# Computational mechanics

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This area involves study and research in the development and application of numerical and computational methods for the solution of a wide range of problems in solid mechanics, fluid mechanics, and materials science. Students will gain experience with developing models of physical systems, formulating the discretized equations for the model systems of partial differential equations, and implementing these equations in computer codes for their solution and analysis.

Students who have completed the course should have an understanding of the modern scientific concepts of mechanical processes modelling. They have to be aware of modern computing tools used in mechanics as well as of the possibilities of modern commercial software packages available on the market.

Students should know the following:

• some explicit and implicit methods of integration of differential equations
• fundamentals of molecular dynamics method
• basics of Finite Element Method
• fundamentals of Computational Mechanics of composite materials
• basic concepts of computational mechanics of non-elastic material

Students should be able:

• to formulate a boundary problem of the theory of elasticity, thermal conductivity, electrostatics, piezoelectricity
• to select methods and solve the problem using existing software, or write a program code
• to analyse the results
• to formulate conclusions and report on progress
• to develop software systems for mechanical processes modelling, working with documentation and using open sources

The course contains the following items:

• Computer modelling as a tool for scientific and engineering work
• Simple numerical scheme for solving one-dimensional problems of physics
• Computational Mechanics of discrete media
• The method of particle dynamics
• Computer modelling of non-elastic deformation and fracture
• Computational mechanics of continuum
• Thermal conductivity
• Electromagnetism
• Mechanics of solids
• Finite element technique
• Computer modelling features of some engineering problems
• The choice of physical models, tools and methods of calculation
• Special methods of calculation tasks at different scale levels
• Modelling of deformation of non-elastic materials
• Defining equations and parameters
• Rheological (structural) models
• Calculation algorithms using the rheological models
• Modelling of related fields
• Piezoelectric
• Ferroelectrics
• Modelling of composite materials
• Methods of homogenization of stress and strain fields
• Modelling of soil