Geodesic
Optimal design of an elastic beam with a unilateral elastic foundation: semicoercive state problem
Applications of Mathematics, Tome 58 (2013) no. 3, pp. 329-346.

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A design optimization problem for an elastic beam with a unilateral elastic foundation is analyzed. Euler-Bernoulli's model for the beam and Winkler's model for the foundation are considered. The state problem is represented by a nonlinear semicoercive problem of 4th order with mixed boundary conditions. The thickness of the beam and the stiffness of the foundation are optimized with respect to a cost functional. We establish solvability conditions for the state problem and study the existence of a solution to the optimization problem.
DOI : 10.1007/s10492-013-0016-4
Classification : 49J15, 49K15, 65K10, 74B99, 74K10, 74P05
Keywords: shape optimization; semicoercive beam problem; unilateral foundation 
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     title = {Optimal design of an elastic beam with a unilateral elastic foundation: semicoercive state problem},
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Šimeček, Roman. Optimal design of an elastic beam with a unilateral elastic foundation: semicoercive state problem. Applications of Mathematics, Tome 58 (2013) no. 3, pp. 329-346. doi : 10.1007/s10492-013-0016-4. http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0016-4/

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