Recommendations

• Dynamik starrer Körper [DSK]

• Statik und Festigkeitslehre [SuF]

• Statik, Elastostatik und Festigkeitslehre [SEF]

• Dynamik nichtlinearer Balken [DyNiLiBa]

• Theoretische Dynamik [TheoDyn]

Description
In this course we aim to provide a theoretical overview of beam theory in the context of continuum mechanics and Lagrangian mechanics and its numerical treatment with an emphasis on geometry. We will introduce the concept of Lie group and their role in the description of the geometrically exact beam model used for large deformations.

• Vector spaces and smooth manifolds
  

• Continuum and Lagrangian mechanics
  

• Linear beam theory
  

• Nonlinear beam theory

  • Finite rotations and Lie groups

  • Geometrically exact beam
    

• R. Abraham and J. E. Marsden. Foundations of mechanics.
  

• Javier Bonet and Richard D. Wood. Nonlinear continuum mechanics for finite element analysis.
  

• R. Courant and D. Hilbert. Methods of mathematical physics. Vol. I.
  

• Philippe G. Ciarlet. Mathematical elasticity. Studies in Mathematics and its Applications. Three-dimensional elasticity.
  

• M. Fecko. Differential Geometry and Lie Groups for Physicists.
  

• H. Goldstein, C.P. Poole, and J.L. Safko. Classical Mechanics.
  

• D. D. Holm. Geometric mechanics. Part II. Rotating, translating and rolling.
  

• J. Lemaitre and J. L. Chaboche. Mechanics of solid materials.
  

• J. M. Lee. Introduction to Smooth Manifolds.
  

• Julia Mergheim. Lecture notes - Nonlinear Finite Element Methods. July 2011.
  

• Jerrold E. Marsden and Thomas J. R. Hughes. Mathematical foundations of elasticity.
  

• Peter J. Olver. Applications of Lie groups to differential equations.
  

• H.-R. Schwarz. Finite element methods.
  

• J. Simo. A finite strain beam formulation. The three-dimensional dynamic problem. Part I.