Numerical simulations and FEM

FEM in metal forming and material engineering


I Lectures *pdf  (Numerical simulations and FEM)                                                     

  Lectures *.pdf  (FEM in metal forming and material engineering)


  Lectures in video (Basic of FEM, in Polish)

  Basic of FEM, book (in Polish)


Numerical simulations and FEM. Annotation.

In the proposed course questions of simulation with the aid of the finite elements method (FEM) of the processes of heat exchange, elastic deformation and flow fluids are examined.

Course consists of three major parts.

            In the first part the theoretical bases of the Finite Element Method (FEM). Necessary aspects of the theory of thermal conductivity for this purpose is presented.

            The second part of the course is dedicated to the solution of boundary-value elastic, elastic –plastic and flow of fluids problems with the aid of FEM.

Algorithms and special features of the application of a FEM to the mechanical and thermal tasks, are given.

            In the third part of the course numerous examples of the commercial programs and FEM programs developer by the author are present.

Parts of course:

1.Bases of the finite elements method.  Temperature problem.

Theoretical basis of the linear theory of elasticity; the principle of virtual work;

formulation of the boundary value problem; the basic principles for solving

problems using the finite element method.

3. The theoretical foundations of the theory of small elastic plastic deformation;

models of the mechanical properties of elastic-plastic materials; theorem on


4. Finite elements method in the theory of plastic flow of the incompressible materials and flow of fluids. 

5. Example of commercial FEM programs for the simulation of the processes of hot deformation of metals. Programs Qform and Forge3. 

6. Basics of program ABAQUS; examples of solving problems of the theory of

elasticity in the program ABAQUS


FEM in metal forming and material engineering. Annotation.

The finite element method (FEM) is widely used in metal forming and material engineering. This method is an approximate method, that's why it requires the use of theoretical training. The following questions are considered in this course.

1. Fundamentals of the FEM.

2. Solving a thermal problems.

3. Solving problems in the theory of elasticity and plasticity.

4. Principles and practical aspects of creating software based on the FEM.

5. Review of existing commercial programs.

The main part of the lab tutorials are dedicated to the development of FEM codes, dedicated to simple problems in material processing.

Initial requirements for students.

Fundamentals of programming, the basics of heat transfer, mechanics, numerical methods, the fundamentals of materials engineering and metal forming.



II Project - P


III Autor: Prof. dr hab. in¿. Andrij Milenin


IV Literature:

1.       Milenin A. Podstawy MES. Zagadnienia termomechaniczne // AGH, 2010.

2.       O.C.Zienkiewicz, R.L.Taylor  The Finite Element Method // Butterworth Heinemann, 3 vol, 5-th Edition, London, 2000

3.       K.J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice Hall Inc.

4.       Segerlind L. J., Applied Finite Element Analysis // J. Wiley & Sons, New York, 1976, 1984, 1987, 427 pp. ISBN 0-471-80662-5.

5.       Kobajashi S., Oh S.I., Altan T., Metal Forming and the Finie Element Metod, Oxford University Press, New York, Oxford, 1989.

6.       Owen D.R.J., Histon E., Finite Elements In Plasticity: Theory and Practice, Pineridge Press, Swansea, 1980.

7.       Wagoner R.H., Chenot J.L., Fundamentals of Metal Forming, John Wiley & Sons, Inc, New York, 1997.

8.       Lenard J.G., Pietrzyk M., Cser L., Mathematical and Physical Simulation of the Properties of Hot Rolled Products, Elsevier, Amsterdam, 1999.



11.    Finite Element Procedures for Solids and Structures  (MIT Open Recourse)





Numerical simulations and FEM

The finite element method is presented on the basis of its applications in metallurgy and materials science. Numerical solutions of partial differential equations and basis of the finite element method are discussed. Methods of switching from differential equation to functional and discretization of the functional are presented. The boundary conditions for various processes are introduced. Searching for a minimum of functional leading to a set of algebraic equations and examples of solutions of these equations for linear and nonlinear problems are shown. The structure of the computer program, which accounts for basic principles of numerical solution of large engineering problems, is presented. Examples of advanced applications in mass and heat transport, metal forming and fluid mechanics are discussed.