A Three-Day Short Course on Finite Element Method

A Three-Day* Short Course     

                     on

Finite Element Method

(with applications to heat transfer, solid and Fluid mechanics)

                        March 21-23, 2013, 

             National Institute of Technology,   

                          Tiruchirappalli

LECTURER

J. N. Reddy

Texas A&M University, College Station

e-mail: jnreddy@tamu.edu

COURSE COODINATOR

K. Baskar

National Institute of Technology, Tiruchirappalli

India - 620 015

.ABOUT THE COURSE 

BACKGROUND 

 

The Finite Element Method (FEM) is a computational tool for solving a variety of practical engineering problems that arise in different fields. It is recognized by developers and users  as one of the most powerful numerical analysis tools ever devised to analyze complex  problems of engineering. The underlying theory of the method is now well established, with  many books and courses providing adequate explanations of the theory. However, most  people using the method, via commercial software or in-house codes, do not often understand  the method as applied to engineering problems, especially in generating input data and  interpreting the results. 

 

COURSE OBJECTIVES 

 

The major problem facing the engineering analyst contemplating the use of the finite element technique lies in acquiring appropriate knowledge to provide assurance that the finite element model produced gives a reasonably reliable representation of the "real life" problems being analyzed. The present course is designed to bridge the gap between the theoretical finite element knowledge and its industrial applications by providing sufficient insights into the relationship between the physical phenomena, governing equations, problem data (e.g., loads, boundary conditions, constitutive behavior, etc), and the finite element model. The lecturers will discuss the intimate connection between these aspects as well as issues such as element selection, mesh design, interpretation of results in light of qualitative understanding of the problem being analyzed. This course is intended to provide graduate students and researchers working in aerospace, automotive, civil, mechanical engineering, and information technology as well as numerical analysts and materials scientists with the theory and applications of linear finite element analysis of problems from heat transfer, solid and structural mechanics, and fluid mechanics. 

 

PROFILE OF PARTICIPANTS 

 

The course is aimed at students, analysts, and researchers who are involved with the analysis of differential equations arising in engineering and applied science, and who are using or plan on using commercially available finite element packages to analyze problems in the aeronautical, automobile, mechanical, civil and other engineering disciplines. Participants are assumed to have knowledge of the basic principles of engineering (i.e., undergraduate degree in engineering). Some knowledge of the finite element method is an advantage, but not essential.  

BENEFITS OF ATTENDING THE COURSE 

 

Persons who have attended the course and followed the material should benefit in strengthening their background in the following areas: 

A strong understanding of the formulative steps involved in the finite element model development of the equations of engineering and applied science, including certain heat transfer, solid and structural mechanics and fluid flow problems. 

Generation of finite element data (e.g., selection of elements and mesh, computation of nodal forces), imposition of boundary conditions, post-computation of stresses and strains, etc.), exploitation of problem symmetries, and interpretation and evaluation of the results. 

 

COURSE MATERIAL AND REFERENCE BOOK 

 

A copy of the overheads used in the presentation of the course will be provided as a part of the course material (by the organizers). The introductory finite element book by JN Reddy is now available and the participants may purchase the book from local vendors. The reference information on the book is Reddy, J. N., An Introduction to the Finite Element Method, Third Edition, McGraw-Hill, New York, 2006. 

 

COURSE CONTENTS

 (actual coverage and sequence may differ depending on the participants background) 

Background: Introduction to numerical methods  

• Overview – basic ingredients of the FEM 
• Comparison with alternative solution methodologies 

The basic concepts in FEM – one-dimensional problems 

•  Axial deformations of a bar 
• Strong and weak forms 
• Essential vs. natural boundary conditions 
• Integral statements (Principle of the minimum potential energy) 
• Methods of approximations (Ritz & Galerkin methods) 
• Accuracy – error measures 
• Finite element approximation functions (linear, quadratic, and cubic elements) 
• Assembly of element equations 
• Illustrative examples and discussion of results in light of physical response 

Extension of the concepts to beams and two-dimensional problem

• Flexure of beams and frames 
• Membrane and heat transfer-like (e.g., ground water flow) problems in 2D 
• 2D Elements types (triangular and quadrilateral elements) 
• Computational examples 

Numerical/computational issues 

•  Subparametric, isoparametric, and superparametric formulations 
• Numerical integration 
• General modeling considerations