Adaptive methods with C1 splines for multi-patch surfaces and shells

Abstract

We introduce an adaptive isogeometric method for multi-patch surfaces and Kirchhoff–Love shell structures with hierarchical splines characterized by $C^1$ continuity across patches. We extend the construction of smooth hierarchical splines from the multi-patch planar setting to analysis suitable $G^1$ surfaces. The adaptive scheme to solve fourth order partial differential equations is presented in a general framework before showing its application for the numerical solution of the bilaplacian and the Kirchhoff–Love model problems. A selection of numerical examples illustrates the performance of hierarchical adaptivity on different multi-patch surface configurations.