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Optimization Analysis Problem
This chapter contains an optimization problem. In an optimization of a static analysis, Structure finds the optimal values of the parameters in your model to achieve a specific design goal (for example, to minimize mass).
mvoo001: Five-Bar Configuration Problem
Analysis Type:
Static
Model Type:
3D
Reference:
Imai, Kanji. Configuration Optimization of Trusses by the Multiplier Method. LA: University of California, UCLA-ENG-7842.
Description:
A five-bar truss has the following conditions for optimization: the cross-section area for bars AB, CD, BE, and CE are kept the same; bar BC has an independent cross-section area, and the load applied on point E is 20000 psi. Find the minimum weight of the truss with the maximum tensile stress in the model under 20000 psi.
Specifications
Element Type:
beam (5)
Units:
IPS
Dimensions:
length A-B, C-D: 240
length B-C: 480
length B-E, C-E: 339.41
Beam Properties:
Area: 0.1
IYY: 0
Shear FY: 0
CY: 1
J: 0
IZZ: 0
Shear FZ: 0
CZ: 1
Material Properties:
Mass Density: 0.1
Cost Per Unit Mass: 0
Young's Modulus: 1.0e7
Poisson's Ratio: 0
Thermal Expansion: 0
Conductivity: 0
Constraints:
Location
Degrees of Freedom
constraint1
all beams
points A and D
fixed in RotX, RotY, and RotZ
fixed in all DOF
Loads:
Location/Magnitude
Distribution
Spatial Variation
load1
point E: -20000
uniform
N/A
Design Variables:
Location:
Min to Max:
Current:
x
length of bar BC
480 to about 0
480
y
length of bars AB and CD
240 to about 0
240
dvar_1
placed on bars AB and CD
0.1 to 10
0.1
dvar_2
placed on bar BC
0.1 to 10
0.1
dvar_4
placed on bar BE and CE
0.1 to 10
0.1
Optimization Parameters
Optimization Goal:
Minimize the total mass of the truss
Limits:
Quantity
Magnitude
measure8
tensile stress over bar BC
<20000
measure9
tensile stress over bar CE
<20000
measure10
tensile stress over bar CD
<20000
measure18
tensile stress over bar BC
-20000
measure19
tensile stress over bar CE
-20000
measure20
tensile stress over bar CD
-20000
Comparison of Results Data
Theory
Structure
% Difference
Goal — minimize total mass
63.5
63.785
0.4488 %
Convergence %: 1%