|
|
|
[Contents] | [Index] |
Collaborator: J. Sprekels, D. Tiba, R. Vodák
Cooperation with: V. Arnautu (``Alexandru Ioan Cuza'' University, Iasi, Romania)
Supported by: DFG-Forschungszentrum ``Mathematik für Schlüsseltechnologien'' (Research Center ``Mathematics for Key Technologies''), project C8
Description: The work for this research project continued in several directions. We have finished paper [1] concerning the optimization of structures like curved rods and shells. This gives a rather complete theoretical treatment of the subject, under low regularity assumptions for the geometry. Numerical experiments involving three-dimensional curved rods are also included. Notice that in [3] the case of planar arches was completely solved. Paper [5] introduces a new approach, based on control theory, for the general linear elasticity system and discusses some thickness optimization problems for plates. In [2] stable approximation methods are investigated in connection with the curved rod model proposed in [4]. It is well known that differential equations involving very small parameters (in this case the ``thickness'' of the rod, i.e. the area of the cross section) may be very difficult to handle via standard finite element methods. This difficulty is known under the name ``locking problem''. We propose a method that can improve the stability properties in computations related to curved rods.
Finally, paper [6] considers a new way to obtain a model for the deformation of elastic curved rods, of asymptotic type. The new estimates that we derive allow to study curved rods with piecewise C1 parametrization.
References:
|
|
|
[Contents] | [Index] |