MECH300H Introduction to Finite Element Methods

Dr. Wenjing Ye

Department of Mechanical EngineeringHong Kong University of Science & Technology

Clear Water Bay, Kowloon, Hong Kong SARTel: +852-2358-7194, Fax: +852-2358-1543

E-mail: mewye@ust.hkCourse Homepage:

http://www.me.ust.hk/~mech300h

Numerical Methods – Definition and Advantages

Definition: Methods that seek quantitative approximations to the solutions of mathematical problems Advantages:

What is a Numerical Method – An Example

Example 1: 0)0( uuudt

du

What is a Numerical Method – An Example

Example 1: 0)0( uuudt

du

What is a Numerical Method – An Example

Example 2: 0t- )0( e52 uuu

dt

du

What is a Numerical Method – An Example

Example 2: 1)0( e52 t- uudt

du

What is a Numerical Method – An Example

Example 3: 1)0( 2 utudt

du

What is a Finite Element Method

Discretization

1-D 2-D

3-D?-D Hybrid

Approximation

Numerical Interpolation

Non-exact Boundary Conditions

Applications of Finite Element Methods

Structural & Stress Analysis Thermal Analysis Dynamic Analysis Acoustic Analysis Electro-Magnetic Analysis Manufacturing Processes Fluid Dynamics