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)
- Reply-to: <drbob at bigfoot.com>
- 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 Defence R&D Canada - Atlantic 9 Grove St., PO Box 1012 Dartmouth NS Canada B2Y 3Z7 Tel 902-426-3100 x389, Fax 902-426-9654 E-mail: chris.purcell at drdc-rddc.gc.ca