A systematic development of solid-shell element formulations for linear and non-linear analyses employing only displacement degrees of freedom

In the present contribution we propose a so-called solid-shell concept which incorporates only displacement degrees of freedom. Thus, some major disadvantages of the usually used degenerated shell concept are overcome. These disadvantages are related to boundary conditions|the handling of soft and hard support, the need for special co-ordinate systems at boundaries, the connection with continuum elements|and, in geometrically non-linear analyses, to a complicated update of the rotation vector. First, the kinematics of the so-called solid-shell concept in analogy to the degenerated shell concept are introduced. Then several modi cations of the solid-shell concept are proposed to obtain locking-free solid- shell elements, leading also to formulations which allow the use of general three-dimensional material laws and which are also able to represent the normal stresses and strains in thickness direction. Numerical analyses of geometrically linear and non-linear problems are nally performed using solely assumed natural shear strain elements with a linear approximation in in-plane direction. Although some considerations are needed to get comparable boundary conditions in the examples analysed, the solid-shell elements prove to work as good as the degenerated shell elements. The numerical examples show that neither thickness nor shear locking are present even for distorted element shapes