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This paper discusses the role that structural stiffness plays in the context of designing adaptive structures. The focus is on load-bearing structures with adaptive displacement control. A design methodology is implemented to minimize the control effort by making the structure as stiff as possible against external loads and as flexible as possible against the effect of actuation. This rationale is tested using simple analytical and numerical case studies.

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 work presents force and shape control strategies for adaptive structures subjected to quasi-static loading. The adaptive structures are designed using an integrated structure-control optimization method developed in previous work, which produces minimum “whole-life energy” configurations through element sizing and actuator placement optimization. The whole-life energy consists of an embodied part in the material and an operational part for structural adaptation during service. Depending on the layout, actuators are placed in series with the structural elements (internal) and/or at the supports (external). The effect of actuation is to modify the element forces and node positions through length changes of the internal actuators and/or displacements of the active supports. Through active control, the stress is homogenized and the displacements are kept within required limits so that the design is not governed by peak demands. Actuation has been modeled as a controlled non-elastic strain distribution, here referred to as eigenstrain. Any eigenstrain can be decomposed into two parts: an impotent eigenstrain only causes a change of geometry without altering element forces while a nilpotent eigenstrain modify element forces without causing displacements. Four control strategies are formulated: (C1) force and shape control to obtain prescribed changes of forces and node positions; (C2) shape control through impotent eigenstrain when only displacement compensation is required without affecting the forces; (C3) force control through nilpotent eigenstrain when displacement compensation is not required; and (C4) force and shape control through operational energy minimization. Closed-form solutions to decouple force and shape control through nilpotent and impotent eigenstrain are given. Simulations on a slender high-rise structure and an arch bridge are carried out to benchmark accuracy and energy requirements for each control strategy and for different actuator configurations that include active elements, active supports and a combination of both.

This paper presents optimization methods to design frame structures from a stock of existing elements. These methods are relevant when reusing structural elements over multiple service lives. Reuse has the potential to reduce the environmental impact of building structures because it avoids sourcing new material, it reduces waste and it requires little energy. When reusing elements, cross-section and length availability have a major influence on the structural design. In previous own work, design of truss structures from a stock of elements was formulated as a mixed-integer linear programming (MILP) problem. It was shown that this method produces solutions which are global optima in terms of stock utilization. This work extends previous formulations to stock-constrained optimization of frame structures subject to ultimate and serviceability limit states hence expanding the range of structural typologies that can be designed through reuse. Fundamental to this method is the globally optimal assignment of available stock elements to member positions in the frame structure. Two scenarios are considered: (A) the use of individual stock elements for each member of the frame, and (B) a cutting stock approach, where multiple members of the frame are cut from a single stock element. Numerical case studies are presented to show the applicability of the proposed method to practical designs. To carry out the case studies, a stock of elements was inventoried from shop drawings of deconstructed buildings. Results show that through reusing structural elements a significant reduction of embodied greenhouse gas emissions could be achieved compared to optimized structures made of new elements.

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.