Mechanical modelling of three-dimensional cracked structural components using the isogeometric dual boundary element method

Abstract

The mechanical modelling of cracked structural components using Linear Elastic Fracture Mechanics (LEFM) concepts has major importance for structural integrity analysis. In addition, the Isogeometric Analysis (IGA) has recently emerged as a robust approach for analysing structural components directly from Computer-Aided Design (CAD) models. In this context, this study presents an isogeometric Dual Boundary Element Method (DBEM) formulation for the mechanical modelling of cracked three-dimensional structural components. The isogeometric formulation is based on NURBS surfaces. It was implemented regarding any polynomial orders for the basis functions. The strong singular and hypersingular integrals required by the DBEM are evaluated by the Guiggiani method. The C1 continuity is achieved at any collocation point inside the NURBS surfaces, ensuring the existence of hypersingular integrals. Consequently, discontinuous boundary elements are no longer required for the isogeometric DBEM, which enables an important reduction on the amount of collocation points at the crack surfaces. The Stress Intensity Factors (SIF) are evaluated by the displacement correlation technique. The geometrically exact description of the crack front eliminates the approximation errors related to the rotation of the displacement discontinuities with respect to the crack front local coordinate systems. Three applications involving edge and embedded cracks are presented. The isogeometric formulation provided accurate SIF results with less degrees of freedom at the crack surfaces in comparison with the conventional DBEM approach. However, the isogeometric DBEM approach has shown to be more expensive in terms of computational time.