Course code: wb1311

Course name: Mechanics 3

This concerns a Course

ECTS credit points: 4

Faculty of Mechanical Engineering and Marine Technology

Section of Engineering Mechanics

Lecturer(s): Keulen, prof.dr.ir. A. van, Rixen, prof.dr.ir. D.J.

Tel.:  015 - 27 86515 / 81523

Catalog data:

Finite Elements method, buckling, plasticity, geometric and material non-linearity, complex construction, design.

Vibrations, dynamic response, modal analysis, resonance, transfer function, numerical sumilation, experimental mechanics.

Course year:

BSc 3^rd year

Course language:

Dutch (English on request)

In case of Dutch: Please contact the lecturer about an English alternative, whenever needed.

Semester:

2B

Hours per week:

6

Other hours:

20

Assessment:

Written exam

Assessment period:

2B / August

(see academic calendar)

Prerequisites (course codes):

wb1212, wb1213-03, wb1214, wb1216 (of wb1308 oud, of wb1211 èn wb1215 samen), wi3097wb

Follow up (course codes):

wb1310, wb1402A, wb1406, wb1409, wb1410, wb1412, wb1413, wb1416, wb1417, wb1418, wb1419, wb1440, ae4-399

Detailed description of topics:

Part A: Statics of constructions

- Buckling phenomena, buckling of beams and plates

- Finite Element method for buckling 

- Computer analysis (Finite Elements) of complex structures and interpretation of results, evaluation criteria

- Geometric non-linearity

- Analysis techniques (incremental methods, iterative methods, incremental-iterative methods)

- Anisotropic and non-linear material behavior

- Plasticity (introduction, yield surface, elastic-purely plastic material model, postulate of Drucker, plastic rate of deformation, isotropic and kinematic stiffening, numerical methods, collapse theorems)

Part B: Dynamics of construction.

- Review of Finite Element modelling and analysis of linear vibrations (system dynamics modelling, modal analysis, internal dynamic loads, lumped mass approximation);

- Free vibration analysis (eigenfrequencies and mode shapes, mode orthogonality, influence of mesh size, power iterations, axisymetric structures);

- Forced vibration analysis: response to harmonic and periodic external loads (transfer function, resonance/anti-resonance, direct solution, truncated mode superposition, damped/undamped systems, elements of experimental modal analysis);

- Transient response analysis (initial conditions, truncated mode superposition, direct time-integration of linear and non-linear systems, time-step size and its impact on numerical stability and accuracy);

- Outline of limitations in elementary linear dynamic analysis a) large deformation, linearized prestressed structures; b) large displacements/rotations, rotor dynamics, multibody analysis;

- Illustrations and examples with ANSYS.

Course material:

•  Lecture notes (available through Blackboard)

References from literature:

• References for Part A (Statics of constructions):
• Fung, Y.C., Foundations of Solid Mechanics, Prentice-Hall, 1965
• Timoshenko, S.P.en Gere, J.M., Theory of elastic stability, Second Edition, McGraw-Hill, 1981
• Bazant, Z.P. en Cedolin, L., Stability of structures; elastic, inelastic, fracture and damage theories, Oxford University Press, 1991
• Crisfield, M.A., Nonlinear Finite Element Analysis of Solids and Structures 
• Bathe, K.J., Finite Element Procedures
• Zienkiewicz, O.C. en Taylor, R.C., The Finite Element Method, Vol.1 + 2, 4th Ed.
• Besseling, J.F. en van der Giessen, E., Mathematical Modelling of Inelastic Deformation
• Koiter, W.T., Stijfheid en Sterkte, deel 1: Grondslagen, Scheltema & Holkema, 1972.
•  
• References for Part B (Dynamics of constructions):
• Géradin, M. and Rixen, D.J., Mechanical Vibrations, Theory and Application to Structural Dynamics, Wiley, 1997.
• Inman, D.J., Engineering Vibration, Second edition, Prentice-Hall, 2001.
• Hughes, T.J.R., The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, 1987.

Remarks assessment, entry requirements, etc.:

Written exam. In addition to the exam, an ANSYS  lab must be completed (20 hours).

It is possible to be exempted from the written exam by performing a project. One then has also to complete the take-home assignements and to get a satisfactory mark for those assignements within the prescribed time period. For the ANSYS lab, no exemption can be obtained.

- The completion of the project is organized in three steps. First, the student must formulate a case-study. Then he must set-up a work-plan. Finally, the problem must be solved.

- Deadlines will be specified during the lectures and on the blackboard site.

Learning goals:

The course aims at enabling the student to apply the fundamentals of Finite Element, dynamics and numerical mathematics for the modelling and analysis of real structures.

As a prerequisite, the student should have a good knowledge and understanding of the basics of mechanics and of the underlying mathematical techniques such as treated in the first two Bachelor years. Using didactical examples, practical cases and the ANSYS assignments we will indicate the importance of properly understanding the domain of application and the limitations of the theory studied earlier. In particular, the danger of inappropriate usage of the theory will be stressed.

   In part A (statics of constructions), one will for instance discuss the onset of buckling and geometric and material non-linearities. The numerical handling of these issues will be explained using a Finite Element software (ANSYS).

   In part B (dynamics of constructions) the theory of vibration (2nd BSc year) and numerical analysis (3rd BSc year) will be combined and furter illustrated using ANSYS examples. In this way the theoretical knowledge acquired earlier will be given more depth and applied to real structures.

Computer use:

Use of the Finite Element software ANSYS.

Laboratory project(s):

Using ANSYS, the students will run several analysis cases.

Design content:

The lectures are designed to give the student confidence in using the computer as analysis tool, namely to use it in the design process. Studying the theory from a design point of view is thus essential here.

Percentage of design:  25%