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 di
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
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: continui
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 follow
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 ),
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 techni
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 p
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 stat
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)