Design and analysis of geodesic tensegrity structures with agriculture applications.

"This report aims to promulgate and elucidate the effective application of scientific principles in the design and optimisation of tensegrity structures for practical applications. By developing the intrinsic geometry of the geodesic dome and applying tensegrity design principles, a range of efficient, lightweight, modular structures are developed and broadly classified as geodesic tensegrity structures. Novel systems for clustering domes in two dimensions are considered and the analytical geometry required to generate various dome structures is derived from first principles. Computational methods for performing the design optimisation of tensegrity structures are reviewed and explained in detail. It is shown how an efficient, unified computational framework, suitable for the analysis of tensegrity structures in general, may be developed using computations which involve the equilibrium matrix of a structure. The importance of exploiting symmetry to simplify structural computations is highlighted throughout, as this is especially relevant in the analysis of large dome structures. A novel approach to generating the global equilibrium matrix of a structure from element vectors and implementing symmetry subspace methods is presented, which relies on the choice of an appropriate coordinate system to reflect the symmetry of a structure. A new algorithm is developed for implementing symmetry subspace methods in a computer program which enables the symmetry-adapted vector basis to be generated more efficiently. Methods for analysing kinematically indeterminate tensegrities and prestressed mechanisms and performing the prestress optimisation of a tensegrity structure are briefly reviewed and explained. Efficient tensegrity modular systems are developed for constructing a range of double-layer geodesic tensegrity domes and grids, based on the pioneering work of the artist, Kenneth Snelson. Finally, the cultural significance of tensegrity technology is illustrated by focusing on a range of novel applications in agriculture and sustainable development and adopting the holistic, "design science, "approach advocated by Buckminster Fuller.

Model updating in structural dynamics: advanced parametrization, optimal regularization, and symmetry considerations

Numerical models are pervasive tools in science and engineering for simulation, design, and assessment of physical systems. In structural engineering, finite element (FE) models are extensively used to predict responses and estimate risk for built structures. While FE models attempt to exactly replicate the physics of their corresponding structures, discrepancies always exist between measured and model output responses. Discrepancies are related to aleatoric uncertainties, such as measurement noise, and epistemic uncertainties, such as modeling errors. Epistemic uncertainties indicate that the FE model may not fully represent the built structure, greatly limiting its utility for simulation and structural assessment. Model updating is used to reduce error between measurement and model-output responses through adjustment of uncertain FE model parameters, typically using data from structural vibration studies. However, the model updating problem is often ill-posed with more unknown parameters than available data, such that parameters cannot be uniquely inferred from the data. This dissertation focuses on two approaches to remedy ill-posedness in FE model updating: parametrization and regularization. Parametrization produces a reduced set of updating parameters to estimate, thereby improving posedness. An ideal parametrization should incorporate model uncertainties, effectively reduce errors, and use as few parameters as possible. This is a challenging task since a large number of candidate parametrizations are available in any model updating problem. To ameliorate this, three new parametrization techniques are proposed: improved parameter clustering with residual-based weighting, singular vector decomposition-based parametrization, and incremental reparametrization. All of these methods utilize local system sensitivity information, providing effective reduced-order parametrizations which incorporate FE model uncertainties. The other focus of this dissertation is regularization, which improves posedness by providing additional constraints on the updating problem, such as a minimum-norm parameter solution constraint. Optimal regularization is proposed for use in model updating to provide an optimal balance between residual reduction and parameter change minimization. This approach links computationally-efficient deterministic model updating with asymptotic Bayesian inference to provide regularization based on maximal model evidence. Estimates are also provided for uncertainties and model evidence, along with an interesting measure of parameter efficiency

Symmetry in Modeling and Analysis of Dynamic Systems

Real-world systems exhibit complex behavior, therefore novel mathematical approaches or modifications of classical ones have to be employed to precisely predict, monitor, and control complicated chaotic and stochastic processes. One of the most basic concepts that has to be taken into account while conducting research in all natural sciences is symmetry, and it is usually used to refer to an object that is invariant under some transformations including translation, reflection, rotation or scaling.The following Special Issue is dedicated to investigations of the concept of dynamical symmetry in the modelling and analysis of dynamic features occurring in various branches of science like physics, chemistry, biology, and engineering, with special emphasis on research based on the mathematical models of nonlinear partial and ordinary differential equations. Addressed topics cover theories developed and employed under the concept of invariance of the global/local behavior of the points of spacetime, including temporal/spatiotemporal symmetries

Group-Theoretic Exploitations of Symmetry in Novel Prestressed Structures

In recent years, group theory has been gradually adopted for computational problems of solid and structural mechanics. This paper reviews the advances made in the application of group theory in areas such as stability, form-finding, natural vibration and bifurcation of novel prestressed structures. As initial prestress plays an important role in prestressed structures, its contribution to structural stiffness has been considered. General group-theoretic approaches for several problems are presented, where certain stiffness matrices and equilibrium matrices are expressed in symmetry-adapted coordinate system and block-diagonalized neatly. Illustrative examples on structural stability analysis, force-finding analysis, and generalized eigenvalue analysis on cable domes and cable-strut structures are drawn from recent studies by the authors. It shows how group theory, through symmetry spaces for irreducible representations and matrix decompositions, enables remarkable simplifications and reductions in the computational effort to be achieved. More importantly, before any numerical computations are performed, group theory allows valuable and effective insights on the behavior or intrinsic properties of a prestressed structure to be gained

Queensland University of Technology: Handbook 1991

The Queensland University of Technology handbook gives an outline of the faculties and subject offerings available that were offered by QUT