Civil Engineering Reference
In-Depth Information
num
element node numbers vector
sense
sense of freedoms to be fixed vector
Dynamic real arrays:
bee
strain-displacement matrix
coord
element nodal coordinates
d
preconditioned rhs vector
dee
stress-strain matrix
der
shape function derivatives with respect to local coordinates
deriv
shape function derivatives with respect to global coordinates
diag precon
diagonal preconditioner vector
eld
element nodal displacements
shape functions
fun
integrating point coordinates
gc
loads generated by gravity
gravlo
global nodal coordinates
g coord
“gathers” the
p
vectors for all elements
g pmul
holds all the products of
km
and
p
g utemp
Jacobian matrix
jac
element stiffness matrix
km
kv
global stiffness matrix
loads
nodal loads and displacements
p
“descent” vector used in equations (3.22)
points
integrating point local coordinates
prop
element properties
r
-coordinates of mesh layout
r coords
stress terms
sigma
stores augmented diagonal terms
store
holds element stiffness matrices
storkm
vector used in equations (3.22)
u
fixed values of displacements
value
weighting coefficients
weights
“old” solution vector
x
“new” solution vector
xnew
x
-coordinates of mesh layout
x coords
y
-coordinates of mesh layout
y coords
z
-coordinates of mesh layout
z coords
5.2 Exercises
1. Derive in terms of local coordinates, any shape function of the following elements:
(a) 6-node triangle
(b) 8-node quadrilateral
(c) 9-node quadrilateral
