Recent developments in the evaluation of the 3D fundamental solution and its derivatives for transversely isotropic elastic materials

Electronic Journal of Boundary Elements

L. Távara¹  F. París¹  V. Mantič¹  J.E. Ortiz¹ 

[1] School of Engineering, University of Seville

关键词: transversely isotropic materials;    Stroh formalism;    fundamental solution;    free-space Green’s functions;    Somigliana identity;    boundary integral equations;    boundary element method;   

DOI  :  

学科分类：农业科学（综合）

来源: Rutgers University Libraries

【 摘 要 】

Explicit closed-form real-variable expressions of a fundamental solution and its derivatives for three-dimensional problems in transversely linear elastic isotropic solids are presented. The expressions of the fundamental solution in displacementsUikand its derivatives, originated by a unit point force, are valid for any combination of material properties and for any orientation of the radius vector between the source and field points. An ex- pression ofUikin terms of the Stroh eigenvalues on the oblique plane normal to the radius vector is used as starting point. Working from this expression ofUik , a new approach (based on the application of the rotational symmetry of the material) for deducing the first and second order derivative kernels,Uik,jandUik,jlrespectively, has been developed. The expressions of the fundamental solution and its derivatives do not suffer from the difficulties of some previous 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 rotational symmetry axis. The expressions ofUik ,Uik,jandUik,jlare presented in a form suitable for an efficient computational implementation in BEM codes.

【 授权许可】

Unknown