Anisotropic elastic applications in composite materials using the isogeometric boundary element method

This paper describes an isogeometric analysis of the boundary element method, called IGABEM, applied to anisotropic 2D plane elastic problems. The Lekhnitskii's anisotropic fundamental solution is used and the singular integral terms is regularized. For the weak singularity kernel, the Telles transform is used. On the other hand, in the strong singularity term, the Singularity Subtraction Technique - SST is used. The shape functions used are the Non-Uniform Rational B-Spline -NURBS. Thus, the same mathematical representation of Computer Aided Design -CAD is used in the implemented computational code. This avoids the generation of meshes and provides an exact representation of most complex geometries. As a reflection of this isoparametric concept, errors from geometric interpolation are excluded, improving numerical results. Furthermore, to increase the numerical efficiency of the code, the NURBS are decomposed into Bezier curves. To evaluate the accuracy of the formulation, complex problems using high-order isogeometric boundary elements are analyzed. Their results are compared to analytical solutions showing good agreement.

Automated summary

This paper presents an isogeometric analysis technique, called IGABEM, for anisotropic 2D plane elastic problems. The method uses the Lekhnitskii's anisotropic fundamental solution and regularizes the singular integral terms. The Non-Uniform Rational B-Spline (NURBS) shape functions are used to avoid mesh generation and accurately represent complex geometries. The numerical results of the high-order isogeometric boundary elements show good agreement with analytical solutions, indicating the accuracy of the formulation.