1. Syllabus

Catalog Description: Credits: 3; Stress-strain analysis and design of machine elements; finite element analysis.

Pre-requisites: CGS 2425 Computer programming for engineers, EGM 4313 Intermediate engineering analysis, and EGM 3520 Mechanics of materials.

Textbook: Kim & Sankar 2008, Introduction to Finite Element Analysis and Design, Wiley.

Course Objectives: This course focuses on the theoretical and computational formulations of the finite element method based on fundamental engineering science principles. Both static and dynamic analyses are covered. The hugely important and fascinating collapse of the Tacoma Narrows Bridge (TNB) forms the main motivational backbone for the course, on which are grafted topics that prepare students to develop a dynamic finite-element model of the TNB. Misleading (wrong) explanations of the TNB collapse over a long period of time, by engineering practitioners and in textbooks, would serve as excellent food for thoughts and lessons to any engineers in their formative years.

Topics covered include, but not limited to, trusses and beams, stiffness matrix formulation by equilibrium and by principle of virtual work (projection, Galerkin method), transformation of coordinates by principle of virtual work (projection), equation of motion, vibration analysis, undamped free vibration, eigenvalue problem, orthogonality of eigenvectors (mode shapes), projection of equation of motion on eigenvector basis, modal decomposition and reconstruction for forced vibration, treatment of damping, etc. Upon completion of this course, students are expected to obtain:

• A basic understanding of the static finite-element formulation for trusses and beams in 1-D, 2-D, 3-D spaces.
• An understanding of some important applications of the principle of virtual work (element stiffness matrix and transformation of coordinates).
• An understanding of structural dynamic formulation, vibration frequency and mode shapes, orthogonality, projection, modal decomposition technique.
• A basic skill in developing finite-element programs.

Calculators during exams: No electronic devices that can connect to the Internet are allowed (tablets, smartphones, cell phones, etc.). Only SAT calculators are allowed; see also SAT calculator policy, Scientific and graphing calculators (wikipedia)

ABET: Contribution of course to meeting the professional component:

EML 4507 supports several program outcomes enumerated in the Mission Statement of the Department of Mechanical and Aerospace Engineering. Specific ME program outcomes supported by this course include: (1) Apply knowledge of calculus based physics (ME Program Outcome M1); (2) Using knowledge of advanced mathematics through multivariate calculus and differential equations (ME Program Outcome M2); (3) Be familiar with linear algebra (ME Program Outcome M3). (4) Being able to work professionally in the mechanical systems area (ME Program Outcome M4).

Mathematical Sciences (15%), Physical Sciences (15%), Engineering Sciences (70%)

ABET: Relationship of course to program outcomes:

This course achieves the following Accreditation Board for Engineering and Technology (ABET) outcomes [note that the outcome number corresponds to the respective ABET outcomes (a) through (k)]:

• (a) Apply knowledge of mathematics, science, and engineering [high coverage; method of assessment is through 7 major formal team written reports, team oral presentations, and two exams to measure Outcome (a)]
• (c) Design a system, component or process to meet desired needs [low coverage; method of assessment is through 7 major formal team written reports, team oral presentations, and two exams related to design of trusses and frames for desired functionalities]
• (e) Identify, formulate, and solve engineering problems [high coverage; method of assessment is through 7 major formal team written reports, team oral presentations, and two exams to measure Outcome (e)]
• (f) Understand professional and ethical responsibilities [medium coverage through the historical case study of the TNB collapse; no assessment]
• (g) Communicate effectively [high coverage; method of assessment is through 7 major formal team written reports, team oral presentations to measure Outcome (g)]
• (h) Understand the impact of engineering solutions in a global, economic, environmental and societal context [medium coverage through the historical case study of the TNB collapse and subsequent design successes; no assessment]
• (i) Recognize the need for, and engage in life long learning [medium coverage through the historical case study of the TNB collapse, recent developments of the finite-element method and its applications; no assessment]
• (k) Use the techniques, skills and modern engineering tools necessary for engineering practice [high coverage; method of assessment is through 7 major formal team written reports involving matlab coding and other software to measure Outcome (k)].

Course wiki

Home page: Loc Vu-Quoc

E-mail: vu-quoc AT ufl.edu MAE Department