Abstract
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.
Highlights
1.1 Previous workAdaptive structures are equipped with sensors and actuators to actively counteract the effect of external loads
The passive solution is obtained using a similar formulation to that given for embodied energy minimization (Section 4) which is reduced to a continuous nonlinear programming problem (NLP) because the actuator position binary variables are excluded
Note that for all configurations, the truss system (AT) performs significantly better than the tensegrity system (ATS) in mass and energy cost terms, including the passive solution obtained for load activation threshold (LAT) = 100%, which agrees with the findings given in (Nanayakkara et al 2020)
Summary
Adaptive structures are equipped with sensors and actuators to actively counteract the effect of external loads. The methods given in (Senatore et al 2019; Wang and Senatore 2020a) have been formulated for pin-jointed configurations in which all elements can take tension and compression, and there is no need to include prestress to ensure cable elements do not slack during adaptation to loading (i.e., stable equilibrium). For this reason, these methods cannot be directly applied to design adaptive tensegrity structures through energy minimization
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