Research colloquium: Spatial extension of a plane finite element code for the analysis of principal stress directions in shell structures modeled with continuum elements

As part of the research colloquium for final theses, doctoral candidates and postdoctoral researchers, we cordially invite you to join us on Tuesday, 02.07.2024, at 16.30 in room 3516 (Mönchebergstr. 7).

Mr. Jonathan Lötz will present his master thesis with the title

"Spatial extension of a plane finite element code for the analysis of principal stress directions in shell structures modeled with continuum elements"

will be presented.

Abstract: This thesis deals with the three-dimensional extension of a finite element program code. First, some continuum mechanical basics are explained. The basis is the momentum balance under the assumption of a deformable body. The linear elastic material law is introduced in the form of a four-stage tensor. In addition, the essential equations for the principle of virtual displacements are derived. Furthermore, the essential aspects of plane and spatial FEM are explained. This divides the area under consideration into finite elements, which are described with the aid of approach functions and load and stiffness tensors. Furthermore, the \textsc{Gauss-Legendre} integration is presented as a programming-oriented integration method. After the basics, the changes that have become necessary as part of the extension are discussed in more detail. These relate in particular to the finite elements used and the export function for the results. After the necessary changes have been made, three examples (beam, slab, shell) are presented on which the displacements and stresses have been determined. Finally, two variants for setting up the stiffness matrix will be compared with regard to their performance.

We look forward to seeing you there!