Optimal design of an elastic beam with a unilateral elastic foundation: Semicoercive state problem |
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Authors: | Roman Šimeček |
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Institution: | 1. Faculty of Science, Dept. of Mathematical Analysis and Applications of Mathematics, Palacky University, T?. 17. listopadu 12, 771 46, Olomouc, Czech Republic
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Abstract: | 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. |
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