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

• Published in: Mathematical and computer modelling of dynamical systems Vol. 21; no. 6; pp. 591 - 612
• Main Authors: Zuyev, Alexander, Sawodny, Oliver
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.11.2015; Taylor & Francis Ltd
• Subjects: Design engineering; Disturbances; Dynamical systems; elastic shell; Finite element method; Galerkin method; Hamilton's principle; Mathematical analysis; Mathematical models; modal solution; Modelling; observability; Parameters; Ritz-Galerkin method; Shells; Shells (structural forms); stabilization; State vectors
• ISSN: 1387-3954; 1744-5051
• DOI: 10.1080/13873954.2015.1065278

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.