Scaled boundary isogeometric analysis for 2D elastostatics

Abstract

A new numerical method, scaled boundary isogeometric analysis (SBIGA) combining the concept of the scaled boundary finite element method (SBFEM) and the isogeometric analysis (IGA), is proposed in this study for 2D elastostatic problems with both homogenous and inhomogeneous essential boundary conditions. Scaled boundary isogeometric transformation is established at a specified scaling center with boundary isogeometric representation identical to the design model imported from CAD system, which can be automatically refined without communication with the original system and keeping geometry invariability. The field variable, that is, displacement, is constructed by the same basis as boundary isogeometric description keeping analytical features in radial direction. A Lagrange multiplier scheme is suggested to impose the inhomogeneous essential boundary conditions. The new proposed method holds the semi-analytical feature inherited from SBFEM, that is, discretization only on boundaries rather than the entire domain, and isogeometric boundary geometry from IGA, which further increases the accuracy of the solution. Numerical examples, including circular cavity in full plane, Timoshenko beam with inhomogenous boundary conditions and infinite plate with circular hole subjected to remotely tension, demonstrate that SBIGA can be applied efficiently to elastostatic problems with various boundary conditions, and powerful in accuracy of solution and less degrees of freedom (DOF) can be achieved in SBIGA than other methods.