Course module – Finite Element Method

Semester: 1

Aims

The course is a Core module for The Masters in Mechanical Engineering, and it is the theoretical foundation and important tools of Computer Aided Engineering (CAE). The course aims students to master the basic concepts, theories and modeling techniques of finite element method (FEM), and solve some static or dynamic problems in practical engineering structures using commercial finite element softwares.

 

Intended learning outcomes

On completion of the unit students will be able to:

1)  Understand the three mechanical governing equations for 2D or 3D solids, trusses, beams and plates, i.e. the geometrical equations for strain-displacement relationships, the constitutive equations for stress-strain relationships and the equilibrium equations for force-stress relationships.

2) Understand Hamilton’s principle to be used to derive discretized FE system equations. Master the methods and procedures of FEM, including domain discretization, displacement interpolation, constructing shape functions, formation of FE equations, coordinate transformation, assembly of global FE equations and solving the global FE equations etc.

3) Understand FEM for different structures, including trusses, beams, frames, 2D or 3D solids, plates or shells. Study their shape functions, strain matrices, stiffness matrices, mass matrices and force vectors etc. Carrying out the case studies for these structures.

4) Understand every key techniques for high-quality FE modeling, including selection of suitable element types, limitation of element distortions, mesh compatibility for different order or type elements, use of symmetries (mirror, axial, cyclic or repetitive symmetries), applications of MPC equations and solving MPC equations etc.

5)  Understand Weighted Residual Approach to be used to solve every field problems. Focus on FEM for 1D or 2D heat transfer problems.

6) Use ANSYS software to analysis two samples: FEM for a frame structure and FEM for a 3D solid problem.

Assessment

Homework exercises         (30%)
Final examination            (70%)
Re-sit: Makeup examination  (100%)

Brief description of unit

Syllabus
1.  Computational Modeling

2.       Introduction to Mechanics for Solids and Structures

3.       Fundamentals for Finite Element Method

4.       FEM for Trusses

5.       FEM for Beams

6.       FEM for Frames

7.       FEM for 2D Solids

8.       FEM for Plates and Shells

9.       FEM for 3D Solids

10.    Special Purpose Elements

11.    Modeling Techniques

12.    FEM for Heat Transfer Problems

Course materials

R.R. Liu, S.S. Quek. The Finite Element Method: A Practical Course, Butterworth-Heinemann Publications. Burlington, 2003

Timetable

Semester 1 (weeks 2-17)
Thursday, 14:00-16:50

Learning and teaching processes

Lectures and experiments on computer

Indicative reading

Zienkiewicz O. C. and Taylor R. L., The Finite Element Method, 5th edition, Butterworth-Heinemann, 2000.

Bathe K. J., Finite Element Procedures, Prentice Hall, Englewood Cliffs, 1996.