IG.810 Optimization Procedure Inimize f(x) Subject to g(x)≤0 start Determine an initial design(xo) h(x)=0 Improve Design computer Simulation Evaluate f(x), g(x), h(x) Change x Converge Does your design meet a N termination criterion? END 16.810(16682) Massachusetts Institute of Technology
Optimization Procedure Improve Design Computer Simulation START Converge ? Y N END ( ) Subj ( ) 0 () 0 f g h d x x x Change x Determine an initial design (x 0 ) termination criterion? Minimize ect to Evaluate f(x), g(x), h(x) Does your design meet a 16.810 (16.682) 11
1G.810 Structural Optimization Selecting the best"structural" design Size optimization Shape optimization Topology Optimization 16.810(16682) Massachusetts Institute of Technology
Structural Optimization Selecting the best “structural” design - Size Optimization - Shape Optimization - Topology Optimization 16.810 (16.682) 12
1G.810 Structural Optimization minimize f(x) subject to g(x)≤0 h(x)=0 BCs are given Loads are given To make the structure strong →Min.fx) e.g. Minimize displacement at the tip 2. Total mass sMc g(x)≤0 16.810(16682) Massachusetts Institute of Technology 13
Structural Optimization ( ) j ( ) 0 () 0 f g h d x x x BC’s are given Loads are given minimize sub ect to 1. To make the structure strong Min. f(x) e.g. Minimize displacement at the tip 2. Total mass d M g(x) d 0 C 16.810 (16.682) 13
IG. A10 Size Optimization Beams minimize f(x) subject to g(x)≤ h(x)=0 Design variables(x) fx): compliance x: thickness of each beam g(x): mass Number of design variables(ndv) 16.810(16682) Massachusetts Institute of Technology
Size Optimization Beams ( ) j ( ) 0 () 0 f g h d x x x minimize sub ect to Design variables (x) f(x) : compliance x : thickness of each beam g(x) : mass Number of design variables (ndv) ndv = 5 16.810 (16.682) 14
IG. A10 Size Optimization Shape are g Topology Optimize cross sections 16.810(16682) Massachusetts Institute of Technology 15
Size Optimization - Shape are given Topology - Optimize cross sections 16.810 (16.682) 15