09-27-2018 | Olivier Bauchau: Solutions of Boundary Value and Periodic Problems for Flexible Multibody Dynamics Systems

107th NIA CFD Seminar Topic: Solutions of Boundary Value and Periodic Problems for Flexible Multibody Dynamics Systems

Date: Thursday, September 27, 2018

Time: 11am-noon (EDT)

Room: NIA, Rm101

Speaker: Olivier A. Bauchau

Abstract: Traditionally, the solution of flexible multibody dynamics problems is obtained via time marching. Many problems, however, are formulated as boundary value or periodic problems. The dynamic response of flexible multibody systems will be investigated via the finite element method, within the framework of the motion formalism, which leads to governing equations presenting low-order nonlinearities. Boundary value and periodic problems require global interpolation schemes that approximate the unknown motion fields over the system’s entire period of response. The classical interpolation schemes developed for linear fields cannot be used for the nonlinear configuration manifolds, such as SO(3) or SE(3), that are used to describe the kinematics of multibody systems. Furthermore, the configuration and velocity fields are related through nonlinear kinematic compatibility equations.

It seems natural to implement the collocation version of the Fourier spectral method to determine periodic solutions of flexible multibody systems. Clearly, special procedures must be developed to adapt the Fourier spectral approach to flexible multibody systems. Assembly of the linearized governing equations at all the grid points leads to the governing equations of the spectral method. Numerical examples illustrate the performance of the proposed approach.

For periodic and boundary value problems, an approach based on the assembly of time- discretized elements provides an alternative approach to the problem. While it does not achieve the exponential convergence of Fourier spectral methods, it is computationally effective. The classical time integration schemes used in structural and multibody dynamics, such as the generalized-&alpha schemes, are not suitable for this approach. Time-discontinuous Galerkin schemes will be shown to be well suited for the solution of such problems.

The development of rigorous motion interpolation schemes also leads to interesting schemes for the spatial discretization of beam and shells. Spectral beam elements will be presented that are far simpler to implement than their counterparts based on the shape function used in classical finite element methods.

Speaker Bio: Dr. Bauchau earned his B.S. degree in engineering at the Université de Liège, Belgium, and M.S. and Ph.D. degrees from the Massachusetts Institute of Technology. He has been a faculty member of the Department of Mechanical Engineering, Aeronautical Engineering, and Mechanics at the Rensselaer Polytechnic Institute in Troy, New York (1983-1995), a faculty member of the Daniel Guggenheim School of Aerospace Engineering of the Georgia Institute of Technology in Atlanta, Georgia (1995-2010), a faculty member of the University of Michigan Shanghai Jiao Tong University Joint institute in Shanghai, China (2010-2015). He is now Igor Sikorsky Professor of Rotorcraft and Langley Professor at the Department of Aerospace Engineering at the University of Maryland.

His fields of expertise include finite element methods for structural and multibody dynamics, rotorcraft and wind turbine comprehensive analysis, and flexible multibody dynamics. He is a Fellow of the American Society of Mechanical Engineers, a Technical Fellow of the American Helicopter Society, and a Fellow of the American Institute of Aeronautics and Astronautics. His book entitled “Flexible Multibody Dynamics” has won the 2012 Textbook Excellence Award from the Text and Academic Authors Association. He is the 2015 recipient of the ASME d’Alembert award for lifelong contributions to the field of multibody system dynamics.