Stress intensity factors assessment in three-dimensional problems using the dual boundary element method in its isoparametric and NURBS-based isogeometric versions

Sérgio Gustavo Ferreira Cordeiro¹; Edson Denner Leonel¹

¹ University of São Paulo

doi:10.20906/CPS/CILAMCE2017-0020

Resumo

The mechanical collapse modelling of cracked structural components due to the fracture has major importance in the mechanical industry. Such analyses are often based on the linear elastic fracture mechanics concepts, which are well established nowadays. However, the application of such theory to structures with complex geometries and boundary conditions is still limited. To enable these analyses, the isogeometric approach has appeared as a promising alternative for generating efficiently complex geometries/topologies and approximating accurately the mechanical fields. In the present study, the classical isoparametric Dual Boundary Element Method (DBEM) and its NURBS-based isogeometric version are utilized for assessing the stress intensity factors (SIF) in 3D structures. The isogeometric formulation is based on the NURBS surfaces of any polynomial orders. The strong and hyper-singular integrals are addressed through the Guiggiani method. The SIF are determined by the displacement correlation technique and the collocation points are defined at the Greville abscissae. The NURBS-based mechanical fields satisfy the Hölder continuity condition at any point at the crack surfaces for polynomial orders higher than or equal to 2. It leads to a reduced number of collocation points at the crack surfaces in comparison with the isoparametric approach with discontinuous elements. The concepts of discontinuous and edge discontinuous collocation strategies for NURBS surfaces are introduced for addressing the tractions discontinuities and edge cracks at the NURBS intersection. One embedded crack problem and one edge crack problem are utilized for analysing the efficiency and accuracy of such approaches. The isogeometric DBEM is more accurate for SIF assessment with fewer degrees of freedom in comparison with the isoparametric approach. However, the computational cost of the isogeometric DBEM analysis is higher than the isoparametric approach due to the recursive nature of the NURBS bases functions. Then, the isoparametric DBEM is

Palavras-chave: Stress Intensity Factors; Dual Boundary Element Method; Isogeometric Analysis; NURBS surfaces