565.616.81 - Applied Finite Element Methods

Expanded Course Description

Proper background preparation includes linear algebra, differential equations and solid mechanics.

Course Structure

The course materials are divided into modules which can be accessed by clicking Modules on course menu. A module will have several sections including the overview, lectures and content, readings, discussions, and assignments. You are encouraged to preview all sections of the module before starting. Most modules run for a period of seven (7) days, exceptions are noted in the Course Outline. You should regularly check the Calendar and Announcements for assignment due dates.

Course Topics

• Finite Element Method Introduction
• 1-D System of Equations, Assembly, Partition, and Solution
• 2-Dimensional Truss – Strong and Weak Formulations
• Galerkin Approach With Trial and Weight Functions
• Linear, Quadratic and Cubic Shape Functions with Global Continuity
• Element Stiffness and Load Matrix with Quadratic Element
• Tapered Elastic Bar Solution
• Two Dimensional Problems and Shape Functions
• Isoparametric Finite Elements
• Derivatives and Jacobians with the Isoparametric Formulation
• Linear Theory of Elasticity and Constant Strain Triangle (CST)
• Isoparametric Four Node Linear Quadrilateral Element and Gauss Quadrature
• Beam and Plate Elements

Course Goals

This course explores the development and application of finite element methods, with emphasis on solid mechanics formulation. One, two and three dimensional elements will be explored through the use of truss, beam, shell and solid element formulations. Isoparametric formulation of elements will be examined and applied to several element types. Meshing and modeling issues will be examined and explored using commercial finite element software.

Course Learning Outcomes (CLOs)

• Apply finite element methods with emphasis on solid mechanics.
• Demonstrate development and application of truss, beam, plate, shell and solid elements.
• Apply isoparametric elements and formulation.
• Demonstrate modeling techniques using ABAQUS commercial finite element software.

Textbooks

Fish, J. and Belytschko, T., (2007). First course in finite elements. West Sussex, England: John Wiley & Sons Ltd.

ISBN-10: 0-470-03580-3 ISBN-13: 978-0-470-03580-1

Textbook information for this course is available online through the appropriate bookstore website: For online courses, search the MBS website.

Other Materials & Online Resources

Additionally, any of the following texts or other texts that you may have from previous courses may be useful for this course if you find yourself struggling with specific skills or interested in further details than covered in class:

• Bathe, K. J. (2006). Finite element procedures. Prentice Hall, Pearson Education, Inc.
• Belytschko, T., Liu, W. K., & Moran, B. (2000). Nonlinear finite elements for continua and structures. Hoboken, NJ: John Wiley & Sons, Ltd.
• Cook, R. D., Malkus, D. S., & Plesha, M. E. (1989). Concepts and applications of finite element analysis (3rd ed.). Hoboken, NJ: John Wiley & Sons, 1989.
• Cook, R. D. (1995). Finite element modeling for stress analysis. Hoboken, NJ: John Wiley & Sons.
• Gosz, M. R. (2006). Finite element method: Applications in solids, structures, and heat transfer. Boca Raton, FL: CRC Press.
• Hughes, T. J. R. (2000). The finite element method: Linear static and dynamic finite element analysis. Mineloa, NY: Dover Publications.
• Logan, D. L. (2012). A first course in the finite element method (5th ed.). Boston, MA: Cengage Learning.
• Mohammadi, S. (2008). Extended finite element method. Hoboken, NJ: Blackwell Publishing.
• Zienkiewicz, O. C., Taylor, R. L., & Zhu, J. Z. (2005). The finite element method: Its basis and Fundamentals (6th ed.). Amsterdam, Netherlands: Elsevier Ltd.
• Zienkiewicz, O. C., and Taylor, R. L. (2005). The finite element method: For solid and structural mechanics (6th ed.). Amsterdam, Netherlands: Elsevier Ltd..

Required Software

ABAQUS

You will need access to a recent version of ABAQUS commercial finite software. A student edition is available for download. The software is free but requires registration using your student email. The student edition is limited to 1,000 nodes, which is sufficient for this course. You will need to run the software in a Windows environment, as it currently does not operate on Mac systems.

Other mathematical software such as Maple, Matlab, or Mathematica are not required for the course, but may be useful for completing some of the assignments. Some of these software titles may be available to students through the University software center. No mathematical software will be permitted to complete the exams.

Student Coursework Requirements

It is expected that each module will take approximately 7–10 hours per week to complete. Here is an approximate breakdown: reading the assigned sections of the texts (approximately 1–2 hours per week), watching the video lectures (approximately 2–4 hours per week), and module assignments (approximately 2–4 hours per week). The video lectures have been developed with the expectation the student writes their own set of course notes in a manner similar to an actual live course setting for maximum retainment of information.

