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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.

This paper reports on experimental testing that was carried out on a prototype adaptive structure designed to counteract the effect of loading through controlled large shape changes. The prototype is 6.6 m truss equipped with 12 linear actuators which has been designed through a method that combines geometry optimization and non-linear shape control. The structure is designed to adapt into target shapes that are optimal under each load case. Shape adaptation is achieved through controlled length changes of linear actuators that strategically replace some of the structure elements. The actuator placement is optimized to control the structure into the required target shapes. This way, material utilization is maximized and thus material energy embodied is reduced. Experimental testing is carried out to verify numerical findings and investigate the feasibility of the design method. The applied load is inferred through a classification model based on supervised learning. A control algorithm based on a linear-sequential form of geometry optimization is proposed. Experimental results show that this method successfully allows for real-time shape adaptation to achieve stress homogenization under various loading conditions. Copyright (C) 2020 The Authors.

This paper presents experimental testing of a new semi-active vibration control device comprising a shape memory polymer (SMP) core that is reinforced by an SMP-aramid composite skin. This control device works as a load-transfer component that can be integrated into truss and frame structures in the form of a joint. At the material level, thermal actuation from ambient (25 degrees C) to transition temperature (65 degrees C) causes a significant 40fold increase in damping due to viscoelastic effects. At the component level, uniaxial tensile and four-point bending tests have shown that tensile strength depends primarily on the bond strength between the reinforcement skin and the structural element while flexural strength depends on the strength of the reinforcement skin fibers. Through cyclic testing, it has been observed that material viscoelasticity is beneficial to ductility and energy dissipation. When the joint core is actuated to the SMP transition temperature, axial and flexural stiffness decrease by up to 50% and 90%, respectively. The property change at material and component levels enable tuning the frequency and damping ratio at the structure level, which has been successfully employed to mitigate the dynamic response of a 1/10 scale three-story prototype frame under resonance and earthquake loadings.

This paper presents numerical and experimental studies on semi-active seismic response control of structures equipped with variable stiffness and damping structural joints. Such adaptive joints, which are comprised of a shape memory polymer (SMP) core reinforced by an SMP-aramid composite skin, function as load-transfer components as well as semi-active control devices. The SMP core material can transition from a glassy to a rubbery state through thermal actuation resulting in a shift of the structural natural frequencies and a parallel increase of damping ratio, which enables a new semi-active control strategy. Control performance has been evaluated on a three-story frame equipped with 12 adaptive joints and subjected to seismic excitations. Full-transient analysis has shown that when the joints are thermally actuated to the transition temperature (65 degrees C), acceleration and base shear are reduced by up to 62% and 65%, respectively. Shake-table tests have been carried out on a 1/10-scale prototype, confirming that through thermal actuation of the adaptive joints the structural damping ratio increases from 2.6% to 11.3% and the first natural frequency shifts by up to 37%. As the structure becomes more flexible, an increase of displacements and interstory drift might occur. However, depending on the seismic excitation, top-story acceleration and base shear are significantly reduced in the range 43%-50% and 35%-51%, respectively. These results confirm that semi-active control through thermal actuation of variable stiffness and damping structural joints is effective to mitigate the structure response under seismic excitation.

Adaptive structures can 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 with traditional passive designs. 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 thus embodied energy is reduced. This paper presents a new design process for adaptive structures based on geometry and member sizing optimization in combination with actuator placement optimization. This method consists of two parts: (1)geometry and sizing optimization through sequential quadratic programming is carried out to obtain shapes that are optimal for each load case; and (2)a formulation based on stochastic search and the nonlinear force method (NFM) is employed to obtain an optimal actuator layout and commands to control the structure into the target shapes obtained from Part 1. A case study of a planar statically indeterminate truss is presented. Numerical results show that 17% and 37% embodied energy savings are achieved with respect to an identical active structure designed to adapt through small shape changes and to a weight-optimized passive structure, respectively. The combinatorial task of optimal actuator placement is carried out efficiently. The method formulated in this work produces actuator layouts that enable accurate geometric nonlinear shape control under quasi-static loading through a low number of actuators compared to the number of members of the structure.

This paper introduces a new semi-active strategy for vibration control of truss and frame structures equipped with variable stiffness and damping joints which consist of a shape memory polymer (SMP) core reinforced by an SMP-aramid composite skin. When the joints are actuated to the transition temperature through thermal actuation, the SMP core transitions from a glassy to a rubbery state through a viscoelastic region, which causes a stiffness reduction and an increase of damping. The mechanic behavior of the joint can be thought of as transitioning from a moment to a pin connection. This way, it is possible to cause a shift of the structure natural frequencies and to increase damping, which is employed to obtain a significant reduction of the dynamic response. This paper comprises two parts: (1) characterization of a variable stiffness and damping material model through experimental testing; (2) numerical simulations of a truss bridge and a four-story frame, which are equipped with variable stiffness and damping joints. The truss bridge (case A) is subjected to a resonance and a moving load while the four-story frame (case B) is subjected to El Centro earthquake loading. For case A under resonance loading, the dynamic response can be reduced exclusively through a frequency shift and ignoring viscoelastic effects. For case A under moving load and case B under earthquake loading, vibration suppression is mostly caused by the increase of damping due to viscoelastic effects. Control time delays due to joint heating have been included in the analysis. When the joints are actuated to the transition range 55°C–65°C, which is specific to the SMP adopted in this study, the acceleration peak amplitude reduces by up to 95% and 87%, for case A and case B, respectively. For both cases, damping increases by up to 2.2% from undamped conditions (25°C). This work has shown that the adoption of variable stiffness and damping structural joints has great potential to enable a new and effective semi-active control strategy to significantly reduce the structure response under a wide range of dynamic loading conditions.

