Finite Element based Simulation, Design and Control of Adaptive Lightweight Structures

This contribution presents a finite element based computational framework and the related algorithms for the virtual design and simulation of controlled smart lightweight membrane structures. Form finding is used to determine the optimal structural shape of tensile structures from an inverse formulation of equilibrium. Also the cutting pattern generation of membranes is integrated in the design process in order to consider fabrication effects already in the earliest possible stage. Active control is adopted for vibration suppression under external loads like e.g. wind. Controller design is based on a state space model that is derived from the finite element model and that preserves the geometrically nonlinear equilibrium state and the prestress effects of the membrane. Discrete time control via an optimal linearquadratic- Gaussian (LQG) regulator is applied. The presented methods and algorithms of all simulation and design steps are illustrated and verified at the example of a controlled 4-point tent.