| dc.description.abstracteng | This work is concerned with the study of
thin structures in Computational Mechanics. This field is
particularly interesting, since together with traditional finite
elements methods (FEM), the last years have seen the development of
a new approach, called discrete differential geometry (DDG). The
idea of FEM is to approximate smooth solutions using polynomials,
providing error estimates that establish convergence in the limit
of mesh refinement. The natural language of this field has been
found in the formalism of functional analysis. On the contrary, DDG
considers discrete entities, e.g., the mesh, as the only physical
system to be studied and discrete theories are being formulated
from first principles. In particular, DDG is concerned with the
preservation of smooth properties that break down in the discrete
setting with FEM. While the core of traditional FEM is based on
function interpolation, usually in Hilbert spaces, discrete
theories have an intrinsic physical interpretation, independently
from the smooth solutions they converge to. This approach is
related to flexible multibody dynamics and finite volumes. In this
work, we focus on the phenomenon of membrane locking, which
produces a severe artificial rigidity in discrete thin structures.
In the case of FEM, locking arises from a poor choice of finite
subspaces where to look for solutions, while in the DDG case, it
arises from arbitrary definitions of discrete geometric quantities.
In particular, we underline that a given mesh, or a given finite
subspace, are not the physical system of interest, but a
representation of it, out of infinitely many. In this work, we use
this observation and combine tools from FEM and DDG, in order to
build a novel discrete shell theory, free of membrane
locking. | de |