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Finite Elements in Elasticity

Fundamentals of theory of elasticity; variational principles; one-, two-, and three-dimensional elasticity finite elements; interpolation methods; numerical integration; convergence criteria; stress interpretation

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Learning Objective:

By the end of the course, students will be able to:

CLO1: Formulate a problem mathematically in its strong and weak form

CLO2: Implement the formulation for basic finite elements in a computer code

CLO3: Solve a practical problem of interest using finite element software and/or by writing code

CLO4: Interpret the results of a finite element analysis correctly

CLO5: Revise a finite element model to achieve greater fidelity

Description:

Fundamentals of theory of elasticity; variational principles; one-, two-, and three-dimensional elasticity finite elements; interpolation methods; numerical integration; convergence criteria; stress interpretation

Prerequisites:

Recommended: CE 570 - Advanced Structural Mechanics (or equivalent); Vector Calculus, Solid and Structural Mechanics; Computer Programming (MATLAB)

Applied / Theory:

https://purdue.brightspace.com

Web Content:

Syllabus, grades, lecture notes, homework assignments, solutions and quizzes.

Homework:

Each homework assignment will have two submissions: Part 1 and Part 2. You will have one week to work on and submit each part. For Part 1, you will solve the homework problems to the best of your ability (even if your solution is incorrect), scan, and submit your work. Homework solutions will be posted after the due date for Part 1. For Part 2, you will use the posted solutions to correct, compare, and comment on your solutions for Part 1. You will be graded for effort and completeness of Part 1 and correctness and comments on Part 2.

Projects:

For the term project, you will use a commercial finite element software such as ABAQUS (or develop your own code) to study a practical problem of your interest. Once you decide on a topic, you will need to identify 3-5 journal articles that describe a finite element model of the problem. Your overall objective will be to replicate some of the finite element results from these articles as best as you can and investigate alternative modeling strategies.

You will complete the project in three phases:

1. Proposal: Describe the topic, summarize relevant articles and propose which results you aim to replicate
2. Progress Report: Describe preliminary efforts to generate the finite element model and any initial results
3. Final Report: Describe the refined finite element model and compare your results to published papers

Your 'Progress Report' should build upon your 'Proposal' and your 'Final Report' should build upon your 'Progress Report'. You may collaborate with your fellow students to discuss and exchange modeling strategies, results and insights. However, you must submit an individual proposal, progress, and final report.

For each phase, you will need to submit individual reports, create a presentation and record a 5-minute video, and submit your presentation video to a discussion board post in Brightspace. Report submission and discussion posts will be evaluated by the instructor and TAs.

Exams:

Quizzes consisting of 8-10 questions each and will not have a time limit. At the beginning of each week, you should complete at least one quiz attempt to check your knowledge of the content. This is highly recommended to ensure you are prepared before a live class session. You are allowed three attempts on each quiz, but only your highest score will be recorded.

Textbooks:

Recommended:

• KD Hjelmstad, Fundamentals of Structural Mechanics, 2nd Ed, Springer
• O.C. Zienkiewicz and R.L. Taylor, The Finite Element Method, Volumes I, II, & III, 6th/7th Edition Butterworth & Heinemann publishers

Computer Requirements:

Students will be expected to complete programming assignments in MATLAB and gain some experience with Finite element software programs such as ABAQUAS, ANSYS, LS-DYNA etc. The choice of software is up to the student.

ProEd Minimum Requirements:

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