Numerical implementation for isogeometric analysis of thin-walled structures based on a Bézier extraction framework: nligaStruct

Abstract

We present an open Octave/Matlab package nligaStruct, for linear and nonlinear isogeometric analysis of thin-walled structures. nligaStruct is an extension of NLIGA in aspect of isogeometric structural analysis. A framework for Bézier extraction of T-spline and NURBS is embedded in the simulation pipeline. Both Reissner–Mindlin and Kirchhoff–Love assumptions are considered in the case of static bending and free vibration analysis of thin-walled structures (plates and shells). The convergence behaviors of these two assumptions for both plate and shell are thoroughly studied and compared. The discrete formulations for large deformation of Kirchhoff–Love shells considering geometrical and material nonlinearity are detailedly derived and carefully implemented. Three types of hyperelastic materials, including St. Venant–Kirchhoff, incompressible neo-Hookean and compressible neo-Hookean, are employed in the large deformation of Kirchhoff–Love shells. A series of popular benchmark examples and their geometrical models are demonstrated in the package. The numerical results are validated by comparing with analytical solutions and that obtained from commercial software. The postprocessing is self-contained and implemented by tessellation of Bézier elements. Finally, complete source codes and the data obtained from numerical examples are fully provided and free to access.