Theorie und Numerik einer oberflächenorientierten Schalenformulierung

This doctorial thesis deals with the derivation of a mechanical model for the simulation of the load-bearing behavior of a strengthening layer made of textile reinforced concrete to strengthen a shell structure. The main focus lies on both the geometrical and physical non-linear three-dimensional shell formulation and on its transfer into an efficient finite element. The distinctive feature of the presented shell formulation is its surface-orientation. This enables the analysis of a strengthening layer applied on one of the outer surfaces of a structure in a very natural way, since a problem-oriented mechanical modeling is achieved. Hereby, in contrast to classical shell theories the three-dimensionality of the material behavior's description can completely maintained. This is necessary, since a more accurate modeling of the material behavior of textile reinforced concrete can only be done three-dimensional. Within the scope of this thesis an anisotropic hyper elastic constitutive relation is given in order to obtain a first approximation of textile reinforced concrete's material behavior against the background of material theory. Furthermore a specification of the hyper elastic constitutive relation is obtained upon the basis of the principle of material symmetry and is prepared for the application in the shell formulation. The numerical solution of the field problem necessitates the transfer of the surface-related shell formulation into a two-dimensional variational formulation in order to obtain a sound mathematical starting point for the conversion into an efficient volume shell element. For the realization of a numerical efficient finite element an element formulation using a low-order ansatz should be favored. Because of reducing the number of degrees of freedom and therewith of possible deformation modes, artificial stiffening effects will appear. A way out is given by a special extention of the assumed natural strain and the assumed strain method for the utilization in the presented surface-related shell formulation. This leads to a slightly higher numerical effort, but allows a reliable and efficient finite element formulation finally verified in distinct meaningful non-linear simulations.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Technische Universität Dresden

Year

2005

Author dc:creator

• Schlebusch, Rainer

Contributors dc:contributor

• Zastrau, Bernd W.
• Kienzler, Reinhold
• Kaliske, Michael

• Locking
• Methode der finiten Elemente
• Schalenformulierung
• Schalentheorie
• Variationsformulierung
• finite element method
• shell formulation
• shell theory
• variational formulation