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Nonlinear Dynamics

, Volume 80, Issue 3, pp 1133–1146 | Cite as

On the use of elastic middle surface approach in the large deformation analysis of moderately thick shell structures using absolute nodal coordinate formulation

  • Antti I Valkeapää
  • Hiroki Yamashita
  • Paramsothy Jayakumar
  • Hiroyuki Sugiyama
Original Paper

Abstract

In this study, a shear deformable shell element is developed based on the elastic middle surface approach using the absolute nodal coordinate formulation (ANCF) for the large deformation analysis of thin to moderately thick shell structures. The bilinear shape function is used to define the global position vector in the middle surface and the transverse gradient vector which defines the orientation and deformation of the cross section within the element. The plane stress assumption is used to remedy the Poisson’s thickness locking exhibited in the ANCF shell element formulated by the continuum mechanics approach, thus the stress distribution along the shell thickness is assumed to be constant. The cross-sectional frame is introduced to define strains of the initially curved shell element using the elastic middle surface approach. The curvature thickness and transverse shear lockings are alleviated using the assumed natural strain method, while the in-plane shear locking is removed using the enhanced assumed strain method. Several numerical examples are presented in order to demonstrate the performance of the shear deformable ANCF shell element based on the elastic middle surface approach developed in this study. The developed element is compared with the continuum mechanics-based ANCF shell element to shed light on the nature of the thickness locking exhibited in the bilinear shell element and its locking remedies.

Keywords

Flexible multibody dynamics Absolute nodal coordinate formulation Large deformation Shell element 

Notes

Acknowledgments

This research is supported by the Automotive Research Center (ARC) in accordance with Cooperative Agreement W56HZV-04-2-0001 U.S. Army Tank Automotive Research, Development and Engineering Center (TARDEC). The support of first author by the National Graduate School in Engineering Mechanics, Finland and the Academy of Finland (#138574) is acknowledged. Financial support for the last author received from FunctionBay Inc. is also acknowledged.

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Antti I Valkeapää
    • 1
  • Hiroki Yamashita
    • 2
  • Paramsothy Jayakumar
    • 3
  • Hiroyuki Sugiyama
    • 2
  1. 1.Department of Mechanical EngineeringLappeenranta University of TechnologyLappeenrantaFinland
  2. 2.Department of Mechanical and Industrial EngineeringThe University of IowaIowa CityUSA
  3. 3.US Army RDECOM TARDECWarrenUSA

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