A projected super-penalty method for the $C^1$-coupling of multi-patch isogeometric Kirchhoff plates

TL;DR

This paper introduces a super-penalty method for achieving $C^1$ continuity in non-conforming multi-patch isogeometric Kirchhoff plates, ensuring optimal accuracy and avoiding locking even on coarse meshes.

Contribution

The paper presents a novel super-penalty strategy based on $L^2$-projection for $C^1$ coupling in isogeometric Kirchhoff plates, with optimal accuracy and robustness on coarse meshes.

Findings

Achieves optimal convergence rates with B-splines.

Substantial accuracy gain over other penalty choices.

Method is lock-free on coarse meshes.

Abstract

This work focuses on the development of a super-penalty strategy based on the $L^2$-projection of suitable coupling terms to achieve $C^1$-continuity between non-conforming multi-patch isogeometric Kirchhoff plates. In particular, the choice of penalty parameters is driven by the underlying perturbed saddle point problem from which the Lagrange multipliers are eliminated and is performed to guarantee the optimal accuracy of the method. Moreover, by construction, the method does not suffer from locking also on very coarse meshes. We demonstrate the applicability of the proposed coupling algorithm to Kirchhoff plates by studying several benchmark examples discretized by non-conforming meshes. In all cases, we recover the optimal rates of convergence achievable by B-splines where we achieve a substantial gain in accuracy per degree-of-freedom compared to other choices of the penalty parameters.