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Table 1: Variants of Karamba
50
20 50
e
e
e
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Figure 1: The License-component
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Figure 2: Category Karamba on the component panel
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Figure 3: Basic example of a statical model in Karamba
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Figure 4: Components for creating beam- (1) and shell-elements (2)
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Figure 5: left: definition of a custom material (1). Right: selection of a material from thematerial library (2)
Figure 6: left: definition of a beam cross section (1); Middle: definition of a shell cross
section (2); Right: selection of a cross section from the cross section library (3)
Figure 7: Component for creating supports.
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Figure 8: definitions of gravity load (1), point load (2), uniformly distributed load on abeam (3) and distributed load on a mesh (4)
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Figure 9: The model gets assembled from the generated structural information.
Figure 10: The model can be evaluated in several ways. Left: analysis of structural re-
sponse under loads; Right: calculation of eigen-modes.
Figure 11: There are three components for visualizing the model: ModelView,BeamView and ShellView
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Figure 12: Retrieval of numerical results: nodal displacements (1), level of material uti-lization (2), resultant cross section forces (3) and reaction forces (4).
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[deg]
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Figure 13: Setting the activation state of all elements of a model with a list of boolean
values.
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Figure 14: The Assemble-component gathers data and creates a model from it.
Figure 15: The Connected Parts-component groups beams into sets of elements that haveat least on node in common each.
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Figure 16: Model is decomposed into its components.
0.005[m]
Figure 17: The LineToBeam-component that turns two lines into beams
11.4[cm]
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0.4[cm]
5[mm]
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1[cm]
Figure 20: The MeshToShell-component turns meshes into shells
Figure 21: A beam decomposed into its individual parts.
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Figure 23: Modification of the default beam properties.
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Figure 24: The orientation of the local beam coordinate system can be controlled withthe OrientateBeam-component.
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90[deg]
Figure 25: Elements can be selected by using their identifiers.
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Figure 26: Metaphor for the six degrees of freedom of a body in three-dimensional space.
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Figure 27: Define the position of supports by node-index or position.
[kN]
[kN m]
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Figure 29: Cantilever with four different kinds of cross section.
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6[cm]
Figure 30: Shell made up of two elements with different thicknesses.
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Figure 31: Spring fixed at one end and loaded by a point load on the other.
ui,rel Fi = ci ui,rel
ui,rel
ci
[kN/m]
[kNm/rad]
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Figure 32: Beam under dead weight, fixed at both supports with a fully disconnectedjoint at one end resulting in a cantilever.
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Figure 33: Properties of a given cross section can be retrieved via the Disassemble CrossSection-component.
Figure 34: Beam positioned eccentrically with respect to the connection line of its two
end-nodes.
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[cm]
Figure 35: The Cross Section Matcher-component returns a standard profile for a
custom profile.
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Figure 37: Cantilever with four different kinds of cross section taken from the standardcross section table.
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Figure 40: The definition of the properties of two materials via the MatProps componentand selection of the second Material from the resulting list.
[kN/cm2]
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[kN/cm2]
[kN/m3]
[1/C]
[kN/cm2]
1.0E 5
1.0E5 = 1.0105 = 0.00001
10[m]
1[mm]
10C
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Figure 41: Partial view of the default data base of materials. SI units are used irrespec-tive of user settings. Automatic conversion ensures compatibility with Imperial units.
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Figure 42: List of materials resulting from the ReadMatTable-component reading thedefault data base of materials. Selection of the default Steel via MatSelect.
Figure 43: Simply supported beam with three loads and three load-cases.
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1
2[m]
1[kN]
2[kN/m]
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Figure 44: Simply supported beam loaded with line loads that approximate a given,evenly distributed surface load on a mesh.
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Figure 46: Orientation of loads on mesh: (a) local; (b) global; (c) global projected toglobal plane.
Figure 47: Line loads on a structure consisting of three beam elements defined in localbeam coordinate systems.
[kN/m]
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[mm/m]
N = 0 A E
A = 25[cm2]
E= 21000[kN/cm2]
0 = 0.00015
N = 78.75[kN]
Figure 48: Pre-tensioned member fixed at both ends and resulting support reactions.
Figure 49: Temperature load on a member which is fixed at both ends.
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14%
100%
[kg]
7850[kg/m3]
Figure 50: Vibration mode of beam with point mass in the middle.
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Figure 51: Left: Deflection of a beam under predefined displacements at its end-supports;Right: PreDisp-component for setting displacement condition at left support.
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Figure 52: Deflection of simply supported beam under single load in mid-span and grav-ity.
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1.0
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Figure 53: Hanging models. Left: Model of Antoni Gaudi for the Temple Expiatori de laSagrada Famlia (from the internet). Right: Some of Heinz Islers hanging models (from theinternet).
Figure 54: Structure resulting from large deflection analysis with the LaDeform-component.
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Figure 56: Pneumatic form resulting from point loads that rotate along with the pointsthey apply to.
Figure 57: Left: 14th eigen-mode with strain display enabled. Right: EigenMode-
component in action.
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Figure 58: Undeflected geometry (upper left corner) and the first nine eigen-modes of thestructure.
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vi
Figure 59: Simply supported steel beam IPE100 of length10[m] in its 14th natural vi-
bration mode.
