On a stress resultant geometrically exact shell model. Part VII: Shell intersections with [formula omitted]-DOF finite element formulations

Abstract

If the mid-surface of a shell is smooth, the classical theory describes the orientation of the director field attached to the mid-surface by two independent (rotational) degrees of freedom. At a shell intersection, where this smoothness assumption no longer holds, it is shown that the director field in the full nonlinear continuum shell equations must be necessarily described by three degrees of freedom. This added degree of freedom, however, is totally unrelated to the so-called drill rotation, widely used as a means of tackling the shell intersection problem. A computational procedure involving a trivial modification of the global singularity-free update procedure described in Part III of this work is described, which completely resolves the shell intersection problem without introducing ‘drill springs’ or related ad-hoc devices. The proposed approach leaves unchanged standard finite element formulations in terms of 5 DOF/node, affects only the global update formulae and exhibits excellent performance, as illustrated by representative numerical simulations.