Lecture 2 Notes: The Finite Element Analysis Process
Reading assignment: Chapter 1, Sections 3.1, 3.2, 4.1
We consider a body (solid or uid) and dene the following quantities:
Su
=
Surface on which displacements, velocities are
prescribed Sf =
f Sf
=
Forc
Lecture 6 Notes: Finite Element Solution Process (Part 1)
In the last lecture, we used the principle of virtual displacements to obtain the following equations:
KU = R
(1)
K=
K (m) m
R = RB +
RS
R
;
K (m) =
B (m)T C (m) B (m) dV
(m)
;
R(m) =
H (m)T f B(m)
Lecture 3 Notes: Analysis of Solids/Structures and Fluids
The fundamental conditions to be satised are:
I. Equilibrium: in solids, F = ma; in uids, conservation of momentum
II. Compatibility: continuity and boundary conditions
III. Constitutive relations:
Lecture 5 Notes: The Finite Element Formulation
In this system, (X, Y, Z) is the global coordinate system, and (x, y, z) is the local coordinate system for
the element i.
We want to satisfy the following equations:
ij,j + fi = 0 in V
ij nj = fi
on Sf
f
u
Lecture 4 Notes: The Principle of Virtual Work
Su = Surface on which displacements are
prescribed Sf = Surface on which loads are
applied
Su Sf = S
;
Sf Su =
Given the system geometry (V, Su , Sf ), loads (f B , f Sf ), and material laws, we calculate:
Lecture 12 Notes: FEA of Heat Transfer/Incompressible Fluid Flow
Reminder: Quiz #1, Oct. 29. Closed book, 4 pages of
notes. Reading assigment: Section 7.4.2
We recall the principle of virtual temperatures.
=
T
T qB dV +
k dV
V
V
T qS dS
Sq
(m) = H (m)
;
Lecture 13 Notes: Physical Explanation of Gauss Elimination
Reading assignment: Sections 8.1, 8.2
Gauss elimination is the direct method of solution, which includes:
LDLT factorization; sparse techniques
Wavefront method
Substructuring, super-element t
Lecture 11 Notes: Heat Transfer
Analysis
Reading assignment: Sections 7.1-7.4.1
To discuss heat transfer in systems, rst let us dene some variables.
(x, y, z, t
)
S
=
=
Temperature
Surface area with prescribed temperature (p )
=
Surface area with prescrib
Lecture 10 Notes: Nonlinear Finite Element Analysis of Solids & Structures
Reading assignment: Sections 6.1, 8.4.1
Discretization of the variational formulation leads to the following equilibrium statement:
t+t
F =
t+t
R
(1)
t+t
F = nodal forces correspon
Lecture 7 Notes: Finite Element Solution Process (Part 2)
Recall that we have established for the general system some expressions:
(1)
KU = R
K = K (m)
K (m) =
;
R = RB + RS
B (m)T C (m) B (m) dV (m)
(2)
V (m)
Then, since C (m)T = C (m) ,
K (m)T =
B (m)T