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This paper developed a novel 6-node triangular boundary crack front element for 3D crack problems. The developed element method was constructed based on an 8-node serendipity element and a distance function that defines the distance from arbitrary point inside the element to the crack front. The specially constructed shape function captures the square-root asymptotic behavior of the distribution of the displacement nearby the crack front. In order to employ the crack front element in the dual boundary element method, conversion from conforming triangular crack front elements to non-conforming triangular ones was performed through a matrix transformation. In the implementation of dual boundary element method, a displacement extrapolation method is adopted to compute the stress intensity factor at the crack front. Finally, three examples were presented to verify the efficiency of our proposed crack front element. In all the numerical examples, the presented crack front element exhibits high accuracy and efficiency in the examples. [ABSTRACT FROM AUTHOR]

This paper presents a new and general construction method of special triangular elements with one edge lying in the crack front. In our method, principal items which represent the asymptotic properties around the crack front in local coordinate system are constructed. Based on the principal items, two groups of basis functions for crack front elements are introduced. Combining undetermined coefficients and basis functions, two types of crack front elements, which are denoted by low order crack front elements and high order ones, are constructed. Secondly, a displacement extrapolation technique with these newly developed elements is proposed. Applying this technique in the BEM applications for crack problems, numerical difficulties, which arise when two vertexes of the assisted line both locate inside the element, can be circumvented conveniently. Finally, two types of elements are employed in the dual boundary element codes for crack problems. Numerical examples are presented to verify the three types of elements. Results show that the stress intensity factors computed by employing these three developed elements are all very accurate compared with the existing results. [ABSTRACT FROM AUTHOR]

In this work, a novel approach is presented for three-dimensional nearly singular boundary element integrals for steady-state heat conduction. Accurate evaluation of the nearly singular integrals is an important issue in the implementation of boundary element method (BEM). In this paper, an exponential transformation is introduced to deal with the nearly singular integrals in three-dimensional BEM. First, a triangle polar coordinate system is introduced. Then, the exponential transformation is performed by five steps. For each step, a new transformation is proposed based on the distance from the source point to surface elements which is expressed as r 2 = O ( A k 2 ( θ ) ρ 2 + r 0 2 ) , and all steps can finally be unified into a uniform formation. Moreover, to perform integrations on irregular elements, an adaptive integration scheme considering both the element shape and the projection point associated with the proposed transformation is introduced. Numerical examples are presented to verify the proposed method. Results demonstrate the accuracy and efficiency of our method. [ABSTRACT FROM AUTHOR]