A local discrete strain gap approach for the isogeometric analysis of thin shell structures

In this paper, we present an isogeometric method for the analysis of thin shell structures, taking into consideration the linear elastic model [1] in a displacement-based formulation. The aim of the present work is to develop a method for the elimination of geometrical locking phenomena typical of vanishing thickness situations. Various methods, including the Discrete Shear Gap method proposed by Bletzinger et al. [2] and generalized subsequently to the so called Discrete Strain Gap method [3], are invoked for the approximation of the appropriate shear strain components causing spurious deformation effects in pure bending situations. In order to apply the methods the discrete equilibrium equations are derived element-wise resorting to the extraction of Bernstein polynomials from the NURBS interpolation basis [4]. This step permits to localize the displacement field over each single element and to apply the interpolation of appropriate strain components through the discrete strain gaps at local nodes. An investigation over a set of benchmark cases is presented.