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Grundlagen der erweiterten Mechanik (FUNDAMENTALS OF ADVANCED MECHANICS)

# Computerorientierte höhere Mechanik (Computer oriented higher mechanics) / Nichtlineare Finite Elemente Methode (Nonlinear finite element method)

### Topic

The fundamentals of computer-oriented nonlinear mechanics are covered. These are the compact representation of mechanical relations in tensor notation and the general statements of nonlinear continuum mechanics.

The fundamentals of the numerical solution of geometrically and physically nonlinear problems of solid mechanics as well as their algorithmic implementation with the help of the Finite Element Method (FEM) are presented. These requirements arise in all complex tasks of structural engineering (concrete construction, steel construction, foundation engineering). The evaluation of numerical results of nonlinear calculations is discussed.

### Computer-oriented higher mechanics

• Definition and meaning of curvilinear coordinate systems
• Extension of the calculus from Cartesian to curvilinear coordinate systems
• Distortion and stress tensors
• Deformation and distortion velocity
• Transport theorems
• Balance equations: Mass balance, momentum balance, angular momentum balance, energy balance
• Entropy inequality

### Nonlinear finite element method

• Mathematical and continuum mechanics basics
• Weak form of equilibrium and associated discretization
• Derivation of the matrix representation
• Solution methods for nonlinear problems
• Consistent linearization of the continuous and discrete weak form
• Element formulations concerning the reference and moment configuration
• Implementation of Newton-Raphson method
• FEM for geometrically nonlinear beams
• Stability analysis of frames/arches
• FEM for geometrically nonlinear plate
• Buckling analysis for plates (garland curves)

### Accompanying material

Lecture notes will be made available in the Moodle workroom BMSD-GEM.

### Degree course

The course is intended for 1st semester students of the master program Bauingenieurwesen (civil engineering).

Examination matters:

Modulhandbuch Master Bauingenieurwesen, Modul 401 (Grundlagen der erweiterten Mechanik)