Acta Mechanica Solida Sinica

, Volume 26, Issue 2, pp 189–196 | Cite as

Hierarchical Stochastic Finite Element Method for Structural Analysis

  • Lufeng Yang
  • Yue’e Zhou
  • Jingjing Zhou
  • Meilan Wang


In this paper, the hierarchical approach is adopted for series representation of the stochastic nodal displacement vector using the hierarchical basis vectors, while the Karhunen-Loève series expansion technique is employed to discretize the random field into a set of random variables. A set of hierarchical basis vectors are defined to approximate the stochastic response quantities. The stochastic variational principle instead of the projection scheme is adopted to develop a hierarchical stochastic finite element method (HSFEM) for stochastic structures under stochastic loads. Simplified expressions of coefficients of governing equations and the first two statistical moments of the response quantities in the schemes of the HSFEM are developed, so that the time consumed for computation can be greatly reduced. Investigation in this paper suggests that the HSFEM yields a series of stiffness equations with similar dimensionality as the perturbation stochastic finite element method (PSFEM). Two examples are presented for numerical study on the performance of the HSFEM in elastic structural problems with stochastic Young’s Modulus and external loads. Results show that the proposed method can achieve higher accuracy than the PSFEM for cases with large coefficients of variation, and yield results agreeing well with those obtained by the Monte Carlo simulation (MCS).

Key words

hierarchical stochastic finite element method random field variational principle Karhunen-Loève series 


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2013

Authors and Affiliations

  • Lufeng Yang
    • 1
  • Yue’e Zhou
    • 1
  • Jingjing Zhou
    • 1
  • Meilan Wang
    • 1
  1. 1.The Key Lab of Engineering Disaster Prevention and Structural Safety of China Ministry of Education, School of Civil Engineering and ArchitectureGuangxi UniversityNanningChina

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