This paper presents the formulation of a new methodology to design adaptive structures. This design method synthesises structural configurations that are optimum hybrids between a passive and an active structure. An optimisation scheme searches for an optimal material distribution and actuation layout to minimise the structure whole-life energy which consists 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, here, strategically located active elements redirect the internal load path to homogenise the stresses and change the shape of the structure to keep deflections within required limits. To ensure the embodied energy saved this way is not used up to by actuation, the adaptive solution is designed to cope with ordinary loading events using only passive load-bearing capacity whilst relying on active control to deal with larger events that have a smaller probability of occurrence. The design methodology has been implemented for statically determinate and indeterminate reticular structures. However, the formulation is general and could be implemented to other structural types. Numerical simulations on a truss system case study confirm that substantial savings up to 50% of the whole-life energy can be achieved by the adaptive solution compared to a passive solution designed using state of the art optimisation methods.

The design methodology described in this paper takes a substantial shift from conventional methods. Traditionally sizing is based on the worst expected load scenario. By contrast to this conventional passive approach the method presented here replaces passive member strategically with active elements (actuators) which are only activated when the loads reach a certain threshold. The structure can withstand low level of loads passively. Above the threshold, actuation comes in to allow the structure to cope with high but rare loading scenarios. Active control introduces operational energy consumption in addition to the energy embodied in a passive design. In this paper we use this dual design to minimize the overall energy required by the structures. This methodology has been used on a simple truss structure and it was showed that it allows significant weight saving compared to conventional passive design. We extend the application of the methodology to a more complex 3D structure. It is confirmed that an optimum activation threshold exists that leads to design that minimises the total energy of the structure. Compared to an optimised passive design we show that the total energy saving is 10-fold.

This paper presents an experimental validation of a new design method for adaptive structures that counteract the effect of loading through shape morphing. The structure is designed to morph into target shapes that are optimal to take external loads through combined optimization of structural layout and actuator placement. The prototype tested in this study is a simply supported spatial truss that spans 6.6 m with a span-to-depth ratio of 44/1. Shape adaptation is achieved through controlled length changes of 12 linear actuators that are strategically integrated into structural elements. A new mechanics-based framework has been formulated to enable real-time control. Linear-sequential shape optimization is employed to predict target shapes under loading. Actuator commands are computed through an iterative process that accounts for geometric nonlinearity. This formulation allows a reduction of computation time by four orders of magnitude compared with a nonlinear programming formulation. Experimental testing has shown that significant stress homogenization is achieved through shape adaptation, which results in up to 45% savings of material mass compared with a weight-optimized passive structure. Depending on the energy source employed for adaptation, the equivalent carbon is reduced by up to 29% and 43% in the case of non-renewable and 100% renewable energy mix, respectively.

This paper gives a proof of equivalence between two existing force methods (FM) for structural analysis: The Integrated Force Method (IFM) and a force method based on singular value decomposition (SVD) of the equilibrium conditions here named as SVD-FM. Recently, these methods have been employed to design and control active structures. Actuation is employed to counteract the effect of external loading by modifying internal forces and the external geometry in order to meet strength and serviceability requirements. Both IFM and SVD-FM offer an effective way to estimate the combined effect of external loading and that of actuation. Generally, the SVD-FM has a lower degree of computational complexity with respect to the IFM, the more so as the structure static indeterminacy increases. However, the IFM has a more intuitive formulation that is preferable pedagogically and it is of value for future extensions to kinematically indeterminate configurations and to geometric non-linear cases.

Adaptive joints are structural joints made of materials with enhanced transduction properties that can vary their stiffness via solid-state actuation (e.g. thermal, mechanical). In this work, stiffness tuning is used to switch the joint between a ‘locked’ (e.g. a moment connection) and a ‘released’ (e.g. pin) state. Previous work has looked into the feasibility of using variable stiffness joints during shape and force control in order to reduce actuation work. This paper focuses on control of the structure dynamic response to loading. The natural frequency of the structure is tuned to escape dangerous resonance conditions in two ways: 1) a geometric reconfiguration via large shape changes or 2) via the change of stiffness of the joints. Two case studies are considered: 1) an active frame integrated with four actuators fitted on tubular elements which are connected by a shape memory polymer joint 2) a planar truss structure. Experimental tests on the active frame have shown that by varying the length of the linear actuators, large shape changes can be employed to effectively change the natural frequency of the structure. During shape change, the joint stiffness is lowered to ease geometric reconfiguration. For the planar truss case study, simulations have shown that the ‘release’ or ‘locking’ of multiple joints can be employed to change the eigenfrequencies, the more so the higher the eigenmode.