Logo Leibniz Universität Hannover
Logo: Institute of Mechanics and Computational Mechanics
Logo Leibniz Universität Hannover
Logo: Institute of Mechanics and Computational Mechanics
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Computational Mechanics

Today powerful commercial Finite Element software is available for engineers to perform computational analyses of mechanical structures. The aim of this module is to guide the students into the basic theories of these computational methods and to prepare them for a competent and critical application of these software programs within the context of linear solid mechanics.

Acquisition of Competence

FE Lösung eines Stabtragwerks
FE solution of a truss system

In this module an introduction to the Finite Element Method (FEM) is provided. The following topics will be discussed:

    • Introduction to FEM on the example of a 1D rod (variational formulation, Galerkin scheme, Ansatz functions, element matrices, assembling process, postprocessing of results,…); Comparison of Finite Element and Finite Difference Methods

    • FE for beams, 2- and 3D continua (isoparametric concept, computational integration)

    • Structure of a FEM software, error analysis

    • Interpretation and critical evaluation of computational results, error analysis

    • Solution of structural dynamic problems (eigenvalue computation, modal superposition, implicit and explicit time integration schemes, damping), problem-depending choice of a suitable scheme

    • generalization: FEM as a method to approximate the solution of partial differential equations; Poisson equation (stationary heat flux, groundwater flow) and advection-diffusion problems

    In this module students will be introduced to commercial Finite Element Method software. Internal processes and algorithms will be studied on a well-structured Finite Element program written in Matlab.


    Ansatz functions of a 4-node plate element

    Form of Teaching

    Normal stress in a beam structure due to bending

    The module “Computational Mechanics” is offered normally each winter term with lectures, exercises and tutorials in German language.

    In addition, the module can be taken each term as a pure online-module that is to say instead of contact classes you will be given materials and help for you own personal study. We provide all learning materials in German language clearly structured on the learning platform ILIAS.

     

    Evaluation

    Information on the exam form and process are published in the StudIP course.