User:Eml4500.f08.wiki1.aguilar/Syllabus

EML 4500 Finite Element Analysis and Design (FEAD), Fall 2008, Dr. L. Vu-Quoc
Course description: Fundamentals of the finite element (FE) method and applications to structural, solid, and bio-mechanics. Principle of vitual work. Derivation of the stiffness matrices for truss, beam, and solid elements. Coordinate transformation for structural elements in 3-D. Direct stiffness method. Static analysis of FE systems with a matrix linear algebra approach, internal structure of a FE code, coding and plotting. Linear stability analysis of truss and beam structures. Applications to aerospace structures and biomechanics. Other topics such as axisymmetric solid elements, dynamic analysis, substructuring analysis, etc. could be taught, depending on the class and the instructor.

Course objective: This course is intended to be the first Finite Element Method (FEM) course for all engineering students. Its objective is to develop a basic understanding of the fundamentals of the FEM through careful derivation of the stiffness matrix from first principles. Fundamental concepts of linear algebra are taught, e.g., inversion and transpose of matrix product, matrix partitioning and solution by static condensation, determinant, eigenvalue problems, etc. For trusses and beams, coordinate transformation of the degrees of freedom from local to global coordinates and the direct stiffness method to assemble element matrices into global matrix is emphasized. The 3-D aspect is emphasized for all truss and beam elements. Euler-Bernoulli beam theory with shear correction, in 3-D, is taught in detail. The connection of linear algebra to the FEM is emphasized, e.g., rigid-body modes and the singularity of the element stiffness matrix. For solid elements, an introduction to the principle of minimum potential energy and the principle of virtual work taught. Commercial codes can be used to train students on practical aspects of FE analysis. Some aspects of buckling analysis and dynamic analysis, and their connection to linear algebra, are addressed.

Topics:

* 3-D truss, beam, and solid structures. Beams with shear correction. * Matrix algebra and its application to finite element solution. * Construction of a FE code, coding and plotting. * Linear stability (buckling) analysis of truss and beam structures. * Applications to mechanical and aerospace engineering, biomechanics, and other engineering    areas (e.g., circuit analysis, heat conduction, etc.) * Class projects: Students will "design" and solve open-ended problems that involve FE model    building and analysis of complex problems (e.g., prostheses, organs, airframes, automobiles,     off-shore platforms, etc.). * Other advanced topics: axisymmetric solid elements, dynamic analysis, nonlinear analysis,    substructuring analyis, etc. depending on mutual interest between the students and the     instructor.

Text and other resources: M. Asghar Bhatti, Finite Element Analysis With Mathematica and Matlab Computations and Practical Applications: Fundamental Concepts John Wiley & Sons (February 4, 2005) ISBN 0471648086 Fri, 07 Jul 2006.

Recommended: * J.S. Przemieniecki, Theory of Matrix Structural Analysis, Dover, 1985, (McGraw-Hill, 1968). ISBN 0-486-64948-2 (Paperback). Library call no. 624.171 P973t. * Y.W. Kwon and H. Bang, Finite Element Method using MATLAB, 2nd edition, CRC Press, 2000. ISBN 0-8493-9653-0. Library call no. TA347.F5 K86 1997 (first edition). * Matlab Guide to Finite Elements: An Interactive Approach, Peter Issa Kattan, Springer Verlag   (February 15, 2003), ISBN 3540438742.

Web pages of related courses: Fall 2006: EML 4500 Finite Element Analysis and Design. Fall 2003: EML 4500 Finite Element Analysis and Design. Spring 2000: EAS 4210C Finite Element for Engineering Mechanics Spring 1999: EAS 4210C Aerospace Structures 2

Grade determination: Tentatively, homework/project and class participation including bonuses (31%), exam1 (23%), exam2 (23%), exam3 (23%). Adjustments to the weights could be made at the end of the course.

Homework: There will be HW assignments, which are to be solved following Cooperative Learning Techniques. HW should be thought of as mini projects, which include "hand solution" with the help of Matlab and the use of the Matlab codes that come with the textbook. Students will also be asked to develop their own Matlab codes. For a tutorial on how to use Matlab, see [|Matlab] matters. See the [|course policy] for more details.

Course outcome: Upon a successful completion of this course, a student is expected to: The above outcomes are consistent with the Departmental and College of Engineering Educational Objectives and meet the following ABET criteria:
 * 1) Have an understanding of matrix linear algebra and its role in the solution of FE systems.
 * 2) Master the derivation of various structural elements in 3-D (truss, beam), and the associated transformation of the stiffness matrix from local coordinates to global coordinates by the Principle of Virtual Work.
 * 3) Know how to correct for shear deformation in Euler-Bernoulli beam.
 * 4) Have a notion of the derivation of the stiffness matrix of solid elements, and their use in a commercial FE code.
 * 5) Know that the concepts of the FEM are also applied to fields other than structural and solid mechanics, e.g., circuit analysis, heat conduction, fluid mechanics, electromagnetics, etc.
 * 6) Develop skills to tackle open-ended problems in FE analysis and design.
 * 7) Develop communication skills, presentation skills, report-writing skills, team work (cooperative learning).
 * 1) Ability to apply knowledge of mathematics, science, and engineering.
 * 2) Ability to identify, formulate, and solve engineering problems.
 * 3) Ability communicate effectively.
 * 4) Ability to use the techniques, skills, and modern engineering tools necessary for engineering practice.

This page was last updated on: Tue, 12 Aug 2008, 17:56:54 EDT