Approximation and optimization of curved mechanical structures
Collaborator: J. Sprekels,
D. Tiba, R. Vodák
Cooperation with: V. Arnautu (``Alexandru Ioan Cuza'' University,
Iasi, Romania)
Supported by: DFG Research Center MATHEON, project C8
Description:
The work for this research project has been continued in several
directions. The paper [1] concerning the
optimization of rods
and shells has been accepted after revision. In [2], a new
reduction approximation
technique has been developed to overcome the
well-known ``locking phenomenon'' in the numerical approximation of
thin curved rods. In this context, we also refer to [4].
A new type of asymptotic analysis for
merely Lipschitzian curved rods
has been developed in the papers [5], [6],
[7].
A considerable part of the results established in this field by
J. Sprekels and D. Tiba within the past years will be contained in the
monograph [3].
References:
- V. ARNAUTU, J. SPREKELS, D. TIBA, Optimization problems
for curved mechanical structures,
WIAS Preprint no. 812, 2003,
to appear in: SIAM J. Control Optim.
-
, A reduction approximation method for
curved rods, WIAS Preprint no. 958, 2004,
to appear in: Numer. Funct. Anal. Optim.
- P. NEITTAANMÄKI, J. SPREKELS, D. TIBA,
Optimization of Elliptic Systems. Theory and Applications,
Springer, to appear 2005.
- J. SPREKELS, D. TIBA, An
approximation method for curved rods, in: Nonlinear Partial
Differential Equations and their Applications, N. Kenmochi, M. Otani,
S. Zheng, eds., vol. 20 of Gakuto Intern. Series Math. Sci.,
Gakkotosho, Tokyo, 2004, pp. 305-314.
- D. TIBA, R. VODÁK, A general
asymptotic model for Lipschitzian curved rods,
WIAS Preprint no. 942, 2004,
to appear in: Adv. Math. Sci. Appl.
- R. VODÁK, A general asymptotic dynamic
model for Lipschitzian curved rods, WIAS Preprint
no. 956, 2004,
submitted.
-
, Asymptotic analysis of
elastic curved rods, WIAS Preprint
no. 986, 2004.
LaTeX typesetting by H. Pletat
2005-07-29