T-Splines for Isogeometric Analysis of the Large Deformation of Elastoplastic Kirchhoff–Love Shells

Abstract

In this paper, we develop a T-spline-based isogeometric method for the large deformation of Kirchhoff–Love shells considering highly nonlinear elastoplastic materials. The adaptive refinement is implemented, and some relatively complex models are considered by utilizing the superiorities of T-splines. A classical finite strain plastic model combining von Mises yield criteria and the principle of maximum plastic dissipation is carefully explored in the derivation of discrete isogeometric formulations under the total Lagrangian framework. The Bézier extraction scheme is embedded into a unified framework converting T-spline or NURBS models into Bézier meshes for isogeometric analysis. An a posteriori error estimator is established and used to guide the local refinement of T-spline models. Both standard T-splines with T-junctions and unstructured T-splines with extraordinary points are investigated in the examples. The obtained results are compared with existing solutions and those of ABAQUS. The numerical results confirm that the adaptive refinement strategy with T-splines could improve the convergence behaviors when compared with the uniform refinement strategy.