Finite Rotation handling in Dolfin
This document describes how three dimensional finite rotations can be handled in Dolfin. Finite rotations are of interest in structural computational mechanics when dealing with Timoshenko beams and Mindlin shells with the so-called drilling degree of freedoms.
The idea is tested by developing a simple nonlinear beam model.
By using the provided library the implementation of Mindlin shell models with drilling degree of freedoms should be rather straighforward. Note however that alleviating shell shear locking would not be as easy as here with beams.
Besides how to handle with finite rotations, this document explains the following techniques
use of
conditionals in UFL expressionscustom
Assemblyprocedurescompiled extension to the Dolfin python interface
A few solution steps of this demo, where a beam is loaded by a force and a coaxial torque at its free end, will look like
