rectangular plate built in on all four edges

huangyhg

rectangular plate built in on all four edges.
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.
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.
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
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.

sorry for spelling wrong, wrongly
you answered your question, proving that the equation is not valid for a built-in rectangular plate.
prex
can i refer you to a web site
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(a2/4-x2)2(b2/4-y2)2/a4b4
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
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.