美国麻省理工大学：《Engineering Design and Rapid Prototyping》Design optimization

16810(16682) Engineering Design and Rapid Prototyping Design optimization IG.810 - Structural Design Optimization Instructor(s) Prof, olivier de Weck Dr. Il Yong Kim January 23, 2004 Massachusetts Institute of Technology

16.810 (16.682) 16.810 (16.682) Engineering Design and Rapid Prototyping Engineering Design and Rapid Prototyping Design Optimization - Structural Design Optimization Instructor(s) Prof. Olivier de Weck Dr. Il Yong Kim January 23, 2004

IG. A10 Course Concept Phase 1 Problem Sketch by hand CAD CAE Rapid Prototyping/ statement Validation Manufacturin /Test hase 2 today Design Optimization Optimum solution Rapid Prototyping/ validatio Manufactural / Test 16.810(16682) Massachusetts Institute of Technology

Course Concept 16.810 (16.682) 2 today

1G.810 Course Flow Diagram Learning/Review Deliverables Design Intro Hand sketching Design Sketch v1 CAD/CAM/CAE Intro CAd design Drawing v1 FEM/Solid Mechanics Overview FEM analysis Analysis output V Manufacturing Produce part 1 Part v1 Training Structural Test Test Experiment data v1 "Traini today Design Optimization Optimization Design/Analysis output v Produce Part 2 Wednesday Part v2 Test Experiment data v2 Final review 16.810(16682) Massachusetts Institute of Technology

Course Flow Diagram 16.810 (16.682) CAD/CAM/CAE Intro Overview Manufacturing Training Structural Test “Training” Design Optimization Hand sketching CAD design FEM analysis Produce Part 1 Test Produce Part 2 Optimization Problem statement Final Review Test Learning/Review Deliverables Design Sketch v1 Part v1 Experiment data v1 Design/Analysis output v2 Part v2 Experiment data v2 Drawing v1 Design Intro today Wednesday FEM/Solid Mechanics Analysis output v1 3

IG.810 What Is Design Optimization? Selecting the"best"design within the available means 1. What is our criterion for best"design? objective function 2 What are the available means? Constraints (design requirements) 3. How do we describe different designs? Design Variables 16.810(16682) Massachusetts Institute of Technology

What Is Design Optimization? Selecting the “best” design within the available means 1. What is our criterion for “best” design? Objective function 2. What are the available means? Constraints (design requirements) 3. How do we describe different designs? Design Variables 16.810 (16.682) 4

IG. 810 Optimization Statement Minimize f(x) Subject to g(x)≤0 h(x)=0 16.810(16682) Massachusetts Institute of Technology

Optimization Statement Minimize Subject to f g h ( x ) ( ) x d 0 ( ) x 0 16.810 (16.682) 5

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