A general, efficient and robust boundary element method (BEM) formulation for the numerical solution of
9 three-dimensional linear elastic problems in transversely isotropic solids is developed in the present work.
The BEM formulation is based on the closed-form real-variable expressions of the fundamental solution
11 in displacements Uik and in tractions Tik , originated by a unit point force, valid for any combination
of material properties and for any orientation of the radius vector between the source and field points.
13 A compact expression of this kind for Uik was introduced by Ting and Lee (Q. J. Mech. Appl. Math.
1997; 50:407–426) in terms of the Stroh eigenvalues on the oblique plane normal to the radius vector.
15 Working from this expression of Uik , and after a revision of their final formula, a new approach (based
on the application of the rotational symmetry of the material) for deducing the derivative kernel Uik, j
17 and the corresponding stress kernel i jk and traction kernel Tik has been developed in the present
work. These expressions of Uik , Uik, j , i jk and Tik do not suffer from the difficulties of some previous
19 expressions, obtained by other authors in different ways, with complex-valued functions appearing for
some combinations of material parameters and/or with division by zero for the radius vector at the
21 rotational-symmetry axis. The expressions of Uik , Uik, j , i jk and Tik have been presented in a form
suitable for an efficient computational implementation. The correctness of these expressions and of their
23 implementation in a three-dimensional collocational BEM code has been tested numerically by solving
problems with known analytical solutions for different classes of transversely isotropic materialsJunta de Andalucía TEP 1207Ministerio de Educación y Ciencia TRA2005-0676
