Force and Shape Control Strategies for Minimum Energy Adaptive Structures

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 aseigenstrain. Anyeigenstraincan be decomposed into two parts: an impotenteigenstrainonly causes a change of geometry without altering element forces while a nilpotenteigenstrainmodify 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 impotenteigenstrainwhen only displacement compensation is required without affecting the forces; (C3) force control through nilpotenteigenstrainwhen 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 impotenteigenstrainare 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.