Folded plate structures : Geometry, mechanics, design

Della Puppa, Giovanni; Trautz, Martin (Thesis advisor); Klinkel, Sven (Thesis advisor)

Aachen (2019, 2020)
Dissertation / PhD Thesis

Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, 2019


This thesis proposes a new investigation paradigm for folded plate structures, focusing on three fundamental aspects, namely Geometry, Mechanics and Design. The tight link among them makes possible to define a unitary handling, with a strong finalization towards practical design tasks. Motivated by previous work of the author as well as by an introductory historical review, the research presented here relies on the use of analytical methods. This approach is intended to disclose a different and more holistic view on folded plate structures, integrating the use of the Finite Element Method. The great variety of forms a faceted geometry can assume is reduced to a common mathematical framework based on 2-dimensional Fourier series. Their combination with Bravais Lattice permits to represent any kind of fold pattern, offering at the same time a great flexibility in geometry transformation and derivation of differential geometry in analytical and continuous terms. On top of this original geometric approach a consistent mechanic framework is built. The latter takes advantage from Kirchoff-Love shell theory and Koiter’s constitution. For this scope a new symbolism and new stress resultants are introduced specifically for folded plate structures. The differential geometry of folded surface is applied in the analytical definition of arbitrary kinematic states, assumed as current configuration. This allows for a direct derivation of the stress field arising from stretching, bending and shearing. The definition of folded modules via geometric parameters permits the identification of mechanically motivated proportioning rules. These are obtained applying homogenization of folded patterns to an equivalent continuum, with subsequent minimization of mechanical quantities. The optimal set of parameters found in this way is valid for any structural scale and any application field. The orientation of the fold module along the principal stress direction is carried out for the case of simply supported plate structures through a semi-analytical procedure. The latter relies on the geometry transformation directly imposed on the Fourier series. The outcome of this thesis is expected to influence both academic and industrial research on folded plate structures, because of the generality and the wide-range applicability of the methods presented here.