Mechanical Systems Design and Control Optimization with Varying Time Domain

This paper presents an integrated methodology for optimal design and control of nonlinear flexible mechanical systems. A design and control sensitivity analysis and multicriteria optimization formulation is derived. This formulation is implemented in an optimum design code and it is applied to the nonlinear behavior response. Damping and stiffness characteristics plus control driven forces are considered as decision variables. A conceptual separation between time variant and time invariant design parameters is presented, this way including the design space into the control space and considering the design variables as control variables not depending on time. By using time integrals through all the derivations, the design and control problems are unified. In the optimization process we can use both types of variables simultaneously or by interdependent levels. Total time is also considered as varying. For treating time domain variation, a unit time interval is mapped onto the original time interval, then treating equally time variant and time invariant problems. The dynamic response and its sensitivity are discretized via space and time finite elements, and are integrated either by at-once integration or step-by-step. Adjoint system approach is used to calculate the sensitivities. The response analysis and corresponding DSA are implemented into an optimal design code.