Optimal Beam and Plate Foundations for Minimum Compliance

[+] Author and Article Information
R. H. Plaut

Department of Civil Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061

J. Appl. Mech 54(2), 255-257 (Jun 01, 1987) (3 pages) doi:10.1115/1.3173003 History: Received August 05, 1986; Online July 21, 2009


Uniform beams and circular plates on nonuniform elastic foundations are considered. They are subjected to a uniformly distributed load and have various boundary conditions. For a specified total stiffness of the foundation, the distribution of foundation stiffness is determined which minimizes the compliance (i.e., the work done by the applied load). The optimal solutions for the beams consist of either a single elastic support or a region of uniform foundation bounded by elastic supports (except at free ends). For the plates, there is a central, circular region with a uniform foundation, bounded by a circular elastic support. In comparison to a uniform foundation, the decrease in compliance may be substantial.

Copyright © 1987 by ASME
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