The Geometric Nonlinear Generalized Brazier Effect: a linearized finite element based solution

A thin walled circular tubular cross section under large bending moments ovalized and this is often denoted as the Brazier effect. This effect can also be seen in other types of profiles such as wind turbine blades. The paper shows that torsional moment gives a similar effect and this has been denoted the generalized Brazier effect. The original work of Brazier dealt with very large deformations that changed the cross section significantly and hereby also the bending moment of inertia and the bending moment capacity.

In this paper the aim is to describe the Brazier effect for smaller deformation not taking into account the change in moment of inertia. However, the generalized Brazier effect gives additional stresses directed perpendicular to the beam axis. In composite structures these extra stresses may influence the fatigue life significantly.

The paper demonstrates a linearized method to solve the complex non-linear geometric problem with a high accuracy. This is of importance in simulations of wind turbine blades, where the wind load simulations are based on small Finite Element models based on beam type elements in order to be realistic. The linearized solution exploits that the generalized Brazier effect is a local effect not influencing the overall mechanical behavior of the structure significantly. The offset is a nonlinear geometric beam-type Finite Element calculation, which takes into account the large displacements and rotations. The beam-type model defines the stresses which mainly are in the direction of the beam axis. The generalized Brazier effect is calculated as a linear load case based on these stresses.