# Contents

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)