1.2. Understanding Theory Reference Notation

The notation defined below is a partial list of the notation used throughout the manual. There are also some tables of definitions given in following sections:

Due to the wide variety of topics covered in this manual, some exceptions will exist.

Table 1.1:  General Terms

TermMeaning
[B]strain-displacement matrix
[C]damping matrix
[Ct]specific heat matrix
[D]elasticity matrix
EYoung's modulus
{F}force vector
[I]identity matrix
{I}current vector, associated with electrical potential degrees of freedom
{J}current vector, associated with magnetic potential degrees of freedom
[K]stiffness matrix
[Kt]conductivity matrix
[M]mass matrix
[O]null matrix
P, {P}pressure (vector)
{Q}heat flow vector
[S]stress stiffness matrix
{T}temperature vector
ttime, thickness
[TR]local to global conversion matrix
u, v, w, {u} displacement, displacement vector
{V}electric potential vector
δUvirtual internal work
δVvirtual external work
{W}fluid flow vector
x, y, zelement coordinate
X, Y, Znodal coordinates (usually global Cartesian)
α coefficient of thermal expansion
εstrain
νPoisson's ratio
σstress

Below is a partial list of superscripts and subscripts used on [K], [M], [C], [S], {u}, {T}, and/or {F}. See also Coupling. The absence of a subscript on the above terms implies the total matrix in final form, ready for solution.

Table 1.2:  Superscripts and Subscripts

TermMeaning
acnodal effects caused by an acceleration field
cconvection surface
crcreep
ebased on element in global coordinates
elelastic
ginternal heat generation
iequilibrium iteration number
based on element in element coordinates
mmaster
nsubstep number (time step)
ndeffects applied directly to node
plplasticity
prpressure
sslave
swswelling
t, ththermal
^(flex over term) reduced matrices and vectors
.(dot over term) time derivative


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