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
wellknown ``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. 305314.
 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.
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