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


by: Jada Daniel

TheoryofElasticityII MEM661

Jada Daniel
GPA 3.65


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 Mechanical Engineering

This 4 page Class Notes was uploaded by Jada Daniel on Wednesday September 23, 2015. The Class Notes belongs to MEM661 at Drexel University taught by Tein-MinTan in Fall. Since its upload, it has received 22 views. For similar materials see /class/212382/mem661-drexel-university in Mechanical Engineering at Drexel University.

Similar to MEM661 at Drexel

Popular in Mechanical Engineering


Reviews for TheoryofElasticityII


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: 09/23/15
THEORY OF ELAS TI CI TY Review of Fourier Series Review ofFourier series Fig 1 A periodic function Piecerwise Continuous Functions A function is said to be pieceewise continuous in an interval if 1 the interval can be divided into a finite number of subintervals in each of whidi is continuous and 2 the limits of as x approadies the endpoints of eadi subinterval are finite Periodic Functions lf fxP fx P gt 0 then the smallestP is said to be the period of De nition ofFourier series If a function fx defined in the interval cc 2L is piecewise continuous then fx2L x and can be expressed in the following Fourier series quotx 041261 cos l71 sin a where the Fourier coefficients 110 11L and l71 are given by 1 5 2L LLferx w 1 cZL n x u x cos dx c LL A L m 1 cZL n x l7 x sin dx d LL R L ltgt It is noted that 202 is the average value of fx and the series converges to the average value at every discontinuity By locating the origin at the midpoint of a period then the function is defined in the interval iL L and the coefficients of Fourier series can be expressed in the following form wm a an JLLfxcosdx f l71 foxsindx g HalfRange Fourier Sine or Cosine Series lf fx defined in the interval 7L L is an even function ie if ex in the interval then we can express the function in the following halfrange Fourier cosine series x 110 nILx 11 cos h 2 n L TM Tan Drexel University 1 November 30 2008 THEORY OF ELAS TI CI TY Review of Fourier Series where 7 2 L 7 2 L n x 110 ifquot fxdx an 7 Iquot fxcosde 1 Similarly if the function is an odd function ie if ex 7fx in the interval iLL then we can express the function in the followinghalfrange Fourier sine series x Eb sin 139 11 L where l71 fxsindx k Example 1 Expand the following function as shown in Fig 2 in the interval 75 5 into a Fourier series 0 7 5 lt x lt 0 wila Oltxlt5 Since the function is neither even nor odd we must use the expressions given in b c and d to obtain the Fourier coefficients 1 5 1 5 110 Elis x x E10 3dx 3 5 an if fxcos dx EKism j 0 5 5 5 5 mt 5 0 5 b lJs fltxgtsjn nlzxdx3 ficosn x 317cosn7r 5 5 5 5 117 5 0 and the Fourier series representation of the function is given by 3 3licosn7r rim 3 6 71x 1 371x 1 57m fx l f i i i j 2 W1 117 5 2 IIK u l u l The Fourier series representations of the function in the interval 75 5 using various numbers 717 5 3 555 of terms are shown in Fig 3 TM Tan Drexel University 2 November 30 2008 THEORY OF ELAS TI CI TY Review of Fourier Series Fig 3 Example 2 Onedimensional Heat Conduction Problems The governing equation for onedimensional heat transfer problems is given by 014xt K 62u3t 1 at 6x where uxt is the temperature distribution along a onedirnensional bar at time t and K is called dijj iAsivity Using the method of separation of variables ie by assuming that uxt UxTt m we can rewrite l in the following form wltxgt 1m um K Tt 0 Since the lefthand side of n is a function of x while the righthand side is a function of t both sides therefore must be equal to a constant say 712 Consequently n becomes U AZU 0 and TKAZT 0 The solutions of the above two equations are given by U AlcosAxBlsinAx and T Cle39mzt 0 Substituting 0 in m yields uxt Clequot 12A1 cositx B1 sin Ax e39mzt A cos Ax Bsin Ax p Constants A and B may be determined by using the boundary and initial conditions Consider for instance the following boundary condition u0tuLt0 q where L is the length of the bar Substituting p in q yields A 0 and Be W sin AL 0 r Since B 0 is trivial we have sinAL 0 TM Tan Drexel University 3 November 30 2008 THEORY OF ELASTI CI TY and the solution p becomes Review of Fourier Series m0r1r2 s L t mlzx xt ZBme L sin L t m1 in which constants 3 may be determined by using the initial condition eg ux0 By expanding into a Fourier sine series as x 2F sin quotMquot u m1 L then we have by comparing eadi term in t and Bm Fm For instance let ux0 25 then we have 25 2F sin m where coefficients Fm can be obtained by using d ie Fm EILZS Sin m x dx 5017 cosmlr Bm L 0 L m7 and the final solution is given by xt 2 5017 cosmlr ETI sin mlzx W1 m7 L 100 jth x 1 37m 1 Z 2t 571x E m l L m l m l 7r L 3 L 5 L TM Tan Drexel University November 30 2008


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

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."

Janice Dongeun University of Washington

"I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

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!"


"Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

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.