STRESS RESULTANT GEOMETRICALLY NONLINEAR SHELL THEORY WITH DRILLING ROTATIONS .3. LINEARIZED KINEMATICS

A consistent formulation of the geometrically linear shell theory with drilling rotations is obtained by the consistent linearization of the geometrically non-linear shell theory considered in Parts I and II of this work. It was also shown that the same formulation can be recover ed by linearizing the governing variational principle for the three-di mensional geometrically non-linear continuum with independent rotation field. In the finite element implementation of the presented shell th eory, relying on the modified method of incompatible modes, we were ab le to construct a four-node shell element which delivers a very high-l evel performance. In order to simplify finite element implementation, a shallow reference configuration is assumed over each shell finite el ement. This approach does not impair the element performance for the p resent four-node element. The results obtained herein match those obta ined with the state-of-the-art implementations based on the classical shell theory, over the complete set of standard benchmark problems.