1G.810 Shape Optimization -spline minimize f(x) subject to g(x)≤ h(x)=0 Hermite, Bezier, B-spline, NURBS, etc. Design variables fx): compliance x: control points of the B-spline g(x): mass (position of each control point Number of design variables(ndv ndy= 8 16.810(16682) Massachusetts Institute of Technology
Shape Optimization B-spline ( ) j ( ) 0 () 0 f g h d x x x Hermite, Bezier, B-spline, NURBS, etc. minimize sub ect to Design variables (x) f(x) : compliance x : control points of the B-spline g(x) : mass (position of each control point) Number of design variables (ndv) ndv = 8 16.810 (16.682) 16
IG- a10 Shape Optimization Fillet problem Hook problem Arm problem 16.810(16682) Massachusetts Institute of Technology
Shape Optimization Fillet problem Hook problem Arm problem 16.810 (16.682) 17
1G.810 Shape Optimization Multiobjective Multidisciplinary Shape Optimization Objective function 1. Drag coefficient, 2. Amplitude of backscattered wave Analysis 1. Computational Fluid Dynamics Analysis 2. Computational electromagnetic Wave Field Analysis Obtain Pareto Front Raino A.E. Makinen et al., "Multidisciplinary shape optimization in aerodynamics and electromagnetics using genetic algorithms, "International Journal for Numerical Methods in Fluids, Vol 30, pp. 149-159, 1999 16.810(16682) Massachusetts Institute of Technology
Shape Optimization Multiobjective & Multidisciplinary Shape Optimization Objective function 1. Drag coefficient, 2. Amplitude of backscattered wave Analysis 1. Computational Fluid Dynamics Analysis 2. Computational Electromagnetic Wave Field Analysis Obtain Pareto Front Raino A.E. Makinen et al., “Multidisciplinary shape optimization in aerodynamics and electromagnetics using genetic algorithms,” International Journal for Numerical Methods in Fluids, Vol. 30, pp. 149-159, 1999 16.810 (16.682) 18
IG A10 Topology Optimization Cells minimize f(x) subject to g(x)≤ h(x)=0 Design variables(x) fx): compliance X: density of each cell g(x): mass Number of design variables(ndv ndv= 27 16.810(16682) Massachusetts Institute of Technology
Topology Optimization Cells ( ) j ( ) 0 () 0 f g h d x x x minimize sub ect to Design variables (x) f(x) : compliance x : density of each cell g(x) : mass Number of design variables (ndv) ndv = 27 16.810 (16.682) 19