On the physical significance of higher order kinematic and static variables in a three-dimensional shell formulation

In recent years, considerable attention has been given to the development o f higher order plate and shell models. These models are able to approximate ly represent three-dimensional effects, while pertaining the efficiency of a two-dimensional formulation due to pre-integration of the structural stif fness matrix across the thickness. Especially, the possibility to use unmod ified, complete three-dimensional material laws within shell analysis has b een a major motivation for the development of such models. While the theoretical and numerical formulation of so-called 7-parameter sh ell models, including a thickness stretch of the shell, has been discussed in numerous papers, no thorough investigation of the physical significance of the additional kinematic and static variables, coming along with the ext ension into three dimensions, is known to the authors. However, realization of the mechanical meaning of these quantities is decisive for both a prope r modeling of shell structures, e.g. concerning loading and kinematic bound ary conditions, and a correct interpretation of the results. In the present paper, the significance of kinematic and static variables, appearing in a 7-parameter model proposed by Buchter and Ramm (1992a) are discussed. It is shown, how these quantities 'refine' the model behavior and how they can b e related to the 'classical' variables, such as 'curvatures' and 'stress re sultants'. Furthermore, the special role of the material law within such a formulation is addressed. It is pointed out that certain requirements must hold for th e variation of kinematic and static variables across the thickness, to ensu re correct results. In this context it is found, that the considered 7-para meter model can be regarded as 'optimal' with respect to the number of degr ees of freedom involved. (C) 2000 Elsevier Science Ltd. All rights reserved .