Modelling and control of a shell structure based on a finite dimensional variational formulation

Alexander Zuyev and Oliver Sawodny

Mathematical and Computer Modelling of Dynamical Systems, 2015, vol. 21, issue 6, 591-612

Abstract: A mathematical model of a controlled shell structure based on Hamilton’s principle and the generalized Ritz–Galerkin method is proposed in this paper. The problem of minimizing the stress energy is solved explicitly for a static version of this model. For the dynamical system under consideration, a procedure for estimating external disturbances and the state vector is derived. We also propose an observer design scheme and solve the stabilization problem for an arbitrary dimension of the linearized model. This approach allows us to perform control design for double-curved shells of complex geometry by combining analytical computation of the controller parameters with numerical data that represent the reference configuration and modal displacements of the shell. As an example, the parameters of our model are validated by results of a finite element analysis for the Stuttgart SmartShell structure.

Date: 2015
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DOI: 10.1080/13873954.2015.1065278

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