Michael Fischer
Michael Fischer did his diploma thesis at the Chair of Structural Analysis at TU München in cooperation with the European aerospace company EADS. He graduated from civil engineering (at TUM) in 2007 and from come.tum/BGCE in 2008. The title of his master's thesis was "Design and implementation of an object-oriented and distributed finite element program". Now he is doing his PhD at the chair of Structural Analysis (see his homepage ) under supervision of Prof. Bletzinger.
Diploma Thesis:
Geometric and volumetric locking effects at solid finite elements and their
avoidance by the EAS method
It is well known that finite elements based upon the virtual work principle often show slow convergence and thus provide inaccurate results. Already in the seventies the term "locking" established itself for the phenomenon that is characterized by a severe underestimation of the displacements. As a consequence, also the quality of results of optimization computations are heavily reduced, especially in the context of solid finite elements at thin structures.
The aims of this diploma thesis were the analysis of geometric and volumetric locking effects at solid finite elements, the investigation of remedies and the implementation of improved element formulations in the company's research code LAGRANGE.
Application of the enhanced finite element formulation in structural optimization.
Starting from the basics of continuum mechanics and the finite element theory, a systematic analysis of locking phenomena is presented, concerning the mathematical, numerical and mechanical point of views.
Focus of observation among the concepts to avoid locking is the Enhanced Assumed Strain Method (EAS). Based on the Hu-Washizu principle, a variational basis and mathematical foundation is developed for this method. The derivation of the theory, the application for solid elements and the efficient implementation of the algorithm in the company's research code LAGRANGE is shown. An overview of other established concepts like Reduced Integration, Assumed Natural Strains method (ANS) and the Discrete Strain Gap method (DSG) is given to provide a framework and a opportunity to draw comparisons.
Several numerical examples compare the efficiency of the different presented concepts against locking and confirm the capability of the proposed EAS-concept. The EAS method provides an highly reliable concept for the elimination of geometric locking effects and makes solid elements competitive compared to structural elements like shells.
