Moving local mesh based on analysis-suitable T-splines and Bézier extraction for extended isogeometric finite element analysis - Application to two-dimensional crack propagation

Abstract

We propose a moving local mesh for extended isogeometric analysis exploiting finite element data structures based on Bézier extraction of analysis-suitable T-splines. The local mesh, which is a refined subdomain, can be translocated over the physical space with no changes in its topological size and its polynomial functions, i.e. the number of elements, polynomial functions and their continuity remain the same for any potential change in the local mesh place. The idea is to consider the whole space as one or multiple domains of uniform rational B-splines, within which a subdomain is refined, in order to obtain two standardized local refinement and Bézier extraction operators. The local operators are compatible with every subdomain that has the same topological size. They are computed one single time and used for each iteration to find new refined control points of another specified subdomain. The computational time of isogeometric analysis is improved using extended sets of control points and parametric knots. These extended sets allow to use predetermined numbers in the connectivity arrays to describe the whole control net and physical mesh regardless of the local mesh place. It means there is no need to rebuild the element connectivity in each iteration for mapping the control points and physical nodes. A description for the implementation of this moving local mesh in isogeometric analysis is given, and three numerical examples in crack propagation analysis are studied. • Moving local mesh without knot reinsertion and element connectivity reconstruction. • A detailed description for the implementation + an updating algorithm. • Three numerical examples in crack propagation analysis for the validation.