A new triangular element for crack front and the application in analysis of crack problems
Received:August 21, 2018  Revised:November 14, 2018
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DOI:10.7511/jslx20180821001
KeyWord:crack front element  crack problems  dual boundary element method  boundary integral equation  shape function
           
AuthorInstitution
周枫林 湖南大学 机械与运载工程学院, 长沙 ;湖南工业大学 机械工程学院, 株洲
谢贵重 湖南大学 机械与运载工程学院, 长沙
张见明 湖南大学 机械与运载工程学院, 长沙
李落星 湖南大学 机械与运载工程学院, 长沙
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Abstract:
      A new type of triangular element one edge of which lies on the crack front is developed for boundary element analysis of crack problems.The shape functions in this type of elements consist of two parts.The major part of the shape functions is constructed to approximate the sharp variation of the physical quantities including displacements and stresses near the crack front in the crack surfaces.The other part is the traditional type of shape functions that are defined for triangular elements.In the major part of the shape functions,an expression similar to √r is involved since it has been theoretically proved that the distribution of the displacement around the crack front is of the same order as that of √r. In the newly defined shape functions,a specially constructed term,which is of the same order as that of √r, is multiplied by the traditional shape functions.In order to guarantee the delta property of the shape functions,however,the values of the specially constructed term at the interpolation points should be divided by the corresponding coefficients of the shape function.The proposed elements should only be applied for approximation of physical quantities near the crack front.The geometric quantities in the same area should be approximated by a traditional method.In the application of this elements in the dual boundary element method for crack problems,the crack of displacements (CODs) in the crack surfaces is first computed.Then an extrapolation method is applied to compute the stress intensity factors at the crack front.As the demonstration example,a circle shaped crack in an infinite domain is considered.Three types of SIFs at the crack front are computed by the dual boundary element method with the new element.Comparisons with the analytical results have been made to demonstrate the validity and accuracy of the element.