Isogeometric analysis for geometrically exact shell elements using Bézier extraction of NURBS with assumed natural strain method

In the present study, isogeometric analysis for geometrically exact shell considering the first-order shear deformation is studied. Since kinematics of the shell is formulated in the form of a general tensor in generalized curvilinear coordinates, isogeometric analysis of arbitrarily shaped shells is possible with a direct geometry link to NURBS. For the first-order shear deformable shell element, the assumed natural strain (ANS) method is normally used to alleviate membrane and transverse shear locking phenomenon. Due to a higher-order regularity between integration knot elements of NURBS basis function has, a locking phenomenon still appears even though the field consistent approach such as ANS is utilized. To solve this problem, we adopted Bézier extraction method which maps a piecewise C⁰ Bernstein polynomials basis onto NURBS basis to reduce element regularity for isogeometric shell analysis. For an arbitrarily shaped shell geometry generation using NURBS of the shell, the point data sets from the exact geometry shape can be used by the global interpolation. The test results of numerical examples using the developed method show the accuracy and robustness with a higher convergence rate of the proposed approach.