Article
MSC:
49J15,
49K15,
65K10,
74B99,
74K10,
74P05 | MR 3066824 | Zbl 06221234 | DOI: 10.1007/s10492-013-0016-4
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
shape optimization; semicoercive beam problem; unilateral foundation
shape optimization; semicoercive beam problem; unilateral foundation
Summary:
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.
References:
[1] Aubin, J. P.: Applied Functional Analysis, 2nd edition. Wiley-Interscience New York (2000). MR 1782330
[2] Chleboun, J.: Optimal design of an elastic beam on an elastic basis. Apl. Mat. 31 (1986), 118-140. MR 0837473 | Zbl 0606.73108
[3] Fučík, S., Kufner, A.: Nonlinear Differential Equations. Studies in Applied Mechanics, Vol. 2. Elsevier New York (1980). MR 0558764
[4] Haslinger, J., Mäkinen, R. A. E.: Introduction to Shape Optimization: Theory, Approximation and Computation. SIAM Philadelphia (2003). MR 1969772 | Zbl 1020.74001
[5] Haslinger, J., Neittaanmäki, P.: Finite Element Approximation for Optimal Shape, Material and Topology Design. J. Wiley & Sons Chichester (1996). MR 1419500
[6] Hlaváček, I., Bock, I., Lovíšek, J.: Optimal control of a variational inequality with applications to structural analysis. I: Optimal design of a beam with unilateral supports. Appl. Math. Optim. 11 (1984), 111-143. DOI 10.1007/BF01442173 | MR 0743922 | Zbl 0553.73082
[7] Horák, J. V., Netuka, I.: Mathematical model of pseudointeractive set: 1D body on nonlinear subsoil. I. Theoretical aspects. Engineering Mechanics 14 (2007), 3311-3325.
[8] Horák, J. V., Šimeček, R.: ANSYS implementation of shape design optimization problems. ANSYS conference 2008, 16. ANSYS FEM Users' Meeting, Luhačovice, 5.--7. November 2008 SVS-FEM Brno (2008), released on CD.
[9] Kufner, A., John, O., Fučík, S.: Function Spaces. Noordhoof International Publishing/Academia Praha Nordhoof/Prague (1977). MR 0482102
[10] Nečas, J., Hlaváček, I.: Mathematical Theory of Elastic and Elasto-Plastic Bodies. An Introduction. Elsevier Amsterdam (1980). MR 0600655
[11] Netuka, H., Horák, J. V.: System beam-spring-foundation after two years. Proceedings, Conference ``Olomouc Days of Applied Mathematics ODAM 2007'' (2007), 18-42 Czech.
[12] Salač, P.: Shape optimization of elastic axisymmetric plate on an elastic foundation. Appl. Math. 40 (1995), 319-338. MR 1331921 | Zbl 0839.73036
[13] Sysala, S.: Unilateral subsoil of Winkler's type: Semi-coercive beam problem. Appl. Math. 53 (2008), 347-379. DOI 10.1007/s10492-008-0030-0 | MR 2433726
Search
Partner of
