Analysis Type:

Static

Model Type:

3D

Reference:

Imai, Kanji. Configuration Optimization of Trusses by the Multiplier Method. LA: University of California, UCLAENG7842.

Description:

A fivebar truss has the following conditions for optimization: the crosssection area for bars AB, CD, BE, and CE are kept the same; bar BC has an independent crosssection 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.

Element Type:  beam (5)  
Units:  IPS  
Dimensions:  length AB, CD: 240 length BC: 480 length BE, CE: 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 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 
Theory  Structure  % Difference  
Goal — minimize total mass  63.5  63.785  0.4488 % 
Convergence %: 1% 