Development of C1 Smooth Basis in Isogeometric Analysis for Multi-Patch Domain

Due to the ever-increasing need for computational accuracy, various new methodologies are being developed or improvised. One such advancement over the standard finite element analysis (FEA) is the isogeometric analysis (IGA) which is a spline-based technique with a framework of FEA. IGA provides the advantage of geometrical exactness and C1 continuous parametric space over the element domain. However, its continuity is compromised (C0) at patches represented by common boundaries (∏i). This junction, in the parametric domain, is defined by the connecting point between two adjacent basis functions of adjoining patches whose end derivatives are discontinuous. Imposing C1 continuity can provide higher numerical accuracy and faster convergence. This study mainly focuses on generating new smooth basis functions, by manipulating the C0 basis of degree (p) >= 2 at neighboring patches in which two dissimilar pth degree curves are locally adjusted to satisfy continuity requirements. We have tested our model by solving Poisson and biharmonic equations that replicate governing differential equations of various structural mechanics problems. Its effectiveness is checked against conventional two patch domains in IGA through displacement plots and error estimates. Moreover, this novel approach can be extended to shell elements, phase-field models, and XIGA.