MathMods :: Joint MSc

Additional Info

• ECTS credits: 6
• University: Gdansk University of Technology
• Semester: 3
• Lecturer 1: Sergey Kshevetsky
• Lecturer 2: Grzegorz Kwiatkowski
• Objectives:

   

  Solid continuum mechanics from many years have a very well developed theory and numerical algorithms and programme packages. These wide fields of modelling will be reviewed in a very concise manner. The course will teach how to simulate elestic and unelastic properties of solids within classial continuum theorz and recent discrete-continuum models. Aspects important for cross-scale simulations (hand-shaking between continuum and molecular approaches) will be underlined. Applications to multi-phase solids (laminates, systems containind nanoparticles, etc), granular solids, multiphase flows with complex geometry will be discussed.

• Topics:

   

  1. Basic continuum theory
  a. Tensors and tensor fields
  b. Analysis of Stress-Strain
  c. Deformation and Strain
  d. Shear Strain
  e. General Elasticity
  f. Waves
  g. Introduction to thermoelasticity
  h. Multi-dimensional theories of thermoelasticity

  2. Plasticity, discrete-continuous models, granular matter, composites, non-newtonian liquids, etc.
  a. Classical continual models of plasticity
  b. Discrete models as generalized solutions of continuum equations
  c. Review of modern discrete-continuous models: three kinds of models
  d. Hybrid discrete-continuous models
  e. Some mathematical results for the theory of elasticity equations
  f. Numerical methods of solving of equations of continual models
  g. Numerical methods of solving of equations of continual models
  h. Newtonian and non-Newtonian fluids
  i. Computer practice in computer solving of equations of discrete-continuum models
  j. Newtonian and non-Newtonian fluids
  k. Granular and multiphase materials, composite materials
  l. Granular and multiphase materials. The case of high-concentrated materials.