Sharp corners

A rectangle with sharp corners is easiest to generate in CalculiX. In practice, these are often made by extrusion.

It is generated by the following code for cgx:

## Define the view.
rot y
rot l 30
rot u 15

## Dimensions
# Rectangle parameters, width, height, wall thickness
valu W  / 50 1000
valu H / 50 1000
valu t / 2 1000
# Profile length
valu L / 200 1000
# Divisions
valu divW 20
valu divH 20
valu divt 4
valu divl 48
# Derived values
valu W2 / W 2
valu H2 / H 2
valu WI - W t

## Geometry
# First corner line
seto l1
    pnt p1 0 W 0
    pnt p2 0 WI t
    line ! p1 p2 divt
setc
# Center point
pnt pm 0 W2 H2
# Rectangle surface
seto Face1
    swep l1 l2 mir pm y divW
    swep l2 l3 mir pm z divH
    swep l3 l4 mir pm y divW
    swep l4 new mir pm z divH
setc
comp Face1 do
merg p Face1
merg l Face1

## Show the geometry
valu showgeom 1
if showgeom > 0
capt Rectangular profile face geometry.
plot pa all
plus la all
plus sa all
stop
hcpy png rectangular-profile-geometry
sys mogrify -trim rectangular-profile-geometry.png
endif

seto profile
swep Face1 Face2 tra L 0 0 divl
setc
comp profile do
elty all he20r
mesh all

## Create the mesh
valu showmesh 1
if showmesh > 0
frame
capt Rectangular profile mesh.
view elem
plot e all n
view surf
stop
hcpy png rectangular-profile-mesh
sys mogrify -trim rectangular-profile-mesh.png
endif

The geometry and resulting mesh look as follows.

Rounded corners

Steel profiles often have rounded corners because of the way they are manufactured. The following code generates such a profile. The basic concept is to create a line and sweep that to form 1/4 of the profile. This is then mirrored two times and merged. By default, the internal radius equals the wall thickness. This is generally considered the minimum value:

## Define the view
rot y
rot r 135
rot u 25

## Parameters
# Width, height and length in [m]
valu B 0.10
valu H 0.15
valu L 0.25
# Wall thickness [m]
valu t 0.004
# Number of elements in Y
valu dy2 6
# Number of elements in Z
valu dz2 8
# Twice the number of elements in the radius
valu dr 8
# Twice the number of elements in X
valu dl 24

# Calculated values
valu B2 / B 2
valu H2 / H 2
valu B2i - B2 t
valu H2i - H2 t
valu Ri t
valu cpy - B2i Ri
valu cpz H2i
valu ncpy - 0 cpy

## Geometry
seto tube-section
pnt ! 0 B2i 0
swep tube-section new tra 0 t 0 4
swep tube-section ln2 tra 0 0 cpz dz2
pnt cpt 0 cpy cpz
swep ln2 ln3 rot cpt x 90 dr
swep ln3 new tra 0 ncpy 0 dy2
copy tube-section new mir z
copy tube-section new mir y
setc
merg p tube-section
merg l tube-section

## Show the geometry
valu showgeom 0
if showgeom > 0
capt Rounded rectangular profile face geometry.
plot pa all
plus la all
plus sa all
stop
hcpy png rounded-rectangular-profile-geometry
sys mogrify -trim roundedrectangular-profile-geometry.png
endif

## Extrude the tube
seto tube
swep tube-section new tra L 0 0 dl
setc
comp tube do

## Mesh the tube
elty all he20r
mesh all

## Show the mesh
valu showmesh 0
if showmesh > 0
frame
capt Rectangular profile mesh.
view elem
plot e all n
view surf
stop
hcpy png rounded-rectangular-profile-mesh
sys mogrify -trim rounded-rectangular-profile-mesh.png
endif

The profile and mesh look as follows.