The finite element method is recognized by developers and users as one of the most powerful numerical analysis tools ever devised to analyze complex problems of engineering.
There exist a large number of general purpose finite element computer programs (For example: NISA, ABAQUS, ADINA, ANSYS, MSCNASTRAN, etc.) with varying degree of sophistication and analysis capabilities to analyze physical problems with complex domains, physical features (e.g., geometric and material nonlinearities), and subjected to thermal, mechanical and/or hydrodynamic loads.
A correct understanding of the theory of nonlinear finite element analysis and applications to various field problems is of paramount importance in modeling practical problems. This course will introduce the basic theory and computer implementation of nonlinear problems arising in heat transfer, fluid mechanics, structural mechanics, as well coupled heat transfer and fluid mechanics problems.
Course objectives
This course is intended to provide aerospace, civil, mechanical engineers as well as numerical analysts and materials scientists with the theory and computer implementation of the nonlinear finite element analysis of problems from heat transfer, fluid mechanics, and solid mechanics. The objectives of the course include:
The theory of nonlinear finite element analysis as applied to representative problems of heat transfer, fluid mechanics, and solid mechanics.
Applications of a finite element computer programs to representative problems of heat transfer, fluid mechanics, and solid mechanics.
Computer implementation of the finite element analysis steps for the model problems.
Computer implementation of various finite element formulations will form an essential part of the course. At the end of the course one would have acquired knowledge of finite-element analysis of many typical linear and nonlinear problems.
Four lectures per day, with 1 hr. 30 min. duration per lecture, are planned. The lectures are followed by computer simulations. A detailed list of contents is as follows.
Course structure
Course contents Day 1: January 7, 2008 General Introduction (Lecture-01)
Mathematical models and numerical methods
Approximate solutions
Need for integral statements
Classical variational methods
The finite element method: basic features
Finite Element Analysis of 1-D Problems (Lecture-02)
Major steps in the finite element formulation
Model 1-D problems involving single variable
Finite element discretization
Weak form development over an element
Finite element model development
Numerical evaluation of coefficient matrices
Post-computation of variables
Numerical example
Finite Element Analysis of 2-D Problems (Lecture-03)
Model 2-D problems involving single variable
Weak form development
Finite element model
Approximation functions
Interpolation functions of higher-order elements
Numerical evaluation of coefficient matrices
Post-computation of variables
A numerical example
Computer Implementation of 2-D Problems (Lecture-04)
Logical units of a typical FEM program
Discussion of FEM2D (Flow chart)
Review of FE formulation of 2-D problem
Parametric formulations
Numerical integration
Element calculations
Discussion of Fortran statements
Day 2: January 8, 2008 Time-Dependent Problems and Modeling Considerations (Lecture-05)
Transient problems
Eigenvalue problems
FE models of eigenvalue problems
Spatial discretization - Weak form
Spatial discretization Ð FE Model
Time approximations
Implicit and Explicit Schemes
Stability of approximation schemes
Numerical examples
Modeling considerations
Nonlinear Finite Element Models of Problems (Lecture-06)
General introduction
Weak form formulation
Finite model development
Iterative solution
Computer Implementation
Nonlinear Finite Element Models of Beams (Lecture-07)
Finite model development
Iterative solution
Shear and membrane locking
Computer Implementation
Nonlinear Plate Bending: CPT and FSDT (Lecture-08)
Finite element models
Plate bending elements of CPT and FSDT
Membrane and shear locking
Computer implementation
Numerical examples
Day 3: January 9, 2008 Nonlinear Analysis of Time-Dependent Problems (Lecture-09)
Governing equations
Revisit of finite element models of discussed earlier in the context of transient analysis
Iterative procedure
Numerical examples
A Review of Continuum Mechanics (Lecture-10)
Concept of continuum
Conservation of mass
Conservation of linear and angular momenta
Conservation of energy
Constitutive Relations
Continuum Formulations of Solid Mechanics Problems (Lecture-11)
Review of nonlinear mechanics of continuum
Updated and total Lagrangian formulations
Computer implementation
Numerical examples
Continuum Formulations of Shells (Lecture-12)
Comments on finite element models of shells
Total Lagrangian formulation of shells
Finite element model
Numerical examples
Day 4: January 10, 2008 Fluid Dynamics and Coupled Fluid Flow and Heat Transfer(Viscous Incompressible Flows) (Lecture-13)
Governing equations
Mixed finite element model
Penalty finite element model
Coupled fluid flow and heat transfer
Solution strategies
Numerical examples
Least-Squares Based Finite Element Models (Lectures-14)
General comments
Mixed formulations
Least-squares formulations
Numerical examples
Tensor-Based Shell Finite Elements (Lectures-15)
General comments
Mixed formulations
Least-squares formulations
Numerical examples
Other Developments: Adaptive and FGM Structures (Lectures-16)
General comments
Mixed formulations
Least-squares formulations
Numerical examples
Summary of the Course, Open Discussion, and Award of Certificates of Participation (Lectures-17)
Discussion
Closure
Comments from the participants
Award of certificates of participation
Benefits
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:
An understanding of the formulative steps involved in the finite element model development of the equations of heat transfer, fluid mechanics, solid mechanics, and coupled heat transfer and fluid mechanics.
