FINITE-ELEMENT ANALYSIS OF SMOOTH, FOLDED AND MULTISHELL STRUCTURES

The paper is concerned with the nonlinear theory and finite element an alysis of shell structures with an arbitrary geometry, loading and bou ndary conditions. A complete set of shell field equations and side con ditions (boundary and jump conditions) is derived from the basic laws of continuum mechanics. The developed shell theory includes the so-cal led drilling couples as well as the drilling rotation. It is shown tha t this property is crucial in the analysis of irregular shell structur es, such as those containing folds, branches, column supports, stiffen ers, etc. The relevant variational principles with relaxed regularity requirements are also presented. These principles provide the mathemat ical basis for the formulation of various classes of shell finite elem ents. The developed finite elements include a displacement/rotation ba sed Lagrange family, a stress resultant based mixed and a semi-mixed f amily as well as so-called assumed strain elements. All elements have six degrees of freedom at each node, three translational and three rot ational ones, including the drilling rotation formulated on the founda tion of an exact (in defined sense) shell theory. As such, they are eq ually applicable to smooth as well as to irregular shell structures. T he general applicability of the developed elements is illustrated thro ugh an extensive numerical analysis of the representative test example s. In order to obtain a still deeper insight into the problem a Lagran ge family of standard degenerated shell elements with five degrees of freedom per node and an element with six degrees of freedom per node b ased on the von Karman plate theory are considered as well. The presen ted numerical results include complex plate and doubly-curved shell st ructures. Linear and non-linear solutions with a pre- and post-bucklin g analysis are discussed.