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Three-Dimensional Plate Theory for Flexible Multibody Dynamics

[+] Author Affiliations
Shilei Han

University of Michigan - Shanghai Jiao Tong University Joint Institute, Shanghai, China

Olivier A. Bauchau

The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong

Paper No. DETC2015-47249, pp. V006T10A033; 18 pages
  • ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Boston, Massachusetts, USA, August 2–5, 2015
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5716-8
  • Copyright © 2015 by ASME


In structural analysis, many components are approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theories, form the basis of the analytical developments. The advantage of these approaches is that they leads to simple kinematic descriptions of the problem: the plate’s normal material line is assumed to remain straight and its displacement field is fully defined by three displacement and two rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite plates, leading to three-dimensional deformations that generate complex stress states. To overcome this problem, several high-order, refined plate theories have been proposed. While these approaches work well for some cases, they often lead to inefficient formulations because they introduce numerous additional variables. This paper presents a different approach to the problem: based on a finite element semi-discretization of the normal material line, plate equations are derived from three-dimensional elasticity using a rigorous dimensional reduction procedure.

Copyright © 2015 by ASME



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