## A mixed formulation for a general shell model.(English)Zbl 0758.73028

A mixed variational formulation for a shell based on Koiter theory is given. Starting up with the Kirchhoff-Love kinematics the orthogonality condition is weakened within the variational process. With that $$C^ 0$$- continuity is sufficient for all variables. In addition, as emphasized by the authors, locking doesn’t appear, since the penalty term causing the locking in Mindlin-Reissner-elements isn’t present. The shear force is decomposed in two parts, the one of which can be approximated in $$L^ 2$$ instead of $$H^ 1$$. By that means the conditions for existence and uniqueness of the solution of the saddle point problem, i.e. ellipticity- and the LBB-condition, are proven. It is also shown, that a piecewise plane approximation of the actual shell geometry is sufficient, i.e. flat elements can be used. The choice of actual shape functions according to the function spaces proposed by the authors, implementation and numerical testing on irregular meshes would be interesting in order to compare them with existing shell elements.
Reviewer: R.Rolfes

### MSC:

 74K15 Membranes 74S30 Other numerical methods in solid mechanics (MSC2010) 74P10 Optimization of other properties in solid mechanics