Finite Elements Method (1D)

1
Finite Elements Method (1D)

• 2003.4.17

2
Node, Elements
1
Local Coordinates
?
Node j
?
Element
Node i
Global Coordinates
3
Sample Truss
1
4
2
P Force
(4)
(5)
(1)
(3)
x
3
1
(2)
Constraint 2
Constraint 1
4
Local Variable to Global Variable with Rotation
1

• Deformation
• Force
• Relation

5
Combining the equation
1

• Element equation ? Global Matrix

6
Elastic Bar
2
T
P
P
(Strain energy Gravity energy)
wdx
Q
Q
TdT
gravity
7
Theory
2

• V(u(x)) functional u(x) function
• At equilbrium, the extension is such that the
  potential energy is a minimum

?
8
Approximation for u(x)
2
Linear Approximation
Shape Function
9
Finite Element Equations