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Optimal Design of an Elastic Plate with Unilateral Elastic Foundation and Rigid Supports, Using the Reissner‐Mindlin Plate Model. I: Continuous Problems
Author(s) -
Hlaváček I.,
Lovíšek J.
Publication year - 1997
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19970770513
Subject(s) - foundation (evidence) , stiffness , mathematics , structural engineering , monotone polygon , variational inequality , mathematical analysis , bending of plates , plate theory , bending , engineering , geometry , boundary value problem , archaeology , history
Abstract Several optimal design problems with a variational inequality with a monotone operator as common state problem are considered. The inequality represents the bending of a Reissner‐Mindlin plate, resting on a unilateral elastic foundation and on some unilateral rigid piers. Both the thickness of the plate and the stiffness of the foundation play the role of design variables. The cost functionals include the intensity of shear stresses, and reactive forces on the piers or the weight of the plate. The solvability of all the problems is proved.