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
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Analysis Type:
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Static
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Model Type:
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3D
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Reference:
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Imai, Kanji. Configuration Optimization of Trusses by the Multiplier Method. LA: University of California, UCLA-ENG-7842.
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Description:
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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.
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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: |
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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% | |||