rectangular plate built in on all four edges. 1

[fmara]

Can any one provide a full length answer to the following
question.

Show that the deflection function

w=q(x^2y^2-bx^2y -axy^2+abxy)

is valid for a rectantular plate, built in on all four edges, of sides a and b & subjected to a uniformly distributed load q.

I know the boundary conditions but seem to lose my way when i do the partial differentiating.
i just need the model anwser to find my way.

Thanking you in advance. fmara.

 

[dbuzz]

Timoshenko's Theory of Plates and Shells (ISBN 0-07-085820-9) has quite a long proof for small deflection of rectangular plates with various egde conditions, including the all egdes built-in case that you are considering.

Do you have access to a University library? It would be certain to have this great book on its shelves.

 

[prex]

If you mean that your formula represents the exact solution, then this is certainly not true: only an infinite series expansion is known to give the exact (theoretical) answer.
Can you better explain your goal, as your question is quite theoretical? You should also specify where the origin of coordinate system is located.
In the site below there is a form for calculating rectangular plates with built-in edges: it is based on a finite difference solution.

prex

http://www.xcalcs.com

Online tools for structural design

 

[fmara]

Here is some backround to my question.My question is taken from an exam paper where one is asked to prove that the above equation satisfyies the governing differential equation of plate behaviour.
I know the boundary conditions for fixed plates are
x=0 w=0 first partial w.r.t =0
x=a w=a first partial w.r.t =a
and so fourth for y

When I do the f.par at x=0 The BCs are not satisfied.
or an i doing it all wroung?
Can you help me out now.

 

[fmara]

Sorry for spelling wrong, wrongly

 

[prex]

You answered your question, proving that the equation is NOT valid for a built-in rectangular plate.


prex

http://www.xcalcs.com

Online tools for structural design

 

[fmara]

Can I refer you to a web site

http://www.city-and-guilds.co.uk/fo...g_contents/eng_council/examrep-part2-2003.pdf

page 21 for your comments.
It contradicts my findings.

Thank you for your time.

 

[fmara]

I have checked that web site and it will not give you access with that address.Frist go to http:

http://www.engc.org.uk

then click on examination it will lead you to city-and-guilds web site, click on examiner report and finaly click on Graduate diploma 2003 pg 24 Q10.
you can review the examiners comment to my qusetion.

thank you.

 

[prex]

As I can't see the question, can't judge about the answer.
The following equation is known to give a first order approximation for the deflection of a built in plate and uniform loading:
w=256f(a[sup]2[/sup]/4-x[sup]2[/sup])[sup]2[/sup](b[sup]2[/sup]/4-y[sup]2[/sup])[sup]2[/sup]/a[sup]4[/sup]b[sup]4[/sup]
where f is the center deflection that must be determined from an energy equation (the origin of coordinates is in the center for this equation).
You'll be able to check out that this equation satisfies the boundary conditions and that your equation does not.

prex

http://www.xcalcs.com

Online tools for structural design

 

[fmara]

The question is the same a my initial query of the 20th of November.
I'd like to thank you prex for the time you have put in answering my question.
fmara.