       RE: Solve of inverse quadratic finite element problem - resend

• To: mathgroup at smc.vnet.net
• Subject: [mg36475] RE: [mg36453] Solve of inverse quadratic finite element problem - resend
• From: "DrBob" <drbob at bigfoot.com>
• Date: Sun, 8 Sep 2002 03:30:58 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```You have three nonlinear (fourth-order) equations and 23 unknowns.  A
faster computer won't help any.

Bobby

-----Original Message-----
From: purcell [mailto:chris.purcell at drdc-rddc.gc.ca]
To: mathgroup at smc.vnet.net
Subject: [mg36475] [mg36453] Solve of inverse quadratic finite element problem -
resend

Would someone with a very fast machine and lots of memory be willing to
try
this Solve for me?
It is the inverse of the 20 node quadratic hexahedral mapping used in
finite element analysis.
None of my computers can handle this - they run out of memory (using
Version 4.2).

(*Hex20 Node definition in global coordinates *)
Clear[
x1, y1, z1,
x2, y2, z2,
x3, y3, z3,
x4, y4, z4,
x5, y5, z5,
x6, y6, z6,
x7, y7, z7,
x8, y8, z8,
x9, y9, z9,
x10, y10, z10,
x11, y11, z11,
x12, y12, z12,
x13, y13, z13,
x14, y14, z14,
x15, y15, z15,
x16, y16, z16,
x17, y17, z17,
x18, y18, z18,
x19, y19, z19,
x20, y20, z20];

(* local coordinates *)
Clear[u, v, w];

(* Global co-ordinates *)
Clear[x, y, z];

(* corner nodes *)
N1= (1-u)*(1-v)*(1-w)*(-2-u-v-w)/8;
N3= (1+u)*(1-v)*(1-w)*(-2+u-v-w)/8;
N5= (1+u)*(1+v)*(1-w)*(-2+u+v-w)/8;
N7= (1-u)*(1+v)*(1-w)*(-2-u+v-w)/8;
N13=(1-u)*(1-v)*(1+w)*(-2-u-v+w)/8;
N15=(1+u)*(1-v)*(1+w)*(-2+u-v+w)/8;
N17=(1+u)*(1+v)*(1+w)*(-2+u+v+w)/8;
N19=(1-u)*(1+v)*(1+w)*(-2-u+v+w)/8;
(*  to u nodes *)
N2= (1-u^2)*(1-v)*(1-w)/4;
N6= (1-u^2)*(1+v)*(1-w)/4;
N14=(1-u^2)*(1-v)*(1+w)/4;
N18=(1-u^2)*(1+v)*(1+w)/4;
(*  to v nodes *)
N4= (1+u)*(1-v^2)*(1-w)/4;
N8= (1-u)*(1-v^2)*(1-w)/4;
N16=(1+u)*(1-v^2)*(1+w)/4;
N20=(1-u)*(1-v^2)*(1+w)/4;
(*  to w nodes *)
N9= (1-u)*(1-v)*(1-w^2)/4;
N10=(1+u)*(1-v)*(1-w^2)/4;
N11=(1+u)*(1+v)*(1-w^2)/4;
N12=(1-u)*(1-v)*(1-w^2)/4;

(* solve the inverse transform *)
Solve[{
x1*N1+x2*N2+x3*N3+x4*N4+x5*N5+x6*N6+x7*N7+x8*N8+x9*N9+x10*N10+
x11*N11+x12*N12+x13*N13+x14*N14+x15*N15+x16*N16+x17*N17+x18*N18+x19*N19+
x20*N20-x==0,
y1*N1+y2*N2+y3*N3+y4*N4+y5*N5+y6*N6+y7*N7+y8*N8+y9*N9+y10*N10+
y11*N11+y12*N12+y13*N13+y14*N14+y15*N15+y16*N16+y17*N17+y18*N18+y19*N19+
y20*N20-y==0,
z1*N1+z2*N2+z3*N3+z4*N4+z5*N5+z6*N6+z7*N7+z8*N8+z9*N9+z10*N10+
z11*N11+z12*N12+z13*N13+z14*N14+z15*N15+z16*N16+z17*N17+z18*N18+z19*N19+
z20*N20-z==0},
{u,v,w}]
Christopher J. Purcell
9 Grove St., PO Box 1012