Prestressed cable-nets and tensile membrane structures are used in civil engineering primarily as roofing systems to cover large column-free spaces. With respect to traditional structures, they can be more cost effective and environmentally sustainable; besides, they can be aesthetically pleasing. For these and other reasons they have become increasingly popular over the last decades. Tensile structures must be prestressed to efficiently withstand external loads; the search for a suitable initial equilibrium shape under given pretensions and given boundary support conditions is called "form-finding". Over time, different ad hoc computational methods have been developed to tackle the form-finding problem, giving rise to a wealth of scientific papers on the topic. The concept of form-finding can also be applied to shell and gridshell structures, often in combination with some kind of structural optimization. In this context, the goal is to determine a form which can carry the primary loads (for instance the self-weight) in a particularly efficient way, for example by minimizing the bending effects. In this thesis, form-finding methods for discrete networks of tension/compression elements and for tensile membrane structures are investigated. The "force density method" is considered in detail, both in its linear version and in its nonlinear variants, which allow different types of constraints to be enforced. The force density approach is implemented in various MATLAB scripts and compared to the "dynamic relaxation method"; numerical examples of form found networks are reported. With reference to structures in compression, the case of a column fabricated using Wire-and-Arch Additive Manufacturing is first considered. Successively some examples of gridshells are presented, in which an optimization problem is formulated considering networks with fixed horizontal projection subjected to vertical nodal loads. Finally, the "surface stress density method" is described as a method which represents an extension of the force density method to the form-finding of isotropically prestressed tensile membrane structures.
Le reti di funi e le tensostrutture a membrana sono principalmente utilizzate nell’ingegneria civile come sistemi di copertura per grandi luci. Rispetto alle strutture tradizionali, possono risultare più convenienti e sostenibili dal punto di vista ambientale; per queste ed altre ragioni, tra cui il loro impatto estetico, sono state sempre più impiegate negli ultimi decenni. Le tensostrutture devono essere pretensionate per resistere efficacemente ai carichi esterni; la ricerca di un’adeguata forma di equilibrio iniziale sotto determinate pretensioni e assegnati vincoli al contorno è conosciuta come "form-finding". Nel corso degli anni, sono stati sviluppati diversi metodi computazionali ad hoc, originando una ricca produzione scientifica. Il concetto di ricerca della forma può essere applicato anche alle strutture a guscio e ai gridshells, spesso in combinazione con qualche tipo di ottimizzazione strutturale. L’obiettivo è quello di determinare una forma che possa sopportare i carichi primari (come il peso proprio) in modo particolarmente efficace, ad esempio minimizzando gli effetti flessionali. In questa tesi vengono studiati metodi di ricerca della forma per sistemi discreti composti da elementi in tensione/compressione e per tensostrutture a membrana. Viene considerato in dettaglio il "force density method", sia nella sua versione lineare che nelle sue varianti non lineari, che consentono di imporre diverse tipologie di vincolo. L’approccio del force density method è implementato in vari script MATLAB e confrontato con il "dynamic relaxation method", discutendo le forme di equilibrio risultanti dalle analisi numeriche. Con riferimento alle strutture soggette a compressione, viene prima esaminato il caso di una colonna fabbricata mediante la tecnologia di manifattura additiva Wire-and-Arch. Vengono inoltre presentati alcuni esempi di gridshells, per i quali viene formulato un problema di ottimizzazione sotto carichi verticali assegnati utilizzando maglie con proiezione orizzontale fissata. Infine, il "surface stress density method" è illustrato come un’estensione del force density method per il form-finding di membrane con pretensione isotropa.
Form-finding of tensile structures and of compression-only gridshells
Bosi, Alessandro
2022/2023
Abstract
Prestressed cable-nets and tensile membrane structures are used in civil engineering primarily as roofing systems to cover large column-free spaces. With respect to traditional structures, they can be more cost effective and environmentally sustainable; besides, they can be aesthetically pleasing. For these and other reasons they have become increasingly popular over the last decades. Tensile structures must be prestressed to efficiently withstand external loads; the search for a suitable initial equilibrium shape under given pretensions and given boundary support conditions is called "form-finding". Over time, different ad hoc computational methods have been developed to tackle the form-finding problem, giving rise to a wealth of scientific papers on the topic. The concept of form-finding can also be applied to shell and gridshell structures, often in combination with some kind of structural optimization. In this context, the goal is to determine a form which can carry the primary loads (for instance the self-weight) in a particularly efficient way, for example by minimizing the bending effects. In this thesis, form-finding methods for discrete networks of tension/compression elements and for tensile membrane structures are investigated. The "force density method" is considered in detail, both in its linear version and in its nonlinear variants, which allow different types of constraints to be enforced. The force density approach is implemented in various MATLAB scripts and compared to the "dynamic relaxation method"; numerical examples of form found networks are reported. With reference to structures in compression, the case of a column fabricated using Wire-and-Arch Additive Manufacturing is first considered. Successively some examples of gridshells are presented, in which an optimization problem is formulated considering networks with fixed horizontal projection subjected to vertical nodal loads. Finally, the "surface stress density method" is described as a method which represents an extension of the force density method to the form-finding of isotropically prestressed tensile membrane structures.| File | Dimensione | Formato | |
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https://hdl.handle.net/10589/218927