This course will consist of the following basic student requirements:

Discussions (10% of Final Grade Calculation)

You are responsible for carefully reading and watching all assigned material and being prepared for discussion. The majority of readings are from the course text. Video lectures provide the primary learning environment, which are supported by the textbook readings and discussion questions.

Post your initial response to the discussion questions by the evening of Day 5 for that module week. Posting a response to the discussion question is part one of your grade for module discussions (i.e., Timeliness).

Part two of your grade for module discussion is your interaction (i.e., responding to classmate postings with thoughtful responses). Just posting your response to a discussion question is not sufficient; we want you to interact with your classmates. Be detailed in your postings and in your responses to your classmates' postings. Feel free to agree or disagree with your classmates. Please ensure that your postings are civil and constructive.

I will monitor module discussions and will respond to some of the discussions as discussions are posted. In some instances, I will summarize the overall discussions and post the summary for the module.

Refer to the Discussion Rubric for information on how Discussions are graded.

Assignments (25% of Final Grade Calculation)

There will be weekly assignments which are worth 25% of the overall grade. The assignments are to be completed individually, but collaboration in understanding of the material is permitted. The assignments are built upon the previous weeks’ material, and designed to sequentially build up the student skill set needed for the finite element method. Students who produce unsatisfactory assignment grades will be asked to resubmit their assignments, as lack of mastery of the skills developed in the assignment has a long term negative impact on the ability to learn the remaining course material. Approximately 10 assignments will be made throughout the semester, with two or three assignments devoted to modeling and application using the commercial finite element code ABAQUS. Include a cover sheet with your name and assignment identifier. Also include your name and a page number indicator (i.e., page x of y) on each page of your submissions. Each assignment should have the problem statement, assumptions, computations, and conclusions/discussion delineated as needed. All figures and tables should be captioned and labeled appropriately.

All assignments are due according to the dates in the Calendar. Late submissions will be reduced by two letter grades (no exceptions without prior coordination with the instructors). Submissions beyond one week from due date will not be accepted.

Refer to the Assignment Rubric for information on how Assignments are graded.

Course Project (10% of Final Grade Calculation)

A Course Project will be assigned several weeks into the course. The last week of the course will be devoted to the course project and final exam. The project permits the student to select an appropriate structure to model.  Students will be required to properly discretize the model into a reasonable number of elements with mesh refinement where appropriate. Students will be required to justify element types selected. Boundary conditions will need to be chosen to accurately represent the real structure. One or more load cases will be applied to the structure. Element stress and nodal displacements will be calculated and compared to estimated values to judge the accuracy of the results. The final product will be a written report.

Refer to the Course Project Guidelines and Rubric for information on the Course Project.

Exams (55% of Final Grade Calculation, combined from 25% for Midterm and 30% for Final)

The Midterm Exam will be available in Module 6 and the Final Exam will be available in Module 14. You will have approximately 3 hours to complete each exam. The exams are open book and open notes. You are not permitted to use any mathematical or finite element software during the exam. 

Grading Policy

Assignments are due according to the dates posted in your Canvas course site. You may check these due dates in the Calendar or the Assignments in the corresponding modules. I will post grades one week after assignment due dates.

I generally do not directly grade spelling and grammar. However, egregious violations of the rules of the English language will be noted without comment. Consistently poor performance in either spelling or grammar is taken as an indication of poor written communication ability that may detract from your grade.

A grade of A indicates achievement of consistent excellence and distinction throughout the course—that is, conspicuous excellence in all aspects of assignments and discussion in every week.

A grade of B indicates work that meets all course requirements on a level appropriate for graduate academic work. These criteria apply to both undergraduates and graduate students taking the course.

EP uses a +/- grading system (see “Grading System”, Graduate Programs catalog, p. 10).

100-98 = A+
97-94 = A
93-90 = A−
89-87 = B+
86-83 = B
82-80 = B−
79-77 = C+
76-73 = C
72-70 = C−
69-67 = D+
66-63 = D
<63 = F

Final grades will be determined by the following weighting:

Course Policies

Successful completion of this course requires that students keep up to date with module lectures and reading assignments. Successful completion of module Assignments is critical, as the course builds upon previous module material, so “skipping” a module is detrimental to successful completion of the following modules. It is highly recommended that students take complete course notes based upon video lectures, as we will work through the details of derivations and problems. Passive participation in video lectures is much less effective. Take advantage of virtual Office Hours to avoid falling behind on course material.

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. 

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. 
 
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.