Parametric Hexahedral Solid FEMs: [Hx,Hy,Hz]=Aconnect4(x,y,z,a,b,c) - File Exchange

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Parametric Hexahedral Solid FEMs

[Hx,Hy,Hz]=Aconnect1(x,y,z,a,... Element Shape Functions Partial Derivatives Terms 29.9.2006 [A.
[Hx,Hy,Hz]=Aconnect2(x,y,z,a,... Element Shape Functions Partial Derivatives Terms 29.9.2006 [A.
[Hx,Hy,Hz]=Aconnect3(x,y,z,a,... Element Shape Functions Partial Derivatives Terms 29.9.2006 [A.
[Hx,Hy,Hz]=Aconnect4(x,y,z,a,... Element Shape Functions Partial Derivatives Terms 29.9.2006 [A.
Gaussparametrichexahedral1.m
Gaussparametrichexahedral2.m
Gaussparametrichexahedral3.m
Gaussparametrichexahedral4.m
fullparametrichexahedral1.m
fullparametrichexahedral2.m
symbolichexahedralsolid1.m
symbolicshapefunctionok1.m
symbolicshapefunctionok2.m
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from Parametric Hexahedral Solid FEMs by Ali OZGUL
Hexahedral solid finite element models
[Hx,Hy,Hz]=Aconnect4(x,y,z,a,b,c)
function [Hx,Hy,Hz]=Aconnect4(x,y,z,a,b,c)

%Element Shape Functions Partial Derivatives Terms 29.9.2006 [A.]
%64NODE-192DOF HEXAHEDRAL SOLID ELEMENT
%Hx=d/dx.[Aconnect]
%Hy=d/dy.[Aconnect]
%Hz=d/dz.[Aconnect]
%[a]:Constant element "x" axis direction dimension
%[b]:Constant element "y" axis direction dimension
%[c]:Constant element "z" axis direction dimension
%[x,y,z]:Global cartesian coordinates.


Hx=[9.0*x*(1-2*x/a)*(1-2*y/b)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*a^2)-(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/a/2048.0
 (36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/a/2048.0+9.0*x*(2*x/a+1)*(1-2*y/b)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*a^2)
 (36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/a/2048.0+9.0*x*(2*x/a+1)*(2*y/b+1)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*a^2)
 9.0*x*(1-2*x/a)*(2*y/b+1)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*a^2)-(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/a/2048.0
 (-27.0)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*a)+(-9.0)*x*(1-6*x/a)*(1-2*y/b)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*a^2)
 27.0*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*a)+(-9.0)*x*(6*x/a+1)*(1-2*y/b)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*a^2)
 9.0*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*a)+81.0*x*(2*x/a+1)*(1-6*y/b)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*a^2)
 9.0*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*a)+81.0*x*(2*x/a+1)*(6*y/b+1)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*a^2)
 27.0*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*a)+(-9.0)*x*(6*x/a+1)*(2*y/b+1)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*a^2)
 (-27.0)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*a)+(-9.0)*x*(1-6*x/a)*(2*y/b+1)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*a^2)
 (-9.0)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*a)+81.0*x*(1-2*x/a)*(6*y/b+1)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*a^2)
 (-9.0)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*a)+81.0*x*(1-2*x/a)*(1-6*y/b)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*a^2)
 (-243.0)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*a)+(-81.0)*x*(1-6*x/a)*(1-6*y/b)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*a^2)
 243.0*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*a)+(-81.0)*x*(6*x/a+1)*(1-6*y/b)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*a^2)
 243.0*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*a)+(-81.0)*x*(6*x/a+1)*(6*y/b+1)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*a^2)
 (-243.0)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*a)+(-81.0)*x*(1-6*x/a)*(6*y/b+1)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*a^2)
 (-9.0)*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*a)+81.0*x*(1-2*x/a)*(1-2*y/b)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*a^2)
 9.0*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*a)+81.0*x*(2*x/a+1)*(1-2*y/b)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*a^2)
 9.0*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*a)+81.0*x*(2*x/a+1)*(2*y/b+1)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*a^2)
