Structural optimization

, Volume 2, Issue 4, pp 213–222 | Cite as

Design of beams, plates and their elastic foundations for uniform foundation pressure

  • K. Dems
  • R. H. Plaut


Beams and circular plates on elastic foundations are considered. In some cases, additional elastic supports are present. The stiffness distribution of the foundation is designed so that the pressure on the foundation is uniform. Sometimes the depth of the beam or plate is also varied, with either a piecewise-constant sandwich or solid cross-section, and a global measure of the deflection is minimized. The total stiffness of the foundation and supports is specified, as well as the volume of the structure. In one type of problem, the edges of the structure are displaced downwards; in the other examples, a downward load is applied. Types of loads include a concentrated central load, a uniform load and a parabolic load. The uniform foundation pressure for the resulting design is often substantially lower than the maximum pressure for a corresponding uniform beam or plate on an elastic foundation with uniform stiffness.


Civil Engineer Maximum Pressure Elastic Foundation Circular Plate Global Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Åkesson, B.; Olhoff, N. 1988: Minimum stiffness of optimally located supports for maximum value of beam eigenfrequencies.J. Sound Vib. 120, 457–463Google Scholar
  2. Dems, K.; Plaut, R.H.; Banach, A.S.; Johnson, L.W. 1987: Optimization of elastic foundation for minimum beam deflection.Int. J. Solids Struct. 23, 1551–1562Google Scholar
  3. Pičuga, A. 1988: Optimality conditions for multiple loaded structures — integrating control and finite element method. In: Rozvany, G.I.N.; Karihaloo, B.L. (eds.)Structural optimization. Dordrecht: KluwerGoogle Scholar
  4. Plaut, R.H. 1987: Optimal beam and plate foundations for minimum compliance.J. Appl. Mech. 54, 255–257Google Scholar
  5. Plaut, R.H. 1989: Simultaneous optimization of beams and their elastic foundations for minimum compliance.J. Appl. Mech. 56, 629–632Google Scholar
  6. Rozvany, G.I N. 1989:Structural design via optimality criteria: the Prager approach. Dordrecht: KluwerGoogle Scholar
  7. Shin, Y.S.; Haftka, R.T.; Plaut, R.H. 1988: Simultaneous analysis and design for eigenvalue maximization.AIAA J. 26, 738–744Google Scholar
  8. Shin, Y.S.; Haftka, R.T.; Watson, L.T.; Plaut, R.H. 1988: Tracing structural optima as a function of available resources by a homotopy method.Comp. Meth. Appl. Mech. Engrg. 70, 151–164Google Scholar
  9. Szelag, D.; Mróz, Z. 1978: Optimal design of elastic beams with unspecified support conditions.Zeit. ang. Math. Mech. 58, 501–510Google Scholar
  10. Taylor, J.E.; Bendsøe, M.P. 1984: An interpretation for minmax structural design problems including a method for relaxing constraints.Int. J. Solids Struct. 20, 301–314Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • K. Dems
    • 1
  • R. H. Plaut
    • 2
  1. 1.Lódź Technical UniversityLódźPoland
  2. 2.Charles E. Via, Jr. Dept. Civil EngineeringVirginia Polytechnic Institute and State UniversityBlacksburgUSA

Personalised recommendations