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 modiÿcations of the solid-shell concept are proposed to obtain locking-free solidshell 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 ÿnally 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. ? 1998 John Wiley & Sons, Ltd.

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 modiÿcations of the solid-shell concept are proposed to obtain locking-free solidshell 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 ÿnally 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. ? 1998 John Wiley & Sons, Ltd.

To describe elastic material behavior the starting point is the isochoric-volumetric decoupling of the strain energy function. The volumetric part is the central subject of this contribution. First, some volumetric functions given in the literature are discussed with respect to physical conditions, then three new volumetric functions are developed which fulfill all imposed conditions. One proposed function which contains two material parameters in addition to the compressibility parameter is treated in detail. Some parameter fits are carried out on the basis of well-known volumetric strain energy functions and experimental data. A generalization of the proposed function permits an unlimited number of additional material parameters.  Dedicated to Professor Franz Ziegler on the occasion of his 60th birthday. [S0021-8936(00)00901-6]

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