Prism solid-shell with heterogonous and hierarchical approximation basis
Lukasz Kaczmarczyk  1@  , Zahur Ullah  2@  , Pearce Chris  3@  
1 : University of Glasgow  -  Website
Glasgow, G12 8QQ -  United Kingdom
2 : University of Glasgow  (Glasgow Univ.)  -  Website
Glasgow G12 8QQ Scotland -  United Kingdom
3 : School of Engineering, The University of Glasgow  (Glasgow Univ.)  -  Website
Glasgow G12 8QQ Scotland -  United Kingdom

A solid-shell element which does not possess rotational degrees of freedom and which is applicable to thin plate/shell problems is considered. The element approximation is constructed in prisms, where displacements on the upper and lower surfaces are approximated in the global coordinate system. In addition, two other fields are defined in the shell natural (local) coordinate system that represent the components of the displacement vector in both the current shell normal direction and the current shell tangent plane. To each field, an arbitrary order of approximation can be defined, and all fields reproduce a complete and conforming polynomial approximation basis for the solid prism element.
In examples (see Figure 1) we will show that this element is free from shear, membrane and thickness locking. It is not necessary to augment the formulation with an assumed natural strain (ANS) field or enhanced assumed strain (EAS) field or to use reduced integration, making the element ideally suited for geometrically and physically nonlinear problems. This work builds on a substantial body of published work by a number of different authors, but most notably [1]. This new element is implemented in our in-house code MoFEM. 

[1] R Hauptmann and K Schweizerhof. A systematic development of ‘solid-shell' element formulations for linear and non-linear analyses employing only displacement degrees of freedom. International Journal for Numerical Methods in Engineering, 42(1):49–69, 1998. 

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