**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

unloading.

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.