Matteo Raffaelli: In this thesis we are concerned with developable surfaces, that is, surfaces that can be produced by bending without stretching or compressing a planar thin sheet of bendable material.
This is a classical family of surfaces, which has been extensively
studied in the past and
which
has an important number of modern applications within
architecture
(e.g.,
Frank Gehry
’s Walt Disney Concert Hall)
, cartography, and
manufacturing.
In particular, we present a novel method for approximating an arbit
rary (doubly
-
curved) surface S
by means of developable surfaces, each
one of which is
tangent
ial
to S along a prescribed curve. Some of the results obtained are then generalized
to
more abstract higher
-dimensional settings.
One can foresee many possible applications in the future, from solar cells
configurations to design of br
idges and buildings, manufacturing
of micro devices,
and perhaps even garnishing
of prepared food.
Main DTU supervisor: Steen Markvorsen from the Mathematics section. Co-supervisor: Jakob Bohr
Published as PhD report: The geometry of generalized flat ribbons.