Download Lecture 6.

FEA Course Lecture VI – Outline
UCSD - 11/06/03
Review of Last Lecture (V) on Heat Transfer Analysis.
3D Elements
1.
2.
3.
4.
5.
Summary of Concepts of Heat Transfer
Thermal Loads and Boundary Conditions
Nonlinear Effects
Thermal transients and Modeling Considerations
Example FE
Finite Elements Principles and
Practices - Fall 03
Introduction to 3D Finite Elements Analysis
3D Solid Elements:
Three dimensional solid that is unrestricted as to shape,
loading, material properties and boundary conditions.
Six stress components and three displacements
components are considered. Beam bending, plane stress
and plate bending are all special cases of a 3D solid.
Solids of Revolution: [Also called Axisymmetric
z
Solid].
These are obtained by revolving a plane figure about an
axis in the plane (i.e., nothing varies with the
circumferential coordinate, Theta). Material points displace
only radially and axially and shear stresses ( ) and ( ) are
both zero.
Finite Elements Principles and
Practices - Fall 03
r
Kinematics in 3D Finite Elements Analysis
Stress-Strain relationship
s = Ee
a) 3D Solid
c
c
s x  (1   )c
 e x 
s  
 e 
(1   )c

c
y
  
 y 
s z  
(1   )c
 e z 

  
 

Symmetric
G
 xy  
  xy 
 yz  
  yz 
G
  
 
G   zx 
 zx  
c
b) Axisymmetric Solid and Isotropic Material
c
c
s r  (1   )c
 e r 
s  
 e 
(1   )c
c
  
   
 
(1   )c
 e z 
s z  

 zr  
G   zr 
Finite Elements Principles and
Practices - Fall 03
E
E
and G 
(1   )(1  2 )
2(1   )
z
r
Kinematics in 3D Finite Elements Analysis
Strain-displacement Relationships
a) 3D solid
u
u  v
 xy 

x
y x
v
v  w
e yy 
 yz 

y
z y
w
w  u
e zz 
 zx 

z
x z
b) axisymmetric
e xx 
u
r
u
e 
r
w
e zz 
z
e rr 
 yz 
 w u

r z
Some notes on Connecting Different Elements – do not mix axisymmetric with
plane elements.
Finite Elements Principles and
Practices - Fall 03
SOLID45 – 8 node
brick.
3D FEA
FEs for 3D Solids
SOLID65 –models
Reinforced Concrete
SOLID72 – 4 node
tetrahedral
SOLID73 - 8-node
brick (6 dof)
SOLID92 – 10 node
tetrahedral
Finite Elements Principles and
Practices - Fall 03
ANSYS Example
Page 716 – Heat Transfer Problem.
Finite Elements Principles and
Practices - Fall 03