Evaluation of strongly singular domain integrals for internal stresses in functionally graded materials analyses using RIBEM

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• 作者：Hai-Feng Peng (1)
  Jian Liu (1)
  Qiang-Hua Zhu (1)
  Ch. Zhang (2)
  
  1. School of Aeronautics and Astronautics ; Faculty of Vehicle Engineering and Mechanics ; Dalian University of Technology ; 116024 ; Dalian ; China
  2. Department of Civil Engineering ; University of Siegen ; D-57068 ; Siegen ; Germany
  
• 关键词：Stress integral equations ; Functionally graded materials ; Strongly singular domain integral ; Singularity separation technique ; Radial integration method
• 刊名：Acta Mechanica Solida Sinica
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：30
• 期：6
• 页码：917-926
• 全文大小：578 KB
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• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Mechanics, Fluids and Thermodynamics
  Engineering Fluid Dynamics
  Numerical and Computational Methods in Engineering
  Chinese Library of Science
  
• 出版者：The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of
• ISSN：1614-3116

文摘

An accurate evaluation of strongly singular domain integral appearing in the stress representation formula is a crucial problem in the stress analysis of functionally graded materials using boundary element method. To solve this problem, a singularity separation technique is presented in the paper to split the singular integral into regular and singular parts by subtracting and adding a singular term. The singular domain integral is transformed into a boundary integral using the radial integration method. Analytical expressions of the radial integrals are obtained for two commonly used shear moduli varying with spatial coordinates. The regular domain integral, after expressing the displacements in terms of the radial basis functions, is also transformed to the boundary using the radial integration method. Finally, a boundary element method without internal cells is established for computing the stresses at internal nodes of the functionally graded materials with varying shear modulus.