Rainer Schlebusch

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.

On the Simulation of Textile Reinforced Concrete Layers by a Surface-Related Shell Formulation

The solution of structural analysis problems, especially of shell tructures, demands an efficient numerical solution strategy. Since unilateral 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 will be carried out by this approach.

On the Numerical Simulation of Thin Textile Reinforced Concrete Layers for the Strengthening of Shell Structures Using a Surface-Related Shell Theory

This contribution deals with the development of a surface-related shell theory and its conversion into the finite element method. In particular, composites made of thin textile reinforced concrete layers are examined for the strengthening of existing shell structures. The theoretical foundation of the shell theory is a modified form of the principle of Hu-Washizu functional. This variational principle permits the adapted formulation of the enhanced assumed strain method, Simo and Rifai [12]. Special attention is paid to the interface between the existing structure and the thin strengthening layer. It is modeled as a contact problem, whereby the contact conditions are introduced by following the continuum based formulation as suggested in Laursen and Simo [8] augmented to problems involving adhesion.

Special aspects of surface-related shell theories with application to contact problems

Publisher Summary Unlike the standard shell theories that refer to the middle surface of the shell, shell theories are introduced in the chapter with an outer shell surface. Fundamental relations of continuum mechanics are the starting-point for the derivation of a surface-related finite shell element. The variational principle of Hu-Washizu is stated and modified. In this formulation, the stress tensor is eliminated from the functional with the aid of an orthogonality condition. This allows introducing additional strain parameters to avoid or reduce locking phenomena respectively, whereby an expansion of the element stiffness matrix can be prevented. The continuum mechanical relationships are prepared for the utilization in the shell theory with a kinematical restriction. The chosen linear ansatz for the displacement field over the thickness is the only restriction of the bodys motion. The contact conditions are introduced by the continuum based formulation as suggested by Laursen and Simo. This formulation is extended to handle adhesion and is used to model the interface behavior in layered structures.