Theory and Numerics of a Surface-Related Shell Formulation

The solution of structural analysis problems, especially of shell structures, demands an efficient numerical solution strategy. Since one-sided contact problems are investigated, the shell model is formulated with respect to one of the outer surfaces, i.e. the shell formulation is surface-related. In particular the investigation of textile reinforced strengthening layers [

2

] will be carried out by this approach.

Since even shells are three-dimensional structures, i.e. bodies, the basic field equations of continuum mechanics must be the starting point. This set of partial differential equations with pertinent boundary conditions has to be solved. An efficient numerical solution of this problem becomes easier, if the problem is reformulated against a background of variational calculus. The discretization of the resulting variational formulation is, among others, the source of several locking phenomena.

The presented shell formulation uses linear shell kinematics with six displacement parameters, circumventing a rotational formulation. This low-order shell kinematics produces parasitical strains and stresses, leading to wrong or even useless results. Therewith an extension and/or adjustment of well- known techniques to prevent or reduce locking like the assumed natural strain (ANS) method [

3

] and the enhanced assumed strain (EAS) method [

4

] has to be performed.

Using these adapted methods, a reliable and efficient solid-shell element with tremendously reduced locking properties is obtained. This concept comprises the utilization of unmodified three-dimensional constitutive relations by a minimal number of kinematical parameters [

1

].With the aid of two nonlinear examples, the reliability and the efficiency of the new solid-shell element is demonstrated.