 (-9.0)*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*a)+81.0*x*(1-2*x/a)*(2*y/b+1)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*a^2)
 (-243.0)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*a)+(-81.0)*x*(1-6*x/a)*(1-2*y/b)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*a^2)
 243.0*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*a)+(-81.0)*x*(6*x/a+1)*(1-2*y/b)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*a^2)
 81.0*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*a)+729.0*x*(2*x/a+1)*(1-6*y/b)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*a^2)
 81.0*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*a)+729.0*x*(2*x/a+1)*(6*y/b+1)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*a^2)
 243.0*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*a)+(-81.0)*x*(6*x/a+1)*(2*y/b+1)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*a^2)
 (-243.0)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*a)+(-81.0)*x*(1-6*x/a)*(2*y/b+1)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*a^2)
 (-81.0)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*a)+729.0*x*(1-2*x/a)*(6*y/b+1)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*a^2)
 (-81.0)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*a)+729.0*x*(1-2*x/a)*(1-6*y/b)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*a^2)
 (-2187.0)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*a)+(-729.0)*x*(1-6*x/a)*(1-6*y/b)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*a^2)
 2187.0*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*a)+(-729.0)*x*(6*x/a+1)*(1-6*y/b)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*a^2)
 2187.0*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*a)+(-729.0)*x*(6*x/a+1)*(6*y/b+1)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*a^2)
 (-2187.0)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*a)+(-729.0)*x*(1-6*x/a)*(6*y/b+1)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*a^2)
 (-9.0)*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*a)+81.0*x*(1-2*x/a)*(1-2*y/b)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*a^2)
 9.0*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*a)+81.0*x*(2*x/a+1)*(1-2*y/b)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*a^2)
 9.0*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*a)+81.0*x*(2*x/a+1)*(2*y/b+1)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*a^2)
 (-9.0)*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*a)+81.0*x*(1-2*x/a)*(2*y/b+1)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*a^2)
 (-243.0)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*a)+(-81.0)*x*(1-6*x/a)*(1-2*y/b)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*a^2)
 243.0*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*a)+(-81.0)*x*(6*x/a+1)*(1-2*y/b)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*a^2)
 81.0*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*a)+729.0*x*(2*x/a+1)*(1-6*y/b)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*a^2)
 81.0*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*a)+729.0*x*(2*x/a+1)*(6*y/b+1)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*a^2)
 243.0*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*a)+(-81.0)*x*(6*x/a+1)*(2*y/b+1)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*a^2)
 (-243.0)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*a)+(-81.0)*x*(1-6*x/a)*(2*y/b+1)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*a^2)
 (-81.0)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*a)+729.0*x*(1-2*x/a)*(6*y/b+1)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*a^2)
 (-81.0)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*a)+729.0*x*(1-2*x/a)*(1-6*y/b)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*a^2)
 (-2187.0)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*a)+(-729.0)*x*(1-6*x/a)*(1-6*y/b)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*a^2)
 2187.0*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*a)+(-729.0)*x*(6*x/a+1)*(1-6*y/b)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*a^2)
