l6a_optimize

l6a_optimize - 16.810 16.810 Engineering Design and Rapid...

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16.810 16.810 Engineering Design and Rapid Prototyping Engineering Design and Rapid Prototyping Instructor(s) Design Optimization - Structural Design Optimization - January 25, 2007 Prof. Olivier de Weck Lecture 6a
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16.810 2 What Is Design Optimization? Selecting the “best” design within the available means 1. What is our criterion for “best” design? 2. What are the available means? 3. How do we describe different designs? Objective function Constraints (design requirements) Design Variables
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16.810 3 Minimize ( ) Subject to ( ) 0 () 0 f g h = x x x Optimization Statement
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16.810 4 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: ( ), ( ) gh xx Cost = f(design) Lift = f(design) Drag = f(design) Mass = f(design) What is “f” for each case?
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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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16.810 6 Improve Design Computer Simulation START Converge ? Y N END Optimization Procedure Minimize ( ) Subject to ( ) 0 () 0 f g h = x x x Change x Determine an initial design (x 0 ) Does your design meet a termination criterion? Evaluate f(x), g(x), h(x)
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16.810 7 Structural Optimization -S izeOpt im izat ion - Shape Optimization - Topology Optimization Selecting the best “structural” design
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16.810 8 minimize ( ) subject to 0 () 0 f g h = x x x BC’s are given Loads are given 1. To make the structure strong e.g. Minimize displacement at the tip 2. Total mass M C Min. f (x) g (x) 0 Structural Optimization
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16.810
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This note was uploaded on 11/08/2011 for the course AERO 16.810 taught by Professor Olivierdeweck during the Winter '07 term at MIT.

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l6a_optimize - 16.810 16.810 Engineering Design and Rapid...

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