### Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

### Prerequisites

2.001 Mechanics and Materials I

### Topics

The objective is to teach in a unified manner the fundamentals of finite element analysis of solids, structures, and fluids. This includes the theoretical foundations and appropriate use of finite element methods.

- The formulation of finite element methods for
**linear static analysis of solids and structures**:- Two- and three-dimensional solids
- Beam, plate and shell structures

- The displacement-based finite element procedures, when they are effective, and mixed finite element methods for almost incompressible media and beams, plates and shells.
- The formulation of finite element methods for
**nonlinear static**analysis:- Geometric nonlinearities (large displacements and large strains)
- Material nonlinearities (nonlinear elasticity and elasto-plasticity)

- The formulation of finite element methods for the analysis of
**heat transfer**in solids: conduction, convection and radiation conditions - The formulation of finite element methods for
**fluid flows**:- Incompressible flows
- Navier-Stokes equations including heat transfer

- The formulation of finite element methods for
**fluid-structure interactions**:- Acoustic fluids coupled to structures
- Navier-Stokes fluids coupled to structures

- The
**appropriate use**of finite element procedures:- Setting up an appropriate model
- Interpreting the results, and assessing the solution error

The methods studied in this course are practical procedures that are employed extensively in the mechanical, civil, ocean and aeronautical industries. Increasingly, the methods are used in computer-aided design.

### Textbook

You will find references to special topics in the textbook.

Bathe, K. J. *Finite Element Procedures*. 2nd ed. Klaus-Jurgen Bathe, 2014. ISBN: 9780979004957.

### Grades

The student’s course grade will be based on:

- Weekly homework, given out Thursdays and to be handed-in the following Thursday, except no homework due on exam days.
- Term project, due on Lec #21 (project proposal due on Lec #8)
- Two 1½ hour exams: Exam 1 tests on all material presented in the course up to and including Lec #11. Exam 2 tests on all material presented in the course.

### Reading Assignments

The reading assignments will be given in the lectures and will refer to the textbook *Finite Element Procedures*. We will discuss specific material in chapters 1, 3, 4, 5, 6, 7, and 8.

#### Other Complementary Reading Material

Kojic, M., and K. J. Bathe. *Inelastic Analysis of Solids and Structures*. Berlin, Germany: Springer-Verlag, 2004. ISBN: 9783540227939.

Chapelle, D., and K. J. Bathe. *The Finite Element Analysis of Shells – Fundamentals*. Berlin, Germany: Springer, 2003. ISBN: 9783540413394.

Bathe, K. J. “The Finite Element Method.” pp. 1253-1264 in *Wiley Encyclopedia of Computer Science and Engineering.* Edited by Benjamin W. Wah. Hoboken, NJ: Wiley-Interscience, 2009. ISBN: 9780471383932.

### 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. Please see this page for a list of alternative finite element analysis packages.

### 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 2.094, they can serve as a useful complement to the materials presented here.

You may also be interested in the course *2.092/2.093 Finite Element Analysis of Solids and Fluids I*.