Syllabus

Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Prerequisites

Course Introduction

We focus on modern practical finite element methods for solids and fluids using physical explanations of the finite element methods. The analysis procedures are used extensively in the various fields of engineering and the sciences.

Some strong reasons for taking this course:

You learn modern analysis techniques used widely in engineering practice and the sciences, and you use these techniques in a general finite element program.
You learn how to establish computational models of problems of solids and fluids, solve them on your laptop, and assess the accuracy of the results.
You capitalize on your knowledge of mechanics, reinforce your knowledge, and solve problems that can only be tackled numerically on the computer.

Great knowledge in your toolbox whatever your goals!

Topics

Finite element analysis of solids, structures, fluid-flows, fluid-structure interactions, steady-state and transient problems.
The finite element methods explained physically: why they work, what they can be used for.
Modeling of problems, solution of response, how to check the results, how to assess the accuracy of the results.
Use of a general finite element computer program.

Hence in the course we focus on the actual analysis of problems, the physical explanation of the finite element methods, and the use of a general computer program. We shall consider solids and fluids and keep the theoretical discussions of finite element methods to a minimum.

The methods studied in this course are practical procedures that are employed extensively in the mechanical, civil, ocean and aeronautical industries.

Textbook

You will find readings and references to special topics in the textbook.

Bathe, K. J. Finite Element Procedures. Cambridge, MA: Klaus-Jürgen Bathe, 2007. ISBN: 9780979004902.

Grades

The student's course grade will be based on:

Weekly homework, usually given out Thursdays and to be handed in the following Thursday.
Term project, graduate students only, due Session #21 (project proposal due Session #6).
Two 1½ hour exams in Sessions #14 and #22.

Use of Finite Element Computer Program

We will use ADINA for all finite element program related homework and for the projects. Two special lectures, Sessions #8 and 9, will be given on the use of and modeling with ADINA for the analysis of solids and structures, fluid flows, i.e. CFD, and fluid flows with structural interactions, i.e. FSI. These lectures will prepare you to complete your homework assignments using ADINA and your project. Please see this page for a list of alternative finite element analysis programs.

Reading Assignments

The reading assignments will be given in each lecture and will refer to the textbook Finite Element Procedures. A list of readings by session is also available on the Calendar page.

Computer Assignments

You will not be required to develop a computer program. However, some homework will require that you use the graphical user interface of the finite element program system ADINA, which can be run on your laptop.

Term Project

Every graduate student taking 2.093 is required to complete a term project; undergraduates taking 2.092 are not required to complete a project. Hence, the only difference between taking 2.093 (graduate students) and 2.092 (undergraduate students) is this requirement regarding the project. Further details about the project are given on the Projects page.

Additional Resources

Prof. Bathe has recorded two video courses on the topics of Linear Analysis and Nonlinear Analysis, now available from MIT OpenCourseWare. While these lectures do not correspond directly to the sequence of topics in 2.092/2.093, they can serve as a useful complement to the materials presented here.

You may also be interested in the course 2.094 Finite Element Analysis of Solids and Fluids II.