algorithms are developed for the computation of upper and lower bounds on the probability of plastic collapse. By varying the magnitude of the fixed load, bounds on the probability distribution function for the collapse load can be computed. Results are given for uniform pressure applied to a rectangular region of the surface of an elastic/plastic half-space. For the corresponding plane problem, results for the classical Hill and Prandtl failure mechanisms are compared. Three-dimensional results are found to differ significantly from those of the plane problem. Comparison is made with results of a previous approximate method for three-dimensional problems.
On Plastic Collapse of Media With Random Yield Strength
Contributed by the Applied Mechanics Division of The American Society of Mechanical Engineers for publication in the JOURNAL OF APPLIED MECHANICSASME . Manuscript received by the ASME Applied Mechanics Division, June 14, 2000; final revision, Feb. 6, 2001. Associate Editor: M.-J. Pindera. Discussion of the paper should be addressed to the Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Ku, A. P., and Nordgren, R. P. (February 6, 2001). "On Plastic Collapse of Media With Random Yield Strength ." ASME. J. Appl. Mech. September 2001; 68(5): 715–724. https://doi.org/10.1115/1.1388011
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