3D-based hp-adaptive first-order shell finite element for modelling and analysis of complex structures - Part 1: The model and the approximation

The paper presents a 3D-based adaptive first-order shell finite element to be applied to hierarchical modelling and adaptive analysis of complex structures. The main feature of the element is that it is equipped with 3D degrees of freedom, while its mechanical model corresponds to classical first-order shell theory. Other useful features of the element are its modelling and adaptive capabilities. The element is assigned to hierarchical modelling and hpq-adaptive analysis of shell parts of complex structures consisting of solid, thick- and thin-shell parts, as well as of transition zones, where h, p and q denote the mesh density parameter and the longitudinal and transverse orders of approximation, respectively. The proposed hp-adaptive first-order shell element can be joined with 3D-based hpq-adaptive hierarchical shell elements or 3D hpp-adaptive solid elements by means of the family of 3D-based hpq/hp- or hpp/hp-adaptive transition elements. The main objective of the first part of our research, presented in this paper, is to provide non-standard information on the original parts of the element algorithm. In order to do that, we present the definition of shape functions necessary for p-adaptivity, as well as the procedure for imposing constraints corresponding to the lack of elongation of the straight lines perpendicular to the shell mid-surface, which is the procedure necessary for q-adaptivity. The 3D version of constrained approximation presented next is the basis for h-adaptivity of the element. The second part of our research, devoted to methodology and results of the numerical research on application of the element to various plate and shell problems, are described in the second part of this paper. Copyright q 2006 John Wiley & Sons, Ltd