Generation of finite element data (e.g., selection of elements and mesh, computation of nodal forces, imposition of boundary conditions, etc.) and proper imposition of boundary conditions, exploitation of problem symmetries, and interpretation and evaluation of the results.
The ability to write a finite element computer module for a physical problem (e.g., user-specified subroutine for a commercial program).
The ability to read and evaluate technical proposals/reports/papers on the finite element analysis of problems in engineering.
The knowledge to teach the finite element analysis procedures to others.
Course pre-requisites
The course is designed for engineers and scientists in industry as well as academia who are interested in the theory and/or applications of the finite element method to Nonlinear problems of heat transfer, fluid mechanics, and structural mechanics. The participants of the course must have a background in differential equations, exposure to the field equations of engineering (i.e., an undergraduate degree in engineering or applied sciences is required), and preferably a first course on the finite element method.
Course material and reference books
A copy of the overheads used in the presentation of the course will be provided. The introductory finite element book by Dr. JN Reddy will be provided by Cranes Software. The reference information on some of his books is as follows:
Reddy, J. N., An Introduction to the Finite Element Method, Third Edition, McGraw-Hill, New York, 2006.
Reddy, J. N., An Introduction to Nonlinear Finite Element Analysis, Oxford University Press, Oxford, UK, 2004.
who should attend
Graduate students, researchers, and engineers from industry who are interested in the theory, implementation, and application of existing finite element codes to linear and nonlinear problems of heat transfer, fluid mechanics, and solid and structural mechanics.
Trainer
About the lecturer (J. N. REDDY)
Dr. Reddy is a Distinguished Professor and inaugural holder of the Oscar S. Wyatt Endowed Chair in Mechanical Engineering at Texas A&M University, College Station, Texas. Dr. Reddy earned a Ph.D. in Engineering Mechanics in 1974 from University of Alabama in Huntsville. He worked as a Post-Doctoral Fellow at the University of Texas at Austin, Research Scientist for Lockheed Missiles and Space Company during l974-75, and taught at the University of Oklahoma from 1975 to 1980, Virginia Polytechnic Institute & State University from 1980 to 1992, and Texas A&M University from 1992 till now.
Dr. Reddy is the author of over 350 journal papers and 15 text books on theoretical formulations and finite-element analysis of problems in solid and structural mechanics (plates and shells), composite materials, computational fluid dynamics, numerical heat transfer, and applied mathematics.
Dr. Reddy received both teaching and research awards from the institutions where he has been a faculty member. He also is the recipient of the 1984 Walter L. Huber Civil Engineering Research Prize of the American Society of Civil Engineers (ASCE), the 1985 Alumni Research Award at Virginia Polytechnic Institute, and 1992 Worcester Reed Warner Medal and 1995 Charles Russ Richards Memorial Award of the American Society of Mechanical Engineers (ASME). He received German Academic Exchange (DAAD) and von Humboldt Foundation (Germany) research awards. Most recently, he received the 1997 Melvin R. Lohmann Medal from Oklahoma State University's College of Engineering, Architecture and Technology, the 1997 Archie Higdon Distinguished Educator Award from the Mechanics Division of the American Society of Engineering Education, the 1998 Nathan M. Newmark Medal from the American Society of Civil Engineers, the 2000 Excellence in the Field of Composites and 2004 Distinguished Research Award from the American Society for Composites, the 2003 Texas A&M Bush Excellence Award for Faculty in International Research award, and the 2003 Computational Solid Mechanics award from USACM.
Professor Reddy is a fellow of the American Academy of Mechanics (AAM), the American Institute of Aeronautics and Astronautics (AIAA), the American Society of Civil Engineers (ASCE), the American Society of Mechanical Engineers (ASME), the American Society for Composites (ASC), International Association of Computational Mechanics (IACM), U.S. Association of Computational Mechanics (USACM), and the Aeronautical Society of India (ASI). He delivered over sixty five plenary, keynote, or general lectures at national and international conferences.
Dr. Reddy serves on the editorial boards of about two-dozen journals. He is the Editor-in-Chief of Applied Mechanics Reviews, Mechanics of Advanced Materials and Structures, International Journal of Computational Methods in Engineering Science and Mechanics and International Journal of Structural Stability and Dynamics. He also serves on the editorial boards of two dozen other journals in numerical and computational methods, applied mechanics, and nonlinear analysis.
Dr. Reddy is one of the few engineer-scientists included in ISI Highly Cited Researchers with over 10,000 citations received to date (with an h-index over 40) for his papers.
Course Fees
Rs. 10,000/- (inclusive of all taxes, meals and snacks). GROUP DISCOUNTS AVAILABLE
For more information, Contact:
Cranes Software International Limited (CSIL)
CAE R&D Services
5th floor, Block I, Shankarnarayana Building
MG road, Bangalore - 560001, India
Tel : +91 (080) 4112 0000
Fax : +91 (080) 4123 1274
Email :
www.cranessoftware.com www.nisasoftware.com
