Transcript MECH300H Introduction to Finite Element Methods Dr. Wenjing Ye

MECH300H Introduction to Finite
Element Methods
Dr. Wenjing Ye
Department of Mechanical Engineering
Hong Kong University of Science & Technology
Clear Water Bay, Kowloon, Hong Kong SAR
Tel: +852-2358-7194, Fax: +852-2358-1543
E-mail: [email protected]
Course 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:
du
u
dt
u ( 0)  u 0
What is a Numerical Method – An
Example
Example 1:
du
u
dt
u ( 0)  u 0
What is a Numerical Method – An
Example
Example 2:
du
 2u  5e - t
dt
u ( 0)  u 0
What is a Numerical Method – An
Example
Example 2:
du
 2u  5e - t
dt
u ( 0)  1
What is a Numerical Method – An
Example
Example 3:
du
 u2  t
dt
u ( 0)  1
What is a Finite Element Method



Discretization
1-D
?-D
2-D
Hybrid
3-D
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