Simultaneous Trajectory and Topology Optimization of Flexible Multibody Systems

摘要

Flexible multibody systems are critical in a vast number of engineering fields, including aerospace, automotive, robotics, and civil. Trajectory optimization can be used to design optimal control paths for these flexible multibody systems to achieve specific objectives and performance goals. During the preliminary design phase, topology optimization can be used to satisfy complex structural requirements without any geometric limitations. Concurrent trajectory and topology optimization can yield better system level performance, but this has not been demonstrated in the literature to date. To address this gap, this work demonstrates a unified approach to perform coupled trajectory and topology optimization. Within this framework, the dynamic system is numerically solved using a backward differentiation formula. A mode-superposition method is employed to reduce the number of degrees of freedom that describe the dynamic deformation of the flexible bodies. An algorithmic differentiation method is used to evaluate partial derivatives needed in Lagrange's equations. An adjoint method is then used to assemble the total derivatives of functions of interest with respect to topology and control design variables. After detailing this framework, a numerical example is implemented for the benchmark cart-pole problem.