NPTEL Syllabus - Finite element method and its implementation for ...

NPTEL Syllabus

Finite element method and its implementation for steady and transient problems - Video course COURSE OUTLINE

NPTEL

A concise introduction to the elementary concepts and methods of finite element analysis, with applications to heat flow, electric potential, solid mechanics, groundwater flow and other engineering problems. Also provides practice in using finite element codes. http://nptel.iitm.ac.in Learning outcomes: After completing this module you should be able to demonstrate a knowledge and understanding of: Fundamentals of the finite element method as an approximation method for analysis of a variety of engineering problems. Differences between mathematical (conceptual) and computer model.

Ocean Engineering

Ability to: Distinguish between strong and weak form of the engineering problem at hand. Understand levels of approximation inherent in computer modelling approaches to the solution of engineering problems. (thinking skills) Develop finite element formulation for analysis of a variety of engineering problems Pre-requisites: including: Engineering mathematics (a) elastostatics of 1-D bars and cables, (b) 2-D and 3-D trusses, (c) heat conduction and (essential) Strength of porous media flow, torsion, electric potential (d) plane strain and plane stress problems (e) materials and structural simple time dependent problems. Use finite element method to solve engineering problems mechanics or equivalent (a)-(e). Use a computer to model and analyse engineering problems (a)-(e). (practical (desirable) skills) Additional Reading:

COURSE DETAIL Sl.no

Syllabus

Class room/Lab Hours

1

1D problems and trusses: Introduction. FE Formulation of 1-D Problems - Physical problem; conceptual model. 1- D problem of heat conduction and elastostatics. Analytical solution. Strong and weak forms. Galerkin approximation. Finite element discretisation. The linear 1D bar: shape functions, load vector and stiffness matrix. Assembly procedure. FE Modelling of Trusses - Stiffness matrix by direct calculation. Assembly procedure. 3-D trusses. Examples

9 (class room)

2

2D scalar problems: FE Modelling of 2-D Potential Flow Problems - Physical problem; conceptual model. Porous media flow; heat conduction; electric potential; torsion of cylindrical members. Strong and weak form. Galerkin approximation. Finite element discretisation. The linear shape triangle: shape functions, load vector and stiffness matrix. Assembly procedure. Finite element programming concepts. Examples.

8 (class room)

3

2D elasticity: FE Modelling of 2-D Elastic Solids - Plane strain and plane stress problems of 2-D elastostatics. Strong and weak form. Galerkin approximation. Finite

6 (class room)

O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu and P. Nithiarasu, Finite element method, 3 Volume set, Elsevier, 2005. Coordinators: Prof. P Nithiarasu College of EngineeringSwansea University

element discretisation. The linear shape triangle: shape functions, load vector and stiffness matrix. Examples

4

1D transient problems: Time dependent phenomenon – Discretisation of transient equations – Finite element formulation – Time stepping approaches – Heat conduction and elasticity – Examples.

5 (class room)

5

Review and Assessment.

2(class room)

6

Using computer codes to solve 1D problems with or without help (computer lab).

3 (lab)

7

Using computer codes to solve 2D scalar problems with or without help (computer lab).

3 (lab)

8

Using computer codes to solve 2D vector problems (computer lab).

3 (lab)

8

Using computer codes to solve 1D dynamic problems (computer lab).

3 (lab)

Total Number of Classroom/Lab hrs.

30/12

References: 1. T.R. Chandrupatla and A.D. Belegundu, Introduction to finite elements in engineering, Prentice Hall (latest edition). 2. T.J.R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover Publications, 2000. 3. R.W. Lewis, P. Nithiarasu and K.N. Seetharamu, Fundamentals of the finite element method for heat and fluid flow, Wiley, 2004. A joint venture by IISc and IITs, funded by MHRD, Govt of India

http://nptel.iitm.ac.in