 2187.0*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*a)+(-729.0)*x*(6*x/a+1)*(6*y/b+1)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*a^2)
 (-2187.0)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*a)+(-729.0)*x*(1-6*x/a)*(6*y/b+1)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*a^2)
 9.0*x*(1-2*x/a)*(1-2*y/b)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*a^2)-(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/a/2048.0
 (36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/a/2048.0+9.0*x*(2*x/a+1)*(1-2*y/b)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*a^2)
 (36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/a/2048.0+9.0*x*(2*x/a+1)*(2*y/b+1)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*a^2)
 9.0*x*(1-2*x/a)*(2*y/b+1)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*a^2)-(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/a/2048.0
 (-27.0)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*a)+(-9.0)*x*(1-6*x/a)*(1-2*y/b)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*a^2)
 27.0*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*a)+(-9.0)*x*(6*x/a+1)*(1-2*y/b)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*a^2)
 9.0*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*a)+81.0*x*(2*x/a+1)*(1-6*y/b)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*a^2)
 9.0*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*a)+81.0*x*(2*x/a+1)*(6*y/b+1)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*a^2)
 27.0*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*a)+(-9.0)*x*(6*x/a+1)*(2*y/b+1)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*a^2)
 (-27.0)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*a)+(-9.0)*x*(1-6*x/a)*(2*y/b+1)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*a^2)
 (-9.0)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*a)+81.0*x*(1-2*x/a)*(6*y/b+1)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*a^2)
 (-9.0)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*a)+81.0*x*(1-2*x/a)*(1-6*y/b)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*a^2)
 (-243.0)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*a)+(-81.0)*x*(1-6*x/a)*(1-6*y/b)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*a^2)
 243.0*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*a)+(-81.0)*x*(6*x/a+1)*(1-6*y/b)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*a^2)
 243.0*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*a)+(-81.0)*x*(6*x/a+1)*(6*y/b+1)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*a^2)
 (-243.0)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*a)+(-81.0)*x*(1-6*x/a)*(6*y/b+1)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*a^2)];


Hy=[9.0*(1-2*x/a)*(36*x^2/a^2-1)*y*(1-2*y/b)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*b^2)-(1-2*x/a)*(36*x^2/a^2-1)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/b/2048.0
 9.0*(2*x/a+1)*(36*x^2/a^2-1)*y*(1-2*y/b)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*b^2)-(2*x/a+1)*(36*x^2/a^2-1)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/b/2048.0
 (2*x/a+1)*(36*x^2/a^2-1)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/b/2048.0+9.0*(2*x/a+1)*(36*x^2/a^2-1)*y*(2*y/b+1)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*b^2)
 (1-2*x/a)*(36*x^2/a^2-1)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/b/2048.0+9.0*(1-2*x/a)*(36*x^2/a^2-1)*y*(2*y/b+1)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*b^2)
 (-9.0)*(1-6*x/a)*(1-4*x^2/a^2)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*b)+81.0*(1-6*x/a)*(1-4*x^2/a^2)*y*(1-2*y/b)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*b^2)
 (-9.0)*(6*x/a+1)*(1-4*x^2/a^2)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*b)+81.0*(6*x/a+1)*(1-4*x^2/a^2)*y*(1-2*y/b)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*b^2)
 (-27.0)*(2*x/a+1)*(36*x^2/a^2-1)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*b)+(-9.0)*(2*x/a+1)*(36*x^2/a^2-1)*y*(1-6*y/b)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*b^2)
 27.0*(2*x/a+1)*(36*x^2/a^2-1)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*b)+(-9.0)*(2*x/a+1)*(36*x^2/a^2-1)*y*(6*y/b+1)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*b^2)
