Statische und dynamische Berechnungen von Schalen endlicher elastischer Deformationen mit gemischten finiten Elementen

This work is concerned with the numerical simulation of shell structures for nonlinear elastostatics and elastodynamics. The quadrilateral continuum based C"0 shell element is based on an extensible director field which accounts for deformation dependent thickness change. The finite element formulation relies on an enhanced assumed strain (EAS) expansion in order to facilitate the use of three-dimensional constitutive models. The nonlinear EAS method advocated by Simo and Armero is recast in a curvilinear coordinate description. Here, the EAS-expansion of the material displacement gradient leads to the local interpretation of enhanced covariant base vectors which are superposed on the compatible covariant base vectors. Two expansions of the enhanced covariant base vectors are given: First an extension of the underlying single extensible shell kinematics and second an improvement of the membrane part of the bi-linear element. Alternatively a nonlinear EAS formulation based on the Green-Lagrangian strain tensor is presented. Furthermore it is investigated if the EAS method is competitive to the assumed natural strain (ANS) method in order to eliminate transverse shear locking. Several possibilities for the finite element discretization of the extensible director field are discussed. It is shown that the simple bi-linear interpolation leads to artificial transverse normal strains which cause locking especially in the thin shell limit. As remedy a simple ANS interpolation is proposed. In addition to the extensible director formulation the 'classical' shell formulation which employs an inextensible director field in combination with the zero normal stress condition is considered. The singularity free description of finite rotations is able to deal with smooth shell midsurfaces as well as with shell intersections. After the spatial finite element discretization of both the extensible and the inextensible shell formulation the temporal discretization is considered. To this end the time stepping algorithm of Simo and Tarnow is extended to the developed shell formulations. The one-step method is able to conserve the total energy and thus furnishes a stable integration algorithm for the nonlinear theory. In contrast to this the Newmark trapezoidal rule exhibits blow-up of the solution for finite step sizes. Several numerical examples for elastostatics and elastodynamics show that the extensible shell formulation is able to deal with thin-shell structures as well as with large strain problems. In this context the conservation properties of the time stepping algorithm ensure the (unconditional) numerical stability. The same holds for the inextensible shell formulation in the case of large deformations and small strains. (orig.)SIGLEAvailable from TIB Hannover: RN 2767(1996,4) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman