# Course Description

Introduction to finite element analysis (FEA) with focus on linear elasticity and heat transfer. Matrix analysis and assembly of solutions. Strong form and weak form as a general solution process for differential equations. Formulation of finite elements and interpolation functions. Overall solution processes with the finite element method. Survey of advanced topics (such as nonlinear problems and dynamic loading). MATLAB used for coding. Presentations for practitioners in industry. Two-hour lecture component complemented by one-hour laboratory component. Use of a modern (commercial) finite element code.

Typically offered Fall & Spring. 3 credits.

Prerequisite: ME 32300

See https://wl.mypurdue.purdue.edu/ for semester specific enrollment.

Lectures: M-W and alternate F (50 min each) Labs: alternate F (100 min each)

#### Prof. Thomas Siegmund

Email
siegmund@purdue.edu
Phone
(49)4-9766
Office
ME 2186

#### Prof. Ganesh Subbarayan

Email
ganeshs@purdue.edu
Phone
(49)4-9770
Office
ME 3172

# Course Outcomes

1. Introduce concepts of finite element analysis
2. Learn the use of matrix methods for solution of truss structures
3. Learn strong and weak form for the solution of differential equations
4. Learn how to define finite elements and finite element approximations
5. Learn how to solve weak form formulations as a finite element approximation
6. Apply these concepts to linear elastic and heat transfer problems
7. Apply a commercial finite element code to linear elastic and heat transfer problems
8. Understand the use of the Finite Element Analysis in engineering practice

# Detailed Topic List

### Fundamentals (3 wks)

1. Review of Linear Elasticity
2. Review of Heat Transfer
3. 1D Bar Problems
4. 2D Bar Problems
5. Assembly and Global Solution

### Strong and Weak Form (4 wks)

1. Strong Form
2. Weak Form
3. Example Problems with Weak Form in Scalar/Vector Problems

### FE Approximations (4 wks)

1. Definition of finite elements in 1D
2. Definition finite elements in 2D
3. Weak Form Statement and Finite Element Approximation
4. Thermal Stress Analysis
5. Numerical Examples

### Computations (4 wks)

1. Matrix Method 1D (MATLAB)
2. Finite Elements 1D (MATLAB)
3. Model Building
4. A Commerical Finite Element Code: Examples

# Laboratories

1. Truss Structures
2. Planar modeling and meshes
3. Heat Transfert - Conduction
4. Convergence
5. Patch Test
6. Elasticity analysis
7. Stress concentration
8. Modeling approaches: what can go wrong?