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Course name ANSYS I Code 0004043100 Credit

points

3

Language of instruction English

Programme Mechanical Engineering and Applied Computer Science

Type of studies MSc studies

Unit running the

programme

Department of Strength of Material and Structures

Course coordinator and

academic teachers

T. Kubiak PhD

Form of classes and

number of hoursSemester Lec. Tut. Lab. Proj. Sem. Credit

points

autumn 15 15 3

Learning outcomes Basic knowledge about finite element method idea of FEM, brief history, types of

elements, solution convergence, error estimation. Method of solution in FEM. Method of

derivation of elemental and structural stiffness matrix for linear one-dimensional and

plane element.

Prerequisites Mathematics I (0001010100, 0001010200), Mathemetics II (0001020100, 0001020200),

Basic Mechanical Engineering I (0001011700), Basic Mechanical Engineering II

(0004022900), Advanced Mechanical Engineering (0004031800)

Course description LECTURE1. Introduction to the finite element method.2. Review of Matrix algebra. Determinants method of calculation. Method of

solution for simultaneous equation in matrix form.

3. Spring element; Stiffness matrices; Calculation of structural stiffness matrix.4. Discretization using spring element.5. Two dimensional rod element stiffness matrix - direct approach.6. Plane trusses method of solution.7. Short review of stress-strain relationship in matrix form, the principle of virtual

work, the principle of complementary virtual work.

8. Elemental stiffness matrix for rod element in plane - virtual work approach.9. Rod element in local and global coordinate system; Transformation of

coordinates.

10. Beam elements in local coordinates system direct approach11. Rigid-jointed plane frames - examples12. Bar and Beam elements in local CS virtual work approach.13. Transformations of coordinates for bar element.14. Constant Strain Triangle (CST) element stiffness matrix for plane strain and

plane stress problem.

15. Bilinear rectangle element. Short review of other elements.TUTORIALS

Tutorials content is the same as lectures content. During tutorials students solve example

of problems presented during lectures.

Form of assessment Final grade = 20 % (Activity during tutorials) + 80% (note obtaining from test)

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Basic reference materials 1. Carl T.F. Ross Advanced Applied Finite Element Methods Horwood Publishing1998

2. S.S. Rao Finite Element Method in Engineering Pergamon Press3. R. Grdzki Introduction to Finite Element Method (in Polish) Politechnika

dzka, d, 2002

Other reference

materials

1. Saeed Moaveni, Finite Element Analysis, Theory and Application with ANSYS,Prentice Hall Inc. New Jersey, 1999

2. Szmelter J., Dacko M., Dobrociski S., Wieczorek M., Finite Element Method inStructural Statics, (in Polish) Arkady, Warszawa, 1972

3. Rakowski G., Kacprzyk Z., Finite Element Method in Structural Mechanics, (inPolish) , Oficyna Wyd. Politechniki Warszawskiej, Warszawa, 1993

e-mail of the course coordinator

and academic teachers

tomek@p.lodz.pl

Average student workload

(teaching hours + individual )

30 + 10 = 40h

Remarks:

Updated on: September 13, 2004