Verbesserung der Ermittlung der Quernormalspannung im Rahmen der Finite-Elemente-Analyse von Faserverbundstoffen

Abstract

The present thesis describes a method which, based on the laminate theory in accordance with Whitney/Pagano, furnishes improved transverse normal stresses. For this purpose, starting from the force equilibriums, a relation is derived between transverse shear stresses and transverse forces. The resulting functional matrix contains on its elements terms which are quadratic in z. This approach has two essential advantages over determining the transverse shear forces from the transverse shear distortions. On one hand, one obtains steady profiles of the transverse shear stresses over the laminate thickness. On the other hand, now it is also possible to calculate the transverse normal stress. For this purpose, the transverse forces must be derived to x and y. The above functional matrix is integrated over z. The execution of these steps comprised two essential points. First, the derivations of transverse forces had to be provided by the B2000 finite element program. This meant that the corresponding B2000 subroutine had to be extended to the calculation of the second derivatives of the interpolation functions. Subsequently, the SPANNUNG.FOR program developed at the Institute for Structural Mechanics of the German Aerospace Research Establishment (DLR), Braunschweig, was extended by the integration of the functional matrix in thickness direction and by the calculation of the transverse normal stress. The efficiency of this method was tested in a number of example calculations. (orig.)Available from TIB Hannover: RN 4948(1995/23) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman