Numerical implementation of Asymmetric Mapping for Weak Singularities in High-Order Boundary Elements

This paper has discussed a cubic subparametric direct boundary element(CSDBE) formulation for linear elastic continuum, which is governed by the Lamé-Navier equation. asymmetric mapping technique is used to integrate the weak singularity term . The induced formulas are coded into a CSDBE and are verified by results of several examples, which are the simply connected region, the multiply connected region and the stress intensity problem. From a physical point of view, the simply connected region is the cantilever beam and the multiply connected region is the plate, which has one or more holes. The stress intensity problem is the double edge notched plate. The proposed numerical integration technique has yielded stable results. In addition, the effectiveness of degree of freedom is discussed through the examples. On the whole, a CSDBE is more effective than a linear boundary element using same the number of degree of freedoms. Considering the polynomial order used in the formulation, these results are natural. Meanwhile, the proposed numerical integration technique and formula derivation method can be used to realize the discontinuous boundary element used to satisfy the Hölder continuity.