Article
MSC:
49A29,
73E99,
73K05,
74C05,
74K10,
74P10 | MR 1620616 | Zbl 1042.74533 | DOI: 10.1023/A:1023228608356
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
elasto-plastic beams; Hencky’s model of plasticity; Mindlin-Timoshenko beam; uncertain data
elasto-plastic beams; Hencky’s model of plasticity; Mindlin-Timoshenko beam; uncertain data
Summary:
We apply the method of reliable solutions to the bending problem for an elasto-plastic beam, considering the yield function of the von Mises type with uncertain coefficients. The compatibility method is used to find the moments and shear forces. Then we solve a maximization problem for these quantities with respect to the uncertain input data.
References:
[1] Ekeland, I., Temam, R.: Convex Analysis and Variational Problems. North-Holland, Amsterdam, 1976. MR 0463994
[2] Hlaváček, I.: Reliable solutions of elliptic boundary problems with respect to uncertain data. Proceedings of the WCNA-96. Nonlinear Analysis, Theory, Methods & Applications 30 (1997), 3879–3890. MR 1602891
[3] Hlaváček, I.: Reliable solution of a quasilinear nonpotential elliptic problem of a nonmonotone type with respect to the uncertainty in coefficients. J. Math. Appl. 212 (1997), 452–466. MR 1464890
[4] Hlaváček, I.: Reliable solutions of problems in the deformation theory of plasticity with respect to uncertain material function. Appl. Math. 41 (1996), 447–466. MR 1415251
[5] Hlaváček, I.: Reliable solution of an elasto-plastic torsion problem. (to appear). MR 1857675
[6] Hlaváček, I.: Reliable solution of a Signorini contact problem with friction, considering uncertain data. (to appear). MR 1731015
[7] Hlaváček, I., Lovíšek, J.: Optimal design of an elastic or elasto-plastic beam with unilateral elastic foundation and rigid supports. Z. Angew. Math. Mech. 72 (1992), 29–43. DOI 10.1002/zamm.19920720104 | MR 1148885
[8] Nečas, J., Hlaváček, I.: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction. Elsevier, Amsterdam, 1981. MR 0600655
[9] Lagnese, J. E., Lions, J.-L.: Modelling Analysis and Control of Thin Plates. Masson, Paris and Springer-Verlag, Berlin, 1989. MR 0953313
[10] Neal, B. G.: Structural Theorems and Their Applications. Pergamon Press, Oxford, 1964. Zbl 0142.23603
[11] Rakowski, J.: The interpretation of the shear locking in beam elements. Comput. & Structures 37 (1990), 769-776. DOI 10.1016/0045-7949(90)90106-C
Search
Partner of
