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Derivative recurrence

• To: mathgroup at smc.vnet.net
• Subject: [mg72679] Derivative recurrence
• From: "KFUPM" <hussain.alqahtani at gmail.com>
• Date: Mon, 15 Jan 2007 04:55:20 -0500 (EST)

Dear All

I have the following

u1(x,x,z,t) = z f1(x,y,t)
u2(x,y,z,t) = z f2(x,y,t)
u3(x,y,z,t) = z f3(x,y,t)

which is basically the displacement fied. I want to compute the strain
which is given in indecial notation as:

Eij = 1/2( dui/dxj + duj/dxj ) where i, j, k go from 1 to 3,,, x1=x, x2
=y, x3=z,

I want mathematica to calculate the strain Eij autmoatically,

for example

when i = 1 and j= 2

E12 =1/2 (du1/dx2+du2/dx1 )     but x1 =x and x2 =y

therefore

E12 =1/2 (du1/dy + du2/dx) = 1/2 ( z df1/dx + z df2/dy),,,   where f1,
f2 and f3 are arbitrary functions.

Eij should generate 3 by 3 matrix containing the strain components.
Frankly, i don't know how to do it using mathematica and i would
appreciate any help in this regard.


Thanks in anticipation