Keywords: smart structures, lightweight structures, control, finite element method, state space approach, form finding, object-oriented programming.

Simulation in the fields of analysis, design and control of flexible mechanical structures is commonly based on the finite element method. In the case of thin and lightweight structures the aim of the computational design process is often to minimize weight while maintaining stress and deformation criteria. Prominent examples in the civil engineering context are large membrane structures such as tents or stadium roofings. Structural adaptivity can be used to increase functionality, improve usability or to create even lighter structures [1].

This contribution presents a computational framework and the related algorithms for the virtual design and simulation of controlled smart lightweight membrane structures. The approach is based on finite element analysis, taking nonlinear and coupled field effects into account. The presented concept aims for mechanically motivated structural design and integration of control aspects from the very beginning of the design process.

Form finding is used to determine the optimal structural shape of tensile structures from an inverse formulation of equilibrium [2]. The algorithm presented turns out to be a very effective alternative for the automated design of surface structures. The final stresses under load and the boundaries of the structure are the major shaping parameters which clearly define the resulting geometry as shape of equilibrium. Also the cutting patterning of membranes is integrated in the design process in order to consider fabrication effects at the earliest possible stage [3].

Active control is adopted for deformation and vibration suppression of the membrane structure 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 tensile structure. Discrete time control via an optimal linear-quadratic-Gaussian (LQG) controller is applied.

It is shown how the methods of form finding, cutting patterning, structural optimization, controller design and transient simulation of the nonlinear and controlled model can be effectively merged into one computational environment. The presented methods and algorithms of all simulation and design steps are illustrated and verified at the example of a controlled four-point tent.

1

M. Fischer, K.-U. Bletzinger, R. Wüchner, "Computational framework for simulation and design of adaptive lightweight structures", IV ECCOMAS Thematic Conference on Smart Structures and Materials, Porto, Portugal, 2009.

2

R. Wüchner, K.-U. Bletzinger, "Stress-adapted numerical form finding of prestressed surfaces by the updated reference strategy", Int. J. Numer. Meth. Engrg., 64, 143-166, 2005. doi:10.1002/nme.1344

3

J. Linhard, R. Wüchner, K.-U. Bletzinger, "Introducing cutting patterns in form finding and structural analysis", in E. Oñate, B. Kröplin, (Editors), "Textile Composites and Inflatable Structures II", Springer, 2008. doi:10.1007/978-1-4020-6856-0_5

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