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.

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As known from nearly incompressible elasticity, selective reduced integration (SRI) is a simple and effective method of overcoming the volumetric locking problem in 2D and 3D solid elements. This method of finite elastoviscoplasticity is discussed as are its well-known limitations. In this context, an isochoric-volumetric decoupled material behavior is assumed and thus the additive deviatoric-volumetric decoupling of the consistent algorithmic moduli tensor is essential. By means of several numerical examples, the performance of elements using selective reduced integration is demonstrated and compared to the performance of other elements such as the enhanced assumed strain elements. It is shown that a minor modification, with little numerical effort, leads to rather robust element behaviour. The application of this process to so-called solid-shell elements for thin-walled structures is also discussed. IntroductionIt is a well-known fact, that the three-dimensional standard linear eight-node displacement element (here denoted as Q1) exhibits severe locking for nearly or fully incompressible material. Rubber elasticity or metal plasticity are examples for nearly incompressible material behavior. Rubber is characterized by a large ratio of the bulk modulus to the shear modulus. In metal plasticity the plastic deformation is isochoric, i.e. fully incompressible, and the compressible part is a result from elastic deformations only, which remain small in many applications. In both cases reliable results with the standard Q1 element cannot be expected. Due to the volumetric locking behavior of the Q1 element, additional measures are necessary to overcome this problem. Various methods are known from literature and are currently discussed. Among others, a brief review of some of these methods is given in the following as a reference for the developments shown in this contribution. Our focus is particularly on the capabilities concerning finite non-linear deformations: