The scaled boundary finite element second order sensitivity desing and fracture mechanics analysis

Xiangyun Long, Chao Jiang, Xu Han, Xingsheng Sun, Dequan Zhang

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


The scaled boundary finite element method is a semi-analytical method that only needs to mesh on the boundary without fundamental solution, which makes it powerful to deal with singular and unbounded problem. This paper aims to propose a second order sensitivity analysis method for the scaled boundary finite element method, which can calculate the second order gradients of the responses with respect to the parameters accurately and efficiently. An improved first order sensitivity analysis method is presented through establishing a new Hamilton eigen-problem equation with only right eigenvectors. The second order Hamilton eigen-problem equation is constructed and the semi-analytical sensitivities of displacements and stresses are further obtained by a series of differential equation. The proposed method is then applied to the shape sensitivity analysis of linear cracked structures and corresponding uncertainty propagation analysis. Finally, two numerical examples are investigated to demonstrate the validity of the proposed method.

Original languageEnglish
Pages (from-to)42-54
Number of pages13
JournalGuti Lixue Xuebao/Acta Mechanica Solida Sinica
Issue number1
StatePublished - Feb 1 2015

Bibliographical note

Publisher Copyright:
©, 2015, Huazhong University of Science and Technology. All right reserved.


  • Fracture mechanics
  • Hamilton eigenproblem equation
  • Sensitivity analysis
  • The scaled boundary finite element method
  • Uncertainty propagation

ASJC Scopus subject areas

  • Mechanics of Materials


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