 9.0*(6*x/a+1)*(1-4*x^2/a^2)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*b)+81.0*(6*x/a+1)*(1-4*x^2/a^2)*y*(2*y/b+1)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*b^2)
 9.0*(1-6*x/a)*(1-4*x^2/a^2)*(36*y^2/b^2-1)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*b)+81.0*(1-6*x/a)*(1-4*x^2/a^2)*y*(2*y/b+1)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*b^2)
 27.0*(1-2*x/a)*(36*x^2/a^2-1)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*b)+(-9.0)*(1-2*x/a)*(36*x^2/a^2-1)*y*(6*y/b+1)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*b^2)
 (-27.0)*(1-2*x/a)*(36*x^2/a^2-1)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*b)+(-9.0)*(1-2*x/a)*(36*x^2/a^2-1)*y*(1-6*y/b)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*b^2)
 (-243.0)*(1-6*x/a)*(1-4*x^2/a^2)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*b)+(-81.0)*(1-6*x/a)*(1-4*x^2/a^2)*y*(1-6*y/b)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*b^2)
 (-243.0)*(6*x/a+1)*(1-4*x^2/a^2)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*b)+(-81.0)*(6*x/a+1)*(1-4*x^2/a^2)*y*(1-6*y/b)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*b^2)
 243.0*(6*x/a+1)*(1-4*x^2/a^2)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*b)+(-81.0)*(6*x/a+1)*(1-4*x^2/a^2)*y*(6*y/b+1)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*b^2)
 243.0*(1-6*x/a)*(1-4*x^2/a^2)*(1-4*y^2/b^2)*(1-2*z/c)*(36*z^2/c^2-1)/(2048.0*b)+(-81.0)*(1-6*x/a)*(1-4*x^2/a^2)*y*(6*y/b+1)*(1-2*z/c)*(36*z^2/c^2-1)/(512.0*b^2)
 (-9.0)*(1-2*x/a)*(36*x^2/a^2-1)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*b)+81.0*(1-2*x/a)*(36*x^2/a^2-1)*y*(1-2*y/b)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*b^2)
 (-9.0)*(2*x/a+1)*(36*x^2/a^2-1)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*b)+81.0*(2*x/a+1)*(36*x^2/a^2-1)*y*(1-2*y/b)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*b^2)
 9.0*(2*x/a+1)*(36*x^2/a^2-1)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*b)+81.0*(2*x/a+1)*(36*x^2/a^2-1)*y*(2*y/b+1)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*b^2)
 9.0*(1-2*x/a)*(36*x^2/a^2-1)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*b)+81.0*(1-2*x/a)*(36*x^2/a^2-1)*y*(2*y/b+1)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*b^2)
 (-81.0)*(1-6*x/a)*(1-4*x^2/a^2)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*b)+729.0*(1-6*x/a)*(1-4*x^2/a^2)*y*(1-2*y/b)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*b^2)
 (-81.0)*(6*x/a+1)*(1-4*x^2/a^2)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*b)+729.0*(6*x/a+1)*(1-4*x^2/a^2)*y*(1-2*y/b)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*b^2)
 (-243.0)*(2*x/a+1)*(36*x^2/a^2-1)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*b)+(-81.0)*(2*x/a+1)*(36*x^2/a^2-1)*y*(1-6*y/b)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*b^2)
 243.0*(2*x/a+1)*(36*x^2/a^2-1)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*b)+(-81.0)*(2*x/a+1)*(36*x^2/a^2-1)*y*(6*y/b+1)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*b^2)
 81.0*(6*x/a+1)*(1-4*x^2/a^2)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*b)+729.0*(6*x/a+1)*(1-4*x^2/a^2)*y*(2*y/b+1)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*b^2)
 81.0*(1-6*x/a)*(1-4*x^2/a^2)*(36*y^2/b^2-1)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*b)+729.0*(1-6*x/a)*(1-4*x^2/a^2)*y*(2*y/b+1)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*b^2)
 243.0*(1-2*x/a)*(36*x^2/a^2-1)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*b)+(-81.0)*(1-2*x/a)*(36*x^2/a^2-1)*y*(6*y/b+1)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*b^2)
 (-243.0)*(1-2*x/a)*(36*x^2/a^2-1)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*b)+(-81.0)*(1-2*x/a)*(36*x^2/a^2-1)*y*(1-6*y/b)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*b^2)
 (-2187.0)*(1-6*x/a)*(1-4*x^2/a^2)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*b)+(-729.0)*(1-6*x/a)*(1-4*x^2/a^2)*y*(1-6*y/b)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*b^2)
 (-2187.0)*(6*x/a+1)*(1-4*x^2/a^2)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*b)+(-729.0)*(6*x/a+1)*(1-4*x^2/a^2)*y*(1-6*y/b)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*b^2)
