A locking-free isogeometric thin shell formulation based on higher order accurate diagonalized strain projection via approximate dual splines

TL;DR

This paper introduces a locking-free isogeometric shell formulation that uses a novel diagonalized strain projection via approximate dual splines, enabling efficient computation and maintaining high accuracy.

Contribution

It proposes a new strain discretization and diagonalization technique that simplifies static condensation in isogeometric shell analysis, improving computational efficiency.

Findings

Achieves computationally efficient strain condensation without matrix inversion.

Maintains higher-order accuracy with optimal convergence rates.

Demonstrates effectiveness through numerical benchmarks on shells and beams.

Abstract

We present a novel isogeometric discretization approach for the Kirchhoff-Love shell formulation based on the Hellinger-Reissner variational principle. For mitigating membrane locking, we discretize the independent strains with spline basis functions that are one degree lower than those used for the displacements. To enable computationally efficient condensation of the independent strains, we first discretize the variations of the independent strains with approximate dual splines to obtain a projection matrix that is close to a diagonal matrix. We then diagonalize this strain projection matrix via row-sum lumping. Due to this diagonalization, the static condensation of the independent strain fields becomes computationally inexpensive, as no matrix needs to be inverted. At the same time, our approach maintains higher-order accuracy at optimal rates of convergence. We illustrate the numerical properties and the performance of our approach through numerical benchmarks, including a curved Euler-Bernoulli beam and the examples of the shell obstacle course.