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 and Structural Optimization and Computational 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:

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%