Mat-1.600 Laskennallisen tieteen ja
tekniikan seminaari
29.3.2004 14.15
U322
Carlo Lovadina, Pavia
Finite element
approximation of Reissner-Mindlin plates:
Problems and a (possible) cure
In this talk we will consider the finite element
approximation
of Reissner-Mindlin plate bending problems. Most part
of the seminar will be devoted to explain why the finite
element discretization is not at all straightforward; in
particular, we will focus on the so-called "shear locking"
phenomenon and on the occurrence of "spurious" modes.
Afterwards, we will present a possible cure (among others
already proposed in the literature) to the above-mentioned
difficulties, by introducing a new finite element scheme
based on the use of non-conforming approximation spaces.
Lourenco Beirao
da Veiga, Pavia
Asymptotic
energy behavior of two classical benchmark shells
We are
interested in the behavior of the energy of linearly elastic
"intermediate" shells as the thickness of the structure tends to zero.
By "intermediate" we intend essentially those problems in which neither
the bending neither the membrane energy dominate the problem
asymptotically. In the firt part of the talk a brief survey both of the
classical mathematical asymptotic theory of shells and of some more
recent results will be given. The latter results will be then applied
to two classical "intermediate" engineering benchmark shell problems,
deriving in particular the asymptotic stiffness of the structure and
the proportion of bending energy at the limit. Finally, we compare the
results with those obtained with some finite element tests.