Numerical Methods in Structural Mechanics

Lecturer:

Tutor:

Supervisor:

Department of Mechanics

Synopsis:

Solving structures using finite element

method

Requirements:

none

Syllabus of lectures:

1. Algorithmization of slope-deflection method. Assembly and analysis of structure.

2. Localization. Transformation of coordinates.

3. Mindlin's beam theory.Finite element method - direct formulation. Integral or „weak“ statements equivalent to the differential equations.

4. Principal of virtual work. Constrained variational principles. Lagrange multipliers. Penalty functions.

5. Analysis of plates. Basic assumptions. Kirchhoff and Mindlin theory.

6. Governing differential equations.Weak formulation. Shear locking.

7. Introduction to shell analysis. Shell as an assembly of flat elemnts.

8. Heat conduction. Governing equations. Steady-state problem.

9. Transient problem.Steady-state flow.

10. Plane-free surface flow.

11. Coupled problems. Biot's consolidation.

12. Errors and recovery processes. Error estimation.

13. Adaptive finite element refinement. Numerical integration.

14. Mesh generation.

Syllabus of tutorials:

Study Objective:

Students will get acquainted with analysis of plates, shells and several special problems of structures solved by finite element method.

Study materials:

1. Bittnar, Z. and Šejnoha, J.: Numerical methods in structural engineering. ASCE Press 1996. 2. Zienkiewicz,O.C., Taylor,R.L.: The Finite Element Method, Volume 1, The Basis, Fifth edition, Butterworth-Heinemann, 2000. 3. Smith, I. M., Griffiths,D.V.: Programming the Finite Element Method, John Wiley & Sons, 1998.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: