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.

First, useful values for defining the geometry are defined:

## 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

Then the geometry is created. First a point which is then extruded into the first line:

## Geometry
seto tube-section
pnt ! 0 B2i 0
swep tube-section new tra 0 t 0 4

The line is swept into a rectagle. Then a line is swept around a point to create a rounded corner:

swep tube-section ln2 tra 0 0 cpz dz2
pnt cpt 0 cpy cpz
swep ln2 ln3 rot cpt x 90 dr

Another line is swept into a surface and the whole mirrored in the z-direction:

swep ln3 new tra 0 ncpy 0 dy2
copy tube-section new mir z

A final mirror in the y-direction and then all is merged:

copy tube-section new mir y
setc
merg p tube-section
merg l tube-section

The following code generated pictures of the planar geometry and the mesh:

## 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 complete profile and mesh look as follows.