Syllabus for ME7873 Energy principles in mechanics with elements ...

Syllabus for ME7873Energy principles in mechanicswith elements of structuraloptimizationCourse InformationFall, 2010Instructor: Dr. Maurizio PorfiriEmail: mporfiri@poly.eduOffice: RH507Phone: 718-260-3681Office Hours: Thursday 5:00-5:55Lecture: Thursday 6:00-8:25 RH708Webpage:My PolyCourse GoalsThis course presents the fundamentals of energy methods in mechanics with elements of structural optimization.Topics include fundamentals of variational calculus, solid mechanics, vibrations, numerical methodsfor variational problems, finite element analysis, and structural optimization. Students will develop a basicknowledge of energy methods that is of sufficient depth to begin reading the subject literature spanning fromreduced order modeling to computational analysis.PrerequisitesIt is assumed that all students have a working familiarity with graduate level solid mechanics and appliedmathematics.Required Text1. Haftka, R. T. and Gurdal, Z. Elements of Structural Optimization, Kluwer, 19922. Mura, T. and Koya, T. Variational Methods in Mechanics, Oxford, 1992ReferencesJournal papers1. Teresi, L. and Tiero, A., 1997: “On Variational Approaches to Plate Models”, Meccanica, 32, 143-156Books1. Gurtin, M. An Introduction to Continuum Mechanics, Academic Press, 19822. Lanczos, C. The Variational Principles of Mechanics, Dover, 19703. Reddy, J. N. Energy and Variational Methods in Applied Mechanics, Wiley, 19841

HomeworkTwo homework will be assigned. Each homework assignment must be typed on a word-processor. Useof LaTeX is encouraged, although other word processing platforms are certainly acceptable. Students musthand-in their own work. Students are permitted to discuss homework questions with other students, althoughthey are not permitted to discuss solutions except in general terms. No late homework will be accepted exceptfor exceptional and documented circumstances. Solutions for all assigned problems will be provided, althoughnot all assigned problems will necessarily be graded. Significant weight in grading will be placed on clarityof presentation.The two homework assignments are due at the start of class on:1. Thursday, 7 October2. Thursday, 11 NovemberExamsThere will be only one mid-term. The exam will be administered in class and will test the student’s comprehensionand ability to apply material learned in class and through assignments. The test is open book andclosed notes. Formula sheets prepared by students will not be allowed. During the exam, before beginning tosolve assigned problems, students should briefly restate the problem and list the data given. Also, studentsshould list the important concepts and formulae used to arrive at the final solution along with detailedwork. Every page of every exam submission should have the student full name and section number. Illegiblework and loose sheets will not be graded. Students must complete the exam on their own. If a studentcannot attend an exam due to a medical condition, certified by a doctor, he/she must notify the instructorin advance. Unexcused absence from an exam will result in a grade of 0 for that exam.ProjectOne project will be assigned to every student team comprising 2-3 students on November 4, 2010. Eachproject must be typed on a word-processor. Use of LaTeX is encouraged, although other word processingplatforms are certainly acceptable. Students will present their projects during the last day of class and mustturn their project to the instructor during that day.Grading policyHomework: 30%Midterm Exam: 30%Project: 40%Extra creditThere are no opportunities for extra credit. The grading policy allows for a “bad score”.Class attendance and absencesThere are no formal requirements for attendance, and there is no direct penalty for missing class. Studentsare strongly encouraged to attend class since some course material will only appear in lectures. Studentsthat miss class are responsible for obtaining class notes from a classmate.2

Honor systemThe honor system is in strictly force for this course. It is assumed that all work submitted by a studentis done so under the honor system code. Homework questions may be discussed with students.Homework solutions may not be discussed. The final exam must be completed individually.ABET a-k criteria compliancea b c d e f g h i j kME5653 ̌ ̌ ̌ ̌ ̌ ̌ ̌ ̌ ̌(a) an ability to apply knowledge of mathematics, science, and engineering(b) an ability to design and conduct experiments, as well as to analyze and interpret data(c) an ability to design a system, component, or process to meet desired needs(d) an ability to function on multi-disciplinary teams(e) an ability to identify, formulate, and solve engineering problems(f) an understanding of professional and ethical responsibility(g) an ability to communicate effectively(h) the broad education necessary to understand the impact of engineering solutions in a global andsocietal context(i) a recognition of the need for, and an ability to engage in life-long learning(j) a knowledge of contemporary issues(k) an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice.3

Tentative Lecture ScheduleLecture Reading Topic of the dayLecture 19/9/10Lecture 29/16/10Lecture 39/23/10Lecture 49/30/10Lecture 510/07/10Lecture 610/14/10Lecture 710/21/10Lecture 810/28/10Lecture 911/04/10Lecture 1011/11/10Lecture 1111/18/10Lecture 1211/23/10Lecture 1312/02/10Lecture 1412/09/10MK Ch 1 and HG Ch 2MK Ch 2 and HG Ch 2MK Ch 3MK Ch 4MK Ch 6 and HG Ch 3MK Ch 8MK Ch 10MK Ch 11MK Ch 14-16HG Ch 3HG Ch 4 and 5HG Ch 6Course overview and maxima/minima offunctionsEuler equationRitz’s methodsMore on Euler equationSubsidiary conditionsGalerkin’s method and fundamentals of finiteelement analysisMidterm examTransformations in variational calculusElasticityEigenvalue problemLinear programmingSelected numerical methods for optimizationPractical problemsProjects4