A selectively reduced degree basis for efficient mixed nonlinear isogeometric beam formulations with extensible directors

TL;DR

This paper introduces a reduced degree basis for isogeometric beam analysis that enhances computational efficiency and accuracy by allowing discontinuities in stress and strain fields, leveraging higher order continuity in displacement fields.

Contribution

It proposes a novel reduced degree basis for stress and strain fields in IGA beam formulations, improving efficiency and accuracy over traditional methods.

Findings

IGA outperforms conventional finite element analysis in accuracy per degree of freedom.

The reduced basis approach significantly improves computational efficiency.

The method ensures accurate rotational coupling and path-independent results.

Abstract

The effect of higher order continuity in the solution field by using NURBS basis function in isogeometric analysis (IGA) is investigated for an efficient mixed finite element formulation for elastostatic beams. It is based on the Hu-Washizu variational principle considering geometrical and material nonlinearities. Here we present a reduced degree of basis functions for the additional fields of the stress resultants and strains of the beam, which are allowed to be discontinuous across elements. This approach turns out to significantly improve the computational efficiency and the accuracy of the results. We consider a beam formulation with extensible directors, where cross-sectional strains are enriched to avoid Poisson locking by an enhanced assumed strain method. In numerical examples, we show the superior per degree-of-freedom accuracy of IGA over conventional finite element analysis, due to the higher order continuity in the displacement field. We further verify the efficient rotational coupling between beams, as well as the path-independence of the results.