Computational Mechanics

, Volume 63, Issue 1, pp 35–48 | Cite as

A beam formulation based on RKPM for the dynamic analysis of stiffened shell structures

  • Y. X. Peng
  • A. M. ZhangEmail author
  • S. F. Li
  • F. R Ming
Original Paper


A beam formulation based on reproducing kernel particle method (RKPM) for the dynamic analysis of stiffened shell structures is presented in this paper. The kinematic description of a beam is obtained based on the Timoshenko beam theory. By using the principle of virtual power, the governing equations of a three-dimensional beam are derived. To obtain the numerical model of stiffened shell structures, two schemes are adopted: one is model stiffeners by the RKPM beam formulation, the other one is model the entire stiffened shell by the RKPM shell formulation. In the first scheme, the coupling model of RKPM shell and beam formulation is obtained by adding the corresponding quantities in their governing equations. In the second scheme, by determining the support domain of a stress point according to which component the stress point is located, the full shell simulation is achieved. The reliability and accuracy of those two schemes are verified by several numerical examples.


RKPM Meshfree method Stiffened shell Timoshenko beam 



The authors thank the National Natural Science Foundation of China (U1430236) for their support.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Y. X. Peng
    • 1
  • A. M. Zhang
    • 1
    Email author
  • S. F. Li
    • 2
  • F. R Ming
    • 1
  1. 1.College of Shipbuilding EngineeringHarbin Engineering UniversityHarbinChina
  2. 2.Department of Civil and Environmental EngineeringUniversity of CaliforniaBerkeleyUSA

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