A space-time finite element model for design and control optimization of nonlinear dynamic response

Issue title: The International Conference on Engineering Dynamics 2007

Article type: Research Article

Authors: Moita, P.P. | Cardoso, J.B. | Valido, A.J.

Affiliations: Escola Superior de Tecnologia de Setúbal, Campus do IPS, 2914-508 Setúbal, Portugal | Instituto Superior Técnico, Departamento de Engenharia Mecânica, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Note: [] Corresponding author. E-mail: [email protected]

Abstract: A design and control sensitivity analysis and multicriteria optimization formulation is derived for flexible mechanical systems. This formulation is implemented in an optimum design code and it is applied to the nonlinear dynamic response. By extending the spatial domain to the space-time domain and treating the design variables as control variables that do not change with time, the design space is included in the control space. Thus, one can unify in one single formulation the problems of optimum design and optimal control. Structural dimensions as well as lumped damping and stiffness parameters plus control driven forces, are considered as decision variables. The dynamic response and its sensitivity with respect to the design and control variables are discretized via space-time finite elements, and are integrated at-once, as it is traditionally used for static response. The adjoint system approach is used to determine the design sensitivities. Design optimization numerical examples are performed. Nonlinear programming and optimality criteria may be used for the optimization process. A normalized weighted bound formulation is used to handle multicriteria problems.

Keywords: Optimization, nonlinear systems, dynamic response, space-time finite elements

Journal: Shock and Vibration, vol. 15, no. 3-4, pp. 307-314, 2008