Memorial University of Newfoundland

Faculty of Engineering and Applied Science

 

 

Engineering: 7934 & 7706

Finite Element Structural Analysis

 

 

Instructor                   Dr. Seshu Adluri                    

Phone                         864-3800                                

Office                          EN-3044                                 

Office Hours               Monday 11:00-11:50 a.m.    

Office Hours               Friday       1:00-1:50 p.m.                              

Website                      www.engr.mun.ca/~adluri/fem/7706/

                                    adluri@mun.ca                     

 

NOTE : 

This course is being offered to Mechanical students as ENG 7934 and Civil Students as ENG 7706.  Naval students can register following directions given by Naval Chair.  For both courses pre-requisites include undergraduate solid mechanics courses. A clear understanding of mechanics in general (including boundary conditions for various applications, material behavior, equilibrium, stress-strain relationships) and concepts of Analysis are also expected.  The students need to brush up on the concepts of Matrices, solution of simultaneous equations, basic calculus such as differentiation, integration, simple differential equations, etc.  (This is not a completely calculus based course –however, familiarity is necessary). Some of these concepts may be reviewed in class as and when time permits.  This course is not a follow up for the applied analysis course ENG 5434.

 

CALENDAR ENTRY:                

Finite Element Structural Analysis includes a review of basic concepts required for FEA, basics of stiffness formulation, direct stiffness method, displacement method, one dimensional elements, trusses and frames. Topics include 1-D fluid and heat transfer elements, automated analysis and modelling concepts, higher order elements, two dimensional elements - plane stress and plane strain, introduction to 3D and other types.  Introduction to advanced topics and isoparametric formulation.

 

COURSE DESCRIPTION:         

Rationale & Outline: This course introduces the basic concepts of the finite element method for stress (and structural) analysis.  The method is the most powerful analytical tool ever invented for this purpose.  It is very versatile and extremely popular.  No student can truly hope to become a competent mechanical designer or structural engineer without a clear understanding of this method. 

The course introduces the basic concepts involved in finite element formulation such as degrees of freedom, stiffness, compatibility and equilibrium, the use of potential energy, matrix methods, constraints etc.  Bars, beams and 2-D plane elements are derived in detail and their use is demonstrated.  While the main emphasis of the course is on understanding the concepts and solving problems through manual computation, a general introduction to computer aided analysis is given depending upon the availability of facilities. 

Introduction to the use of non-solid elements is given by way of heat transfer and fluid mechanics.

 

PREREQUISITES:  ENGI undergraduate solid mechanics courses
ENG 6705 & ENG 5312   OR   ENG 5931 & ENG 4430

COREQUISITES:                       A good working knowledge of matrices, calculus, computers, spreadsheets, etc., is required. 

SCHEDULE:                              LECTURE: MWF 12:00-12:50 pm        Room: EN2040

                                                TUTORIAL: Some portion of the lab slots may be used for tutorials

                                                Lab: Tues 1:00-2:50                             Room: EN3000/3029

CREDIT VALUE:                       3 credits

 

RESOURCES:                           www.engr.mun.ca/~adluri/courses/fem/7706/

 

Text book:  Logan, D.L., A First Course in the Finite Element Method  

REFERENCES:  Additional Reading:

Additional references as given during class and as cited in the textbook

MAJOR TOPICS:                     

    1. Review of basic concepts required for FEA
    1. Direct stiffness method
    2. Minimization of potential energy and related concepts
    3. Springs and One dimensional bars
    4. Analysis of trusses, 2-D and 3-D
    5. Development of Beam (and Grid) equations (optional)
    6. Analysis of general Frames, etc. (optional)
    1. Modeling concepts, Meshing, Symmetry, element choice, etc.
    2. Computer implementation
    1. 1-D elements such as Fluid and Heat transfer elements
    2. Introduction to Calculus of Variations.
    3. Lagrange's Equations.
    4. Rayleigh-Ritz methods
    5. 1-D and 2-D elements
    1. Two dimensional elements - plane stress and plane strain
    2. Introduction to CS Triangles and LS Triangles
    3. Problems in structural mechanics
    4. Isoparametric formulation -intro.
    5. Introduction to advanced topics

Any of the above may be extended with related topics and applications depending upon time and interest.

Expectations:  The students taking this course must make use of the knowledge from previous courses in solid mechanics and analysis.  At the end of this course, the students are expected to clearly demonstrate a basic understanding of the underlying principles of stiffness method of finite element analysis, formulation different categories of elements, element assembly and manual solutions to matric equations of typical 1-D & 2-D problems.  

ASSESSMENT: 

Assignments (manual)           10%                  Assignments are due one week from announcement unless otherwise agreed upon. 

Assignments (computer)        5%                    May include computer work and the use of software such as, ANSYS, ABAQUS, PRO-ENGINEER, Spread Sheets, Maple/Mathcad.

Midterm                                 25%                  June 16

Final exam                              60%                 

Exam policy: The formula sheet is as per the announcement in the class.  All or a subset of the preannounced formula sheet will be provided in the exam.  No extra text or notes are permitted in the exam.  Electronic storage/retrieval devices are not permitted in the exam.  Please see the appropriate guidelines from the University regarding such matters. 

Comprehensive examples will be discussed primarily during tutorials. During tutorials, the students may be required to solve the problems in class to gain practice. Tutorials and labs dealing with computer work are compulsory.

Please note that prewritten solutions may or may not be available for the assignments.  However, the tutorials are specifically marked for discussing the relevant solutions.  At that time, if the students ask for it, the problems can be discussed and may be partially or fully solved in class.  If the students do not raise their need for discussion of the problems, the time will be spent on solving other example problems, etc.  The same policy holds for midterm exams and quizzes, if any.

The students are expected to solve the assignment problems by themselves in order to reinforce the class instruction.  Please refer to copying policy of the University if there is any doubt.  Help with the assignment problems can be sought during contact hours and/or tutorial time. 

ACADEMIC INTEGRITY AND PROFESSIONAL CONDUCT:

 

Students are expected to conduct themselves in all aspects of the course at the highest level of academic integrity. Any student found to commit academic misconduct will be dealt with according to the Faculty and University practices. More information is available at www.engr.mun.ca/undergrad/academicintegrity.

 

Students are encouraged to consult the Faculty of Engineering and Applied Science Student Code of Conduct at http://www.engr.mun.ca/policies/codeofconduct.php and Memorial University’s Code of Student Conduct at http://www.mun.ca/student/home/conduct.php.

 

INCLUSION AND EQUITY: 

 

Students who require physical or academic accommodations are encouraged to speak privately to the instructor so that appropriate arrangements can be made to ensure your full participation in the course.  All conversations will remain confidential.

 

The university experience is enriched by the diversity of viewpoints, values, and backgrounds that each class participant possesses.  In order for this course to encourage as much insightful and comprehensive discussion among class participants as possible, there is an expectation that dialogue will be collegial and respectful across disciplinary, cultural, and personal boundaries.

 

STUDENT ASSISTANCE:  Student Affairs and Services offers help and support in a variety of areas, both academic and personal.  More information can be found at www.mun.ca/student. 

 

 

Manual Assignments:

 

Assign1,  A1Sol,  Assign2, A2sol, Assign3, A3Sol, Assign4,  A4Sol, Assign5, A5Sol,

Note:  Assignment 4 has a 30% bonus question

 

ABAQUS:  Tutorial1,  Tutorial2, Tutorial3, Tutorial4, Tutorial5, Tutorial6,

Assign1, Assign2, Assign3, Assign4,

 

 

Past Final Exam

 

Element Matrices