Error-controlled adaptive LR B-splines XIGA for assessment of fracture parameters in through-cracked Mindlin-Reissner plates

Abstract

This paper presents an error-controlled adaptive extended isogeometric analysis (XIGA) for assessment of fracture behavior for through-cracked Mindlin-Reissner plates. The locally refined (LR) B-splines that facilitate the local refinement are used as the basis functions for the approximations, while the kinematics of plates are described in terms of the Mindlin-Reissner plate theory. Appropriate enrichment functions for cracked plates are incorporated into the formulation to represent geometrically displacement discontinuities across the crack faces and singularity of the stress in the vicinity at the crack tips, thus cracks are modeled topologically independent of the computational mesh. Here we extend the Zienkiewicz-Zhu method-based error estimation to the XIGA formulation for cracks in Mindlin-Reissner plates such that non-smoothnesses and stress singularity are reflected accurately. We conduct the error-controlled adaptivity for local mesh refinement to enhance the accuracy and performance. Fracture parameters (i.e., mixed-mode intensity factors) are calculated through the contour interaction integral method in the context of Mindlin-Reissner plate theory. Several numerical examples for through-cracked plates are studied to show the accuracy and effectiveness of the proposed formulation in modeling fracture of cracked moderately thick plates.