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Engineering Optimization

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Introduction

 

Maple lets you minimize or maximize objective functions with respect to constraints.

 

Optimization:-Minimizex2+sinx+y,x+2 y=9

−0.980004457937920792,x=0.0469482872699630,y=4.47652585636502

(1)

 

The objective function can be a sum-of-squares error for parameter estimation, or the

 

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weight of a mechanical device

• 

cost of production

• 

or energy required for a process

 

The constraints can be limits on the

 

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dimensions of a mechanical device, or the allowable stresses

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minimum and maximum process temperatures

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or amount of base materials

 

Units can be employed in the objective function or the constraints.

 

You can use Maple's built-in linear, nonlinear, and quadratic optimizers, or the optional Global Optimization Toolbox.

Example - Fuel Pod Design Optimization

 

You are designing a fuel pod with a hemispherical cap, cylindrical mid-section and conical cap.

 

 

What are values of L, H and R that minimize the surface area while maintaining the volume V at 3 m3?

 

restart:withOptimization:

Objective function - surface area of pod

obj124πR2+2πRL+πRH2+R2:

Constraint on the volume area of pod

cons11243πR3+π R2L+13πR2H=3m3:


All dimensions must be greater than 0

cons20R,0L,0H:


Hence the optimized dimensions are

dimensionsMinimizeobj,cons1,cons2,initialpoint=H=1m,L=1m,R=1m

10.2533536615869920m2,H=0.785093823049978m,L=0.392546902492684m,R=0.877761593519080m

(2)


Check that the constraint on the pod volume is satisfied

evalcons1,dimensions2

3.00000000039170m3=3m3

(3)

Applications

Welded Beam Design Optimization

Helical Spring

Optimize a Rankine Cycle

Chemical Kinetics Parameter Estimation

PV Diode Parameter Estimation