Blending moving least squares techniques with NURBS basis functions for nonlinear isogeometric analysis

IsoGeometric Analysis (IGA) is increasing its popularity as a new numerical tool for the analysis of structures. IGA provides: (i) the possibility of using higher order polynomials for the basis functions; (ii) the smoothness for contact analysis; (iii) the possibility to operate directly on CAD geometry. The major drawback of IGA is the non-interpolatory characteristic of the basis functions, which adds a difficulty in handling essential boundary conditions. Nevertheless, IGA suffers from the same problems depicted by other methods when it comes to reproduce isochoric and transverse shear strain deformations, especially for low order basis functions. In this work, projection techniques based on the moving least square (MLS) approximations are used to alleviate both the volumetric and the transverse shear lockings in IGA. The main objective is to project the isochoric and transverse shear deformations from lower order subspaces by using the MLS, alleviating in this way the volumetric and the transverse shear locking on the fully-integrated space. Because in IGA different degrees in the approximation functions can be used, different Gauss integration rules can also be employed, making the procedures for locking treatment in IGA very dependent on the degree of the approximation functions used. The blending of MLS with Non-Uniform Rational B-Splines (NURBS) basis functions is a methodology to overcome different locking pathologies in IGA which can be also used for enrichment procedures. Numerical examples for three-dimensional NURBS with only translational degrees of freedom are presented for both shell-type and plane strain structures.