Full Content is available to subscribers

Subscribe/Learn More  >

Three-Dimensional Non-Linear Shell Theory for Flexible Multibody Dynamics

[+] Author Affiliations
S. L. Han

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

O. A. Bauchau

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

Paper No. DETC2015-47163, pp. V006T10A031; 19 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 flexible multibody systems, many components are approximated as shells. Classical shell theories, such as Kirchhoff or Reissner-Mindlin shell theory, form the basis of the analytical development for shell dynamics. 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 shells, leading to three-dimensional deformations that generate complex stress states. To overcome this problem, a novel three-dimensional shell theory is proposed in this paper. Kinematically, the problem is decomposed into an arbitrarily large rigid-normal-material-line motion and a warping field. The sectional strains associated with the rigid-normal-material-line motion and the warping field are assumed to remain small. As a consequence of this kinematic decomposition, the governing equations of the problem fall into two distinct categories: the global equations describing geometrically exact shells and the local equations describing local deformations. The governing equations for geometrically exact shells are nonlinear, two-dimensional equations, whereas the local equations are linear, one dimensional, provide the detailed distribution of three-dimensional stress and strain fields. Based on a set of approximated solutions, the local equations is reduced to the corresponding global equations. In the reduction process, a 9 × 9 sectional stiffness matrix can be found, which takes into account the warping effects due to material heterogeneity. In the recovery process, three-dimensional stress and strain fields at any point in the shell can be recovered from the two-dimensional shell solution. The proposed method proposed is valid for anisotropic shells with arbitrarily complex through-the-thickness lay-up configuration.

Copyright © 2015 by ASME



Interactive Graphics


Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature

Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal

Citing articles are presented as examples only. In non-demo SCM6 implementation, integration with CrossRef’s "Cited By" API will populate this tab (http://www.crossref.org/citedby.html).

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In