Helicoidal Shell Theory

DIA-SR 08-07The scientific activity of Professor Teodoro Merlini in the field of solid mechanics began in the early nineties. Starting from Reissner's 1965 note, and Fraeijs de Veubeke's variational works, he derived weak forms of the governing nonlinear equilibrium equations, keeping the material rotation within a consistent variational formulation. This formulation connects the rotation field with a workless stress field, the axial vector of the Biot stress tensor, which must be retained as a primary unknown field. These variational forms are successfully exploited in computational finite elasticity; an efficient 3D finite element based on independent rotations, and with internal constant rotation and Biot-axial fields, was delivered in the years 1995–1997. In order to obtain finite elements with a continuous rotation field, a consistent development of the previous ideas led to the establishment of a new modeling of the continuum, called the helicoidal modeling. With the valuable contribution of Ph. D. Marco Morandini, a successful 3D helicoidal finite element – endowed with a frame-invariant interpolation scheme – was developed and published in the years 2003–2005. Since then, the technology of this element has been used to build a new solid shell theory and the corresponding shell finite element. These last developments are fully detailed in this series of reports.