 2187.0*(6*x/a+1)*(1-4*x^2/a^2)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*b)+(-729.0)*(6*x/a+1)*(1-4*x^2/a^2)*y*(6*y/b+1)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*b^2)
 2187.0*(1-6*x/a)*(1-4*x^2/a^2)*(1-4*y^2/b^2)*(1-6*z/c)*(1-4*z^2/c^2)/(2048.0*b)+(-729.0)*(1-6*x/a)*(1-4*x^2/a^2)*y*(6*y/b+1)*(1-6*z/c)*(1-4*z^2/c^2)/(512.0*b^2)
 (-9.0)*(1-2*x/a)*(36*x^2/a^2-1)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*b)+81.0*(1-2*x/a)*(36*x^2/a^2-1)*y*(1-2*y/b)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*b^2)
 (-9.0)*(2*x/a+1)*(36*x^2/a^2-1)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*b)+81.0*(2*x/a+1)*(36*x^2/a^2-1)*y*(1-2*y/b)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*b^2)
 9.0*(2*x/a+1)*(36*x^2/a^2-1)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*b)+81.0*(2*x/a+1)*(36*x^2/a^2-1)*y*(2*y/b+1)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*b^2)
 9.0*(1-2*x/a)*(36*x^2/a^2-1)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*b)+81.0*(1-2*x/a)*(36*x^2/a^2-1)*y*(2*y/b+1)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*b^2)
 (-81.0)*(1-6*x/a)*(1-4*x^2/a^2)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*b)+729.0*(1-6*x/a)*(1-4*x^2/a^2)*y*(1-2*y/b)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*b^2)
 (-81.0)*(6*x/a+1)*(1-4*x^2/a^2)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*b)+729.0*(6*x/a+1)*(1-4*x^2/a^2)*y*(1-2*y/b)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*b^2)
 (-243.0)*(2*x/a+1)*(36*x^2/a^2-1)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*b)+(-81.0)*(2*x/a+1)*(36*x^2/a^2-1)*y*(1-6*y/b)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*b^2)
 243.0*(2*x/a+1)*(36*x^2/a^2-1)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*b)+(-81.0)*(2*x/a+1)*(36*x^2/a^2-1)*y*(6*y/b+1)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*b^2)
 81.0*(6*x/a+1)*(1-4*x^2/a^2)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*b)+729.0*(6*x/a+1)*(1-4*x^2/a^2)*y*(2*y/b+1)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*b^2)
 81.0*(1-6*x/a)*(1-4*x^2/a^2)*(36*y^2/b^2-1)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*b)+729.0*(1-6*x/a)*(1-4*x^2/a^2)*y*(2*y/b+1)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*b^2)
 243.0*(1-2*x/a)*(36*x^2/a^2-1)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*b)+(-81.0)*(1-2*x/a)*(36*x^2/a^2-1)*y*(6*y/b+1)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*b^2)
 (-243.0)*(1-2*x/a)*(36*x^2/a^2-1)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*b)+(-81.0)*(1-2*x/a)*(36*x^2/a^2-1)*y*(1-6*y/b)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*b^2)
 (-2187.0)*(1-6*x/a)*(1-4*x^2/a^2)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*b)+(-729.0)*(1-6*x/a)*(1-4*x^2/a^2)*y*(1-6*y/b)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*b^2)
 (-2187.0)*(6*x/a+1)*(1-4*x^2/a^2)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*b)+(-729.0)*(6*x/a+1)*(1-4*x^2/a^2)*y*(1-6*y/b)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*b^2)
 2187.0*(6*x/a+1)*(1-4*x^2/a^2)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*b)+(-729.0)*(6*x/a+1)*(1-4*x^2/a^2)*y*(6*y/b+1)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*b^2)
 2187.0*(1-6*x/a)*(1-4*x^2/a^2)*(1-4*y^2/b^2)*(6*z/c+1)*(1-4*z^2/c^2)/(2048.0*b)+(-729.0)*(1-6*x/a)*(1-4*x^2/a^2)*y*(6*y/b+1)*(6*z/c+1)*(1-4*z^2/c^2)/(512.0*b^2)
 9.0*(1-2*x/a)*(36*x^2/a^2-1)*y*(1-2*y/b)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*b^2)-(1-2*x/a)*(36*x^2/a^2-1)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/b/2048.0
 9.0*(2*x/a+1)*(36*x^2/a^2-1)*y*(1-2*y/b)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*b^2)-(2*x/a+1)*(36*x^2/a^2-1)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/b/2048.0
 (2*x/a+1)*(36*x^2/a^2-1)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/b/2048.0+9.0*(2*x/a+1)*(36*x^2/a^2-1)*y*(2*y/b+1)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*b^2)
 (1-2*x/a)*(36*x^2/a^2-1)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/b/2048.0+9.0*(1-2*x/a)*(36*x^2/a^2-1)*y*(2*y/b+1)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*b^2)
 (-9.0)*(1-6*x/a)*(1-4*x^2/a^2)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*b)+81.0*(1-6*x/a)*(1-4*x^2/a^2)*y*(1-2*y/b)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*b^2)
