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Publication# Design of adaptive structures through energy minimization: extension to tensegrity

Résumé

This paper gives a new formulation to design adaptive structures through total energy optimization (TEO). This methodology enables the design of truss as well as tensegrity configurations that are equipped with linear actuators to counteract the effect of loading through active control. The design criterion is whole-life energy minimization which comprises an embodied part in the material and an operational part for structural adaptation during service. The embodied energy is minimized through simultaneous optimization of element sizing and actuator placement, which is formulated as a mixed-integer nonlinear programming problem. Optimization variables include element cross-sectional areas, actuator positions, element forces, and node displacements. For tensegrity configurations, the actuators are not only employed to counteract the effect of loading but also to apply appropriate prestress which is included in the optimization variables. Actuator commands during service are obtained through minimization of the operational energy that is required to control the state of the structure within required limits, which is formulated as a nonlinear programming problem. Embodied and operational energy minimization problems are nested within a univariate optimization process that minimizes the structure’s whole-life energy (embodied + operational). TEO has been applied to design a roof and a high-rise adaptive tensegrity structure. The adaptive tensegrity solutions are benchmarked with equivalent passive tensegrity as well as adaptive truss solutions, which are also designed through TEO. Results have shown that since cables can be kept in tension through active control, adaptive tensegrity structures require low prestress, which in turn reduces mass, embodied energy, and construction costs compared to passive tensegrity structures. However, while adaptive truss solutions achieve significant mass and energy savings compared to passive solutions, adaptive tensegrity solutions are not efficient configurations in whole-life energy cost terms. Since cable elements must be kept in tension, significant operational energy is required to maintain stable equilibrium for adaptation to loading. Generally, adaptive tensegrity solutions are not as efficient as their equivalent adaptive truss configurations in mass and energy cost terms.

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Concepts associés (12)

Design

vignette|Chaise de Charles Rennie Mackintosh, 1897.
Le design, le stylisme ou la stylique est une activité de création souvent à vocation industrielle ou commerciale, pouvant s’orient

Structure

A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buil

Actionneur

Dans une machine, un actionneur est un objet qui transforme l’énergie qui lui est fournie en un phénomène physique qui fournit un travail, modifie le comportement ou l’état d'un système.
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Publications associées (36)

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Adaptive structures modify their geometry and internal forces through sensing and mechanical actuation in order to maintain optimal performance under changing actions. Previous work has shown that well-conceived adaptive design strategies achieve substantial whole-life energy savings compared to traditional passive designs. The whole-life energy comprises an embodied part in the material and an operational part for structural adaptation
This thesis presents a new method to design adaptive structures capable of large and reversible shape changes achieved through actuation. To this end, linear actuators are strategically fitted within selected elements of reticular (e.g. trusses and frames) structures. Structural adaptation through controlled large shape changes allows a significant stress redistribution so that the design is not governed by extreme loads with long return periods. This way, material utilization is maximized and thus, embodied energy is reduced. A set of target shapes that counteract the effect of peak loads are first obtained through geometry and sizing optimization. Strategies have been developed to reduce the uncertainty due to the presence of multiple local minima so that the computational efficiency is improved and the convergence is guaranteed.
A method is formulated to obtain a suitable actuator layout in order to control the structure into the target shapes. This is a challenging task due to the combinatorial nature of the actuator placement process which, in this case, includes geometric nonlinearity. A heuristic for near-neighbor generation based on the actuator control efficacy is employed to explore effectively the large search space. The heuristic has significantly improved convergence, which is important for structures with complex topologies that are made of many elements. A framework for real-time control combining shape optimization and nonlinear force method is proposed. The objective of the control framework is to minimize the operational energy for shape adaptation while satisfying stress and element buckling limits. A linear-sequential formulation is presented, allowing a computationally-efficient implementation of real-time shape control through a mechanics-based formulation.
Through a nested univariate optimization scheme, an adaptive structure with minimum whole-life energy requirements is synthesized. Numerical case studies demonstrate that whole-life energy savings can be achieved compared to weight-optimized passive structures for the configurations studied in this thesis. Structures that adapt to loading through large shape changes achieve marginal whole-life energy savings with respect to structures that adapt to loading through small shape changes. Nevertheless, significant embodied energy (and thus material mass) savings are achieved with respect to weight-optimized passive structures as well as to structures that adapt through small shape changes.
Experimental studies at various scales are carried out to verify numerical findings and investigate the feasibility of the design method. Experimental testing has demonstrated that significant stress homogenization through large-shape changes is achievable. The control framework allows for real-time shape adaptation to achieve stress homogenization under various loading conditions. An energy appraisal carried out on a near-full-scale prototype confirms that considerable savings of the total energy can be achieved by adaptive solutions.

Arka Prabhata Reksowardojo, Gennaro Senatore, Ian Smith

Adaptive structures have the ability to modify their shape and internal forces through sensing and actuation in order to maintain optimal performance under changing actions. Previous studies have shown that substantial whole-life energy savings with respect to traditional passive designs can be achieved through well-conceived adaptive design strategies. The whole-life energy comprises an embodied part in the material and an operational part for structural adaptation. Structural adaptation through controlled large shape changes allows a significant stress redistribution so that the design is not governed by extreme loads with long return periods. This way, material utilization is maximized and embodied energy is reduced. A design process based on shape optimization has been formulated to obtain shapes that are optimal for each load case. A geometrically non-linear force method is employed to control the structure into required shapes. This paper presents the experimental testing of a small-scale prototype adaptive structure produced by this design process. The structure is a simply supported planar truss. Shape adaptation is achieved through controlled length changes of turnbuckles that strategically replace some of the structural elements. The stress is monitored by strain sensors fitted on some of the truss elements. The nodal coordinates are monitored by an optical tracking system. Numerical predictions and measurements have a minimum Pearson correlation of 0.86 which indicates good accordance. Although scaling effects have to be further investigated, experimental testing on a small-scale prototype has been useful to assess the feasibility of the design and control methods outlined in this work. Results show that stress homogenization through controlled large shape changes is feasible.

2019Using a previously developed design methodology it was shown that optimal material distribution in combination with strategic integration of the actuation system lead to significant whole-life energy savings when the design is governed by rare but strong loading events. The whole-life energy of the structure is made of an embodied part in the material and an operational part for structural adaptation. Instead of using more material to cope with the effect of loads, the actuation system redirects the internal load-path to homogenise the stresses and change the shape of the structure to keep deflections within limits. This paper presents a systematic exploration of the domain in which adaptive two-dimensional pin-jointed structures are beneficial in terms of whole-life energy and monetary costs savings. Two case studies are considered: a vertical cantilever truss representative of a multi-storey building supported by an exoskeleton structure and a simply supported truss beam which is part of a roof system. This exploration takes five directions studying the influence of: (1) the structural topology (2) the characteristics of the load probability distribution (3) the ratio of live load over dead load (4) the aspect ratio of the structure (e.g. height-to-depth) (5) the material energy intensity factor. Results from the main five strands are combined with those from the monetary cost analysis to identify an optimal region where adaptive structures are most effective in terms of both energy and monetary savings. It was found that the optimal region is broadly that of stiffness-governed structures. For the cantilever case, the optimal region covers most of the application domain and it is not very sensitive to either live-to-dead-load or height-to-depth ratios thus showing a wide range of applicability, including ordinary loading scenarios and relatively deep structures.

2018