Geometrically exact static isogeometric analysis of an arbitrarily curved spatial Bernoulli-Euler beam

TL;DR

This paper develops a geometrically exact isogeometric model for arbitrarily curved spatial Bernoulli-Euler beams, accurately capturing nonlinear strain distributions and the effects of curviness on structural response.

Contribution

It introduces a novel isogeometric approach incorporating the complete beam metric and exact constitutive relations for curved beams, ensuring objectivity and path-independence.

Findings

The model accurately predicts nonlinear responses of curved beams.

Curviness significantly influences structural behavior and must be considered in modeling.

Two basis update methods are effectively applied in the context of finite rotations.

Abstract

The objective of this research is the development of a geometrically exact model for the analysis of arbitrarily curved spatial Bernoulli-Euler beams. The complete metric of the beam is utilized in order to include the effect of curviness on the nonlinear distribution of axial strain over the cross section. The exact constitutive relation between energetically conjugated pairs is employed, along with four reduced relations. The isogeometric approach, which allows smooth connections between finite elements, is used for the spatial discretization of the weak form. Two methods for updating the local basis are applied and discussed in the context of finite rotations. All the requirements of geometrically exact beam theory are satisfied, such as objectivity and path-independence. The accuracy of the formulation is verified by a thorough numerical analysis. The influence of the curviness on the structural response is scrutinized for two classic examples. If the exact response of the structure is sought, the curviness must be considered when choosing the appropriate beam model.