A Space-Time Finite Element Model for Design and Control Optimization of Nonlinear Dynamic Response

P.P Moita,J.B Cardoso,A.J Valido

doi:10.1155/2008/721760

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.

Highlights

Structures and flexible mechanical systems, on the one hand, as well as optimal design and optimal control, on the other hand, have been traditionally treated with separated formulations
This paper presents an integrated methodology for optimal design and control of nonlinear flexible mechanical systems
In order to implement it, one uses: (i) a nonlinear structural finite element technique to model large displacements, referring all the quantities to an inertial frame and using stress and strain measures that are invariant with the rigid body motion; (ii) a conceptual separation between time variant and time invariant design parameters, this way including the design space into the control space and considering the design variables as control variables not depending on time

Summary

Introduction

Structures and flexible mechanical systems, on the one hand, as well as optimal design and optimal control, on the other hand, have been traditionally treated with separated formulations. This paper presents an integrated methodology for optimal design and control of nonlinear flexible mechanical systems. In the optimization process we can use both types of variables simultaneously or by interdependent levels. Both types are designated here as design variables. P.P. Moita et al / A space-time finite element model for design and control optimization of nonlinear dynamic response a space-time finite element discretization is utilized and the solution of the dynamic equations is obtained by at-once integration. The response analysis and corresponding DSA are implemented in the interactive optimal design code OPTIMISE in order to use optimality criteria or nonlinear programming optimization runs

Response analysis modeling

Design sensitivity analysis modeling

The optimum design problem

Nonlinear impact absorber

Vehicle suspension

Concluding remarks