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Figure 60: Cantilever with initially regular mesh after application of theForceFlowFinder-component.
45%
20
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MaxIter Iter
n[kg]
Iter
Overdrive = m
(m + 1) n
m n
[m]
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Figure 61: Triangular mesh of beams before (a) and after (b) applying theFindForcePath-component.
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Figure 63: Cross section optimization with the OptiCroSec-component on a simply sup-ported beam.
Figure 64: Cross section optimization with the OptiCroSec-component on a cantilever
discretized with shell elements.
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1.4
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lb
100%
fy
10%
20%
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Figure 65: Simply supported beam under axial and transversal point-load: List of axial
deformation energy and bending energy for each element and load case.
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Figure 66: Partial view of a model.
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Figure 67: Color plot of strains with custom color range.
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3rd
Figure 68: Local axes of cantilever composed of two beam elements, reaction force andmoment at support.
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100
100
100
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Figure 69: Simply supported beam under axial and transverse point-load: List of nodaldisplacements: vectors with translations and rotations for each node and load case.
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Figure 70: Approximation of principal strains in a simply supported slab simulated withbeam elements under a point-load. Irregularity of principal strain directions is due to the
irregularity of the element grid.
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Figure 71: Beam under axial and transverse point-load: Reaction forces and moments forboth load cases.
[kN]
[kN m]
Figure 72: Simply supported beam under axial and transverse point-load: Utilization ofthe cross sections of the elements.
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100%
0.26
0.05
Figure 73: Simply supported beam consisting of two elements under axial and transversepoint-load: List of displacements along the axis: three components of translations and
rotations for each section and load case.
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Figure 74: Display of resultant displacements on beam cross section.
Figure 75: Rendered images of the beam. Left: Cross section-option enabled. Right:
Axial Stress enabled.
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Figure 76: Mesh of beams under dead weight with Render Color Margin set to 5%.
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Figure 77: Moment My (green) about the local beam Y-Axis and shear force Vz (blue) inlocal Z-direction.
1kN
3kN
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Figure 78: Normal force N, shear force V and resultant moment M at a cross sectionwith local coordinate axes XYZ. Force and bending moment components are positive in thedirection of the local coordinate axes.
Figure 79: Simply supported beam under axial and transverse point-load: List of normalforces, shear forces and moments for all elements and all load cases.
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2[kN m]
M =F L/4 = 1[kN]8[m]/4 = 2[kN m]
3[kN]
1.5[kN]
1.5[kN]
Figure 80: Simply supported beam under axial and transverse point-load: List of normalforces, shear forces and moments for all elements and all load cases along an the elements.
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Figure 81: Cantilever consisting of triangular shell elements: Flow lines (green) of forcein horizontal direction.
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0.5[m]
5[deg]
[deg]
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Figure 83: Cantilever analyzed as shell structure: directions of second principal normalforces at element centers.
[kN/m]
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Figure 84: Triangular mesh of shell elements and principal stress directions at their cen-
troids. Colors indicate the resultant displacement.
Figure 85: Principal stress lines: they are tangent to the first and second principal stress
direction. The coloring reflects the level of material utilization.
90[deg]
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Figure 86: Resultant displacement of a shell.
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+1
1
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Figure 87: Unified mesh generated from Breps using the MeshBreps-component; cre-ated by Moritz Heimrath.
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Figure 88: In- and output of the MeshBreps-component; created by Moritz Heimrath.
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Figure 89: Random points in a unit volume connected to their nearest neighbor in a 5-Dsetting
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Figure 90: The elements A and B of the original model are connected resulting inthe additional element C.
[m]
[m]
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0.0
1.0
Figure 92: Definition for optimizing the shape of a simply supported beam under mid-
span single load.
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Figure 93: Result of shape optimization (thick red line) for a simply supported beam
under mid-span single load using the first 30 eigen-forms the thin red lines as axes ofthe design space.
Figure 94: Proximity Stitch-mapping with the same set-up as in fig. 91but fifteen
random connections instead of two.
[0, 1]
p1
l1 pn
[ln1 minOff set, ln1 + maxOffset]
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Figure 95: Simple Stitch-mapping with the same set-up as in fig. 91but fifteen random
connections instead of two.
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Figure 96: Stacked Stitch-mapping with the same set-up as in fig. 91but fifteen ran-
dom connections instead of two.
Figure 97: User defined Iso-lines (red) and stream-lines (green) on a rectangular shellpatch.
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10000
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E
E
E[kN/cm2]
Table 2: Youngs Modulus of materials
E
E
[kN/cm2]
[kN/m3]
a= g = 9.81[kg m/s2] f =m a
m
f = 9.81N
f = 10N
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= E
E
kN
100kg 1kN
0.981kN
1kN
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L
L/300
L/150
1.5
1.5
1/100
n
n3
nneigh
0.5 n n2neigh
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Wy Wz
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lk
fy E
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Ncr = 2 E I
l2
k
Nbrd
Nb,Rd= Afy
M1= Afyd
fy
M1 1.0
= 1
+
2
21.0
= 0.5[1 + (0.2) +2
]
=
Afy
Ncr
y z
y y
y = z = 0.3 y
z
Wy
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Wz Wy,pl Wz,pl Ay
Az
N >0
N
Nrd
Nb,rd