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