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Abstract: Planar bar-and-joint mechanisms with one degree-of-freedom are widely used in deployable structures and machines. Such mechanisms are designed to undergo a specific motion, which can be described mathematically by plotting out the compatibility conditions, resulting in a curve called the compatibility path. It has been observed that compatibility paths can develop singularities similar to that of equilibrium paths of elastic structures.

This dissertation studies singularities occurring in compatibility paths with the aid of knowledge in the theory of structural stability. An analogy is set up between the equilibrium path of elastic structures and the compatibility path of mechanisms with a single degree-of-freedom incorporating different types of bifurcation, effects of imperfections and detection of singularities. It is shown that the fundamentally distinct critical points such as limit points and bifurcation points can also appear in the compatibility path. Methods used to study singularities for compatibility conditions of mechanisms and equilibrium of structures are unified so that they can be used for both cases. A formulation of potential energy for mechanisms is also proposed in analogy with the potential energy function used in structural analysis.

Further analysis of the mechanisms is carried out to demonstrate that singularities of compatibility paths can also be dealt with by elementary catastrophe theory similar to stability theory. A relationship is established between the mathematical formulation of different compatibility bifurcations and the canonical forms of catastrophe types. Examples of mechanisms demonstrating the existence of cuspoids of the compatibility conditions are given. An overall classification of the compatibility paths is also proposed.

Keywords: bifurcation, catastrophe types, compatibility condition, compatibility path, elementary catastrophe theory, equilibrium path, imperfection, Jacobian matrix, mechanism with one degree-of-freedom, potential energy

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In this dissertation, we explore the possibilities of systematically constructing large structural mechanisms using existing spatial overconstrained linkages with only revolute joints as basic elements. The first part of the dissertation is devoted to structural mechanisms (networks) based on the Bennett linkage, a well-known spatial 4R linkage. This special linkage has been used as the basic element. A particular layout of the structures has been identified allowing unlimited extension of the network by repeating elements. As a result, a family of structural mechanisms has been found which form single-layer structural mechanisms. In general, these structures deploy into profiles of cylindrical surface.
Meanwhile, two special cases of the single-layer structures have been extended to form multi-layer structures. In addition, according to the mathematical derivation, the problem of connecting two similar Bennett linkages into a mobile structure, which other researchers were unable to solve, has also been solved. A study into the existence of alternative forms of the Bennett linkage has also been done. The condition for the alternative forms to achieve the compact folding and maximum expansion has been derived. This work has resulted in the creation of the most effective deployable element based on the Bennett linkage. A simple method to build the Bennett linkage in its alternative form has been introduced and verified. The corresponding networks have been obtained following the similar layout of the original Bennett linkage.

The second effort has been made to construct large overconstrained structural mechanisms using hybrid Bricard linkages as basic elements. The hybrid Bricard linkage is a special case of the Bricard linkage, which is overconstrained and with a single degree of mobility. Starting with the derivation of the compatibility condition and the study of its deployment behaviour, it has been found that for some particular twists, the hybrid Bricard linkage can be folded completely into a bundle and deployed to a flat triangular profile. Based on this linkage, a network of hybrid Bricard linkages has been produced. Furthermore, in-depth research into the deployment characteristics, including kinematic bifurcation and the alternative forms of the hybrid Bricard linkage, has also been conducted.
The final part of the dissertation is a study into tiling techniques in order to develop a systematic approach for determining the layout of mobile assemblies. A general approach to constructing large structural mechanisms has been proposed, which can be divided into three steps: selection of suitable tilings, construction of overconstrained units and validation of compatibility. This approach has been successfully applied to the construction of the structural mechanisms based on Bennett linkages and hybrid Bricard linkages. Several possible configurations are discussed including those described previously.
All of the novel structural mechanisms presented in this dissertation contain only revolute joints, have a single degree of mobility and are geometrically overconstrained. Research work reported in this dissertation could lead to substantial advancement in building large spatial deployable structures.
 

Keywords: Structural mechanism; deployable structure; 3D overconstrained linkage; network; tiling technique; Bennett linkage; hybrid Bricard linkage; alternative form.

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Based on the need for effective solutions of structures response to seismic loading, this thesis includes the theoretical background, and explanation of several methods. There are many theories in the community, but the ones chosen to be looked closer at here are Modal response spectrum analysis for symmetric and asymmetric plan structures, Modal Pushover Analysis for symmetric and asymmetric plan structures and Linear and Non-Linear Response History Analysis. The theory has been adapted from published papers and books on the topic.

The report is divided into three main sections, numerical methods for solving of dynamic problems, elastic analysis and inelastic analysis. The chapters on Elastic and Inelastic analysis are further divided into sections on symmetric and asymmetric plan. Elastic analyses by hand calculations and SAP2000 have been performed on a 2D-frame, a SAP2000 Elastic Response spectrum analysis has been performed on a 3D-frame, and an inelastic modal pushover analysis in SAP2000 has been performed on a 2D frame. The target for this inquiry is to discover advantages and disadvantages in the different methods and comparing them.
Author: Helge Dørheim | Size: 10.5 MB | Format: PDF | Quality: Unspecified | Publisher: Norwegian University of Science and Technology | Year: 2012 | pages: 90

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