l6 - 16.810 16.810 Engineering Design and Rapid Prototyping...

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16.810 16.810 Engineering Design and Rapid Prototyping Engineering Design and Rapid Prototyping Lecture 6 Design Optimization - Structural Design Optimization - Instructor(s) Prof. Olivier de Weck January 11, 2005

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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 2
Optimization Statement Minimize Subject to f g h ( x ) ( ) 0 x () = 0 x 16.810 3

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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) Lift = f(design) What is “f” for each case? Drag = f(design) Mass = f(design) 16.810 4
16.810 5 f (x) : Objective function to be minimized g (x) : Inequality constraints h (x) : Equality constraints x : Design variables Minimize ( ) () 0 () 0 f Subject to g h = x x x Optimization Statement

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Optimization Procedure Improve Design Computer Simulation START Converge ? Y N END ( ) Subj ( ) 0 () 0 f g h = 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 6
Structural Optimization Selecting the best “structural” design -S izeOpt im izat ion

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Structural Optimization ( ) j ( ) 0 () 0 f g h = 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 g (x) 0 2. Total mass M C 16.810 8
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• Winter '07
• OlivierdeWeck
• Mathematical optimization, design variables, structural optimization, topology optimization, Structural Design Optimization

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l6 - 16.810 16.810 Engineering Design and Rapid Prototyping...

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