1   Mathematical Background  

  • Matrix algebra
  • Linear systems of  equations
  • Eigenvalue problems

2   Basic Equations of the Theory of Elasticity

  • Trusses and beams
  • Plates in plane stress
  • Plates in bending (incl. edge effect at boundaries)
  • Spatial structures

3   Finite Element Method for Truss and Beam Structures

  • Introductory example: plane truss system
  • Elastic springs
  • Beams  in bending (incl. hinges, warping torsion)
  • Spacial truss and beam structures
  • Modeling (incl. eccentric beam axes, support conditions,  symmetrical systems)
  • Quality assurance (types of errors, checking of a FE analysis)

4   Finite Element Method for Plate, Shell and Solid Structures

  • Approximation character of  the finite element method (with in introductory example)
  • Finite elements for plates in plane stress and in bending, shell elements, solid elements
  • Transition between beam, plate and solid elements
  • Modeling
    • FE meshing, singularities,
    • Modeling of plates in plane stress (incl. elements with/without shear locking, columns),
    • Modeling of plates in bending (incl. shear rigid /shear flexible elements, edge effect, hard/soft line supports, columns, flat slabs with drop panels, T-beams, mounting parts,
    • Foundation slabs: subgrade reaction model, continuum model, Pasternak model, FE model,
    • Modeling of shell structures
    • 3D building models
  • Quality assurance (incl. Types of errors, error estimation, checking of a FE analysis)

5   Dynamic Analysis of Structures

  • Basic concepts of dynamics
    • Inertial forces (incl. rotational masses)
    • Coulomb damping, Rayleigh damping, hysteretic damping
    • Equations of motion
  • Free vibrations (eigenfrequencies and modes)
  • Forced vibrations with harmonic excitation (incl. complex notation)
  • Forced vibrations wit general dynamic excitation
    • Direct numerical integration,
    • Modal analysis,
    • Fourier transform
  • Earthquake excitation
    • Time history analysis,
    • Response spectrum analysis
  • Modeling
    • Discretisation in space and time,
    • Kondensation method,
    • Building models: beam models, 3D building models,
    • Soil-structure interaction (incl. spring-damper models, FE models: Lysmer-Kuhlemeyer dampers, transmitting boundaries, SBFEM)