IG. A10 Constraints Design requirements 2.R Manufacturing Cost(C) Cs3.6S/part Inequality constraints Performance(81, 82, fi) Displacement≤0.078 Displacement 82 First natural frequency fi2 195 Hz Mass (m) m≤0.27lbs Equality constraints Load Case(F FI=50 lbs /F2=50 lbs/F3=100 lbs The part has to conform to the interface requirements and geometrical boundary conditions shown on page 2 of this document. This requirement cannot be waived. Low manufacturing cost is the first priority for this product. Next, the customer cares possible. These priorities are shown in the Ishii-matrix below: ttribute Constrain OptimizeAccept Performance 16.810(16682) Massachusetts Institute of Technology
Constraints - Design requirements Inequality constraints Equality constraints 16.810 (16.682) 6
IG. A10 Objective Function A criterion for best design(or goodness of a design) Manufacturing Cost(C) Cs3.6S/part Performance(81, 82, fi) Displacement≤0.078 Displacement 82<0.012 mm First natural frequency fi2 195 Hz Mass (m) m≤0.27lbs Objective function Surface Quality(Q) Load Case(F FI=50 lbs/F2= 50 lbs/F3=100 lbs The part has to conform to the interface requirements and geometrical boundary conditions shown on page 2 of this document. This requirement cannot be waived. Low manufacturing cost is the first priority for this product. Next, the customer cares possible. These priorities are shown in the Ishii-matrix below: ttribute Constrain OptimizeAccept Performance 16.810(16682) Massachusetts Institute of Technology
Objective Function - A criterion for best design (or goodness of a design) Objective function 16.810 (16.682) 7
IG. A10 Design Variables Parameters that are chosen to describe the design of a system Design variables are" controlled by the designers 0.500 0.500 0500 Design ±0.100 freedom: The position of upper holes along the design freedom line 16.810(16682) Massachusetts Institute of Technology
Design Variables Parameters that are chosen to describe the design of a system Design variables are “controlled” by the designers The position of upper holes along the design freedom line 16.810 (16.682) 8
IG. A10 Design Variables For computational design optimization Objective function and constraints must be expressed as a function of design variables(or design vector X Objective function: f(x) Constraints: g(x), h(x) Cost= f(design) Displacement = f(design) What is "f for each case? Natural frequency = f(design) Mass = f(design) 16.810(16682) Massachusetts Institute of Technology
Design Variables For computational design optimization, Objective function and constraints must be expressed as a function of design variables (or design vector X) Objective function: f ( x ) Constraints: g ( x), h ( x ) Cost = f(design) Displacement = f(design) What is “f” for each case? Natural frequency = f(design) Mass = f(design) 16.810 (16.682) 9
IG. 810 Optimization Statement Minimize f(x) Subject to g(x)≤0 h(x)=0 f(x): Objective function to be minimized g(x): Inequality constraints h(x): Equality constraints X: Design variables 16.810(16682) Massachusetts Institute of Technology 10
Optimization Statement ( ) () 0 () 0 f h d x x x Minimize Subject to g f(x) : Objective function to be minimized g(x) : Inequality constraints h(x) : Equality constraints x : Design variables 16.810 (16.682) 10