A modified approach for a scaled boundary shell formulation in structural isogeometric analysis

Abstract

In this contribution, an efficient modification of the scaled boundary finite element method for shells is presented to compute accurate results for h-refinement. While previous works on the scaled boundary shell formulation showed inaccurate and unstable results for fine meshes, this modification overcomes such problems by the assumption of a linear force distribution over the thickness. Furthermore, the shell formulation is derived in the framework of isogeometric analysis by discretizing the bottom surface of the shell as a reference surface. This leads to a solution for in-plane directions in a weak sense, while the scaling direction is solved analytically by a modified Padé expansion. Therefore, the normal vector on the reference surface is constructed and the shell is scaled along that leading to an extensible shell formulation incorporating a three-dimensional linear elastic constitutive relation. Since the isogeometric analysis is utilized, an exact derivation of the normal vector and its gradient is possible. Initial curvature locking and Poisson’s thickness locking are eliminated inherently while shear locking and volumetric locking are alleviated by mesh refinement. The power of the modified approach is presented by standard benchmark problems and compared to the results of the unmodified approach and standard shell formulations.