New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

Stru Des Sens AnaOpt

by: Rollin Mann DVM

Stru Des Sens AnaOpt EGM 6365

Rollin Mann DVM
GPA 3.79


Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Class Notes
25 ?




Popular in Course

Popular in Engineering & Applied Science

This 18 page Class Notes was uploaded by Rollin Mann DVM on Saturday September 19, 2015. The Class Notes belongs to EGM 6365 at University of Florida taught by Staff in Fall. Since its upload, it has received 6 views. For similar materials see /class/207077/egm-6365-university-of-florida in Engineering & Applied Science at University of Florida.

Similar to EGM 6365 at UF

Popular in Engineering & Applied Science


Reviews for Stru Des Sens AnaOpt


Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/19/15
Sequential linear approximation Jaco F Sch utte EGM 6365 Structural Optimization Fall 2005 Introduction Using local approximations advantageous when high computational cost is associated with f g Ag Ax Usually cost of optimization algorithm operations is negligible compared to above Sequential Linear Programming Inimilnize f X subject to gjx 2 0 j 1 H779 Start with initial trial design x0 Obtain linear approximations around X0 offand g using 1st order Taylor expansion u a 111iui1uizo j39lxm J39 a 11 UI quot Kn 11 I 1 subject to mix A E 1711 J i ll j It V l l uquot Tl quot X0 and m ltf r 7139 1 ll Sequential Linear Programming con nued Move limits ah am must be small to maintain accuracy in approximation f ll al C One dimen3ona example 6f 5x x0 xL Sequential Linear Programming con nued Method iterates by replacing x0 by XL from previous step and constructing a new Hneanza on Algorithm terminated when either rate of change stopping criterion is met KuhnTucker optimality conditions are adequately satisfied Example 631 111ini1nize fX 7quot I 7 11 subject to g1 r 2 I 1 Starting point Move Ilmlts 61Lx all11OocOx Example 631 continued Constraint functions and derivatives evaluated at xu yield 91X025717123 92XO77117 72m 72 W1 72 Valixo 2 i 72 72 Vgg 21f V92XO 2 Example 631 continued 1St order Taylor expansion linearization gives the following equations for constraints Example 631 continued om 1000 h I W 39I I 3 8m soillutio without VLmDveM39 ES 5 I quot 32L I 6013 6 I E L g 3Equot r 4 I 5 5 Ew 4040 a r 7 IFIX luv rayt I E 18 200 Z Kquot I i 7 7 2 397 77 14 3 quot 3 000 203 ALDO 600 800 I 100 Example 631 continued 20 First iteration with move limits yield x1 2 0 f 60 39 85 If move limits were not imposed X1 5 0 f 22 o Ignoring move limits result in large constraint violations and inaccurate values forfif cost function is nonlinear Sequential Linear Programming con nued Advantages LP packages are readily available in most mathematical software packages Matlab Numerical recipes in C Octave etc Simple implementation Requires only 1St order derivatives which are easily obtained by finite difference methods Objective function software considerations Computational cost Sequential Linear Programming con nued Disadvantages Choice of move limits are important because Too large will cause inaccuracies and prevent convergence Too small translates to large a large number of iterations gt excessive computational effort Optimum is to have initially large move limits which are reduced as optimum is approached Reduction rate is problem dependent and can be obtained by monitoring the fitness value Rate is reduced 1050 iffl 2f s Typical starting values of move limits are 1030 of design variable range Sequential Linear Programming con nued Disadvantages continued lf starting design x0 is infeasible a combination of approximation and move limits may result in algorithm remaining in infeasible region lf solution of problem does not lie at a vertex of a constraint set it may alternate between to fixed points This may be solved by appropriate reduction of move limits Relaxation of constraints If an infeasible starting point is obtained it becomes necessary to relax constraints to allow algorithm to escape from infeasible region minilnize fx0 Z ri 7 Tm dip In 13971 X0 017i n 01739 r subject to gJXOZJT7TUZ 33 J j 177g 1 71 1 X0 L11 g 1391 7 17m g um and 3 Z 0 where 16 is an additional design variable and k is a scaling weight to ensure that the minimization of 16 receives priority overf Example 632 Uywngioquot 773 X 10 4 E 0y compression 4833 X 10 4 E Allowable 6y 3 X 1031 1351quot f2 Pa f34117 f4723p Example 632 continued By nondimensionalizing design variables 3103 1 103 1 t 11 AlE 2 AZE We can formulate the optimization problem as lnlnllnlze fr11 g i 1 1 1 2 subject to 1811 G l g S 3 005 g 11 3 01546 t 005 g 42 3 01395 t with lowerbounds on X1 and X2 005 Example 632 continued First iteration x50101 gt 75 132 feasible am 117 00L 239 1 2 07 300 1732 an I luiuimizc fL subjevt to 1811 001 009 This problem is solved to yield 1 1 010316 1 2 011 and f 446410


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Kyle Maynard Purdue

"When you're taking detailed notes and trying to help everyone else out in the class, it really helps you learn and understand the I made $280 on my first study guide!"

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

Parker Thompson 500 Startups

"It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.