 (-9.0)*(6*x/a+1)*(1-4*x^2/a^2)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*b)+81.0*(6*x/a+1)*(1-4*x^2/a^2)*y*(1-2*y/b)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*b^2)
 (-27.0)*(2*x/a+1)*(36*x^2/a^2-1)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*b)+(-9.0)*(2*x/a+1)*(36*x^2/a^2-1)*y*(1-6*y/b)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*b^2)
 27.0*(2*x/a+1)*(36*x^2/a^2-1)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*b)+(-9.0)*(2*x/a+1)*(36*x^2/a^2-1)*y*(6*y/b+1)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*b^2)
 9.0*(6*x/a+1)*(1-4*x^2/a^2)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*b)+81.0*(6*x/a+1)*(1-4*x^2/a^2)*y*(2*y/b+1)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*b^2)
 9.0*(1-6*x/a)*(1-4*x^2/a^2)*(36*y^2/b^2-1)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*b)+81.0*(1-6*x/a)*(1-4*x^2/a^2)*y*(2*y/b+1)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*b^2)
 27.0*(1-2*x/a)*(36*x^2/a^2-1)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*b)+(-9.0)*(1-2*x/a)*(36*x^2/a^2-1)*y*(6*y/b+1)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*b^2)
 (-27.0)*(1-2*x/a)*(36*x^2/a^2-1)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*b)+(-9.0)*(1-2*x/a)*(36*x^2/a^2-1)*y*(1-6*y/b)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*b^2)
 (-243.0)*(1-6*x/a)*(1-4*x^2/a^2)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*b)+(-81.0)*(1-6*x/a)*(1-4*x^2/a^2)*y*(1-6*y/b)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*b^2)
 (-243.0)*(6*x/a+1)*(1-4*x^2/a^2)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*b)+(-81.0)*(6*x/a+1)*(1-4*x^2/a^2)*y*(1-6*y/b)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*b^2)
 243.0*(6*x/a+1)*(1-4*x^2/a^2)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*b)+(-81.0)*(6*x/a+1)*(1-4*x^2/a^2)*y*(6*y/b+1)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*b^2)
 243.0*(1-6*x/a)*(1-4*x^2/a^2)*(1-4*y^2/b^2)*(2*z/c+1)*(36*z^2/c^2-1)/(2048.0*b)+(-81.0)*(1-6*x/a)*(1-4*x^2/a^2)*y*(6*y/b+1)*(2*z/c+1)*(36*z^2/c^2-1)/(512.0*b^2)];

Hz=[9.0*(1-2*x/a)*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*z*(1-2*z/c)/(512.0*c^2)-(1-2*x/a)*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*(36*z^2/c^2-1)/c/2048.0
 9.0*(2*x/a+1)*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*z*(1-2*z/c)/(512.0*c^2)-(2*x/a+1)*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*(36*z^2/c^2-1)/c/2048.0
 9.0*(2*x/a+1)*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*z*(1-2*z/c)/(512.0*c^2)-(2*x/a+1)*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*(36*z^2/c^2-1)/c/2048.0
 9.0*(1-2*x/a)*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*z*(1-2*z/c)/(512.0*c^2)-(1-2*x/a)*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*(36*z^2/c^2-1)/c/2048.0
 (-9.0)*(1-6*x/a)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*(36*z^2/c^2-1)/(2048.0*c)+81.0*(1-6*x/a)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*z*(1-2*z/c)/(512.0*c^2)
 (-9.0)*(6*x/a+1)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*(36*z^2/c^2-1)/(2048.0*c)+81.0*(6*x/a+1)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*z*(1-2*z/c)/(512.0*c^2)
 (-9.0)*(2*x/a+1)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*(36*z^2/c^2-1)/(2048.0*c)+81.0*(2*x/a+1)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*z*(1-2*z/c)/(512.0*c^2)
 (-9.0)*(2*x/a+1)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*(36*z^2/c^2-1)/(2048.0*c)+81.0*(2*x/a+1)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*z*(1-2*z/c)/(512.0*c^2)
 (-9.0)*(6*x/a+1)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*(36*z^2/c^2-1)/(2048.0*c)+81.0*(6*x/a+1)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*z*(1-2*z/c)/(512.0*c^2)
 (-9.0)*(1-6*x/a)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*(36*z^2/c^2-1)/(2048.0*c)+81.0*(1-6*x/a)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*z*(1-2*z/c)/(512.0*c^2)
 (-9.0)*(1-2*x/a)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*(36*z^2/c^2-1)/(2048.0*c)+81.0*(1-2*x/a)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*z*(1-2*z/c)/(512.0*c^2)
 (-9.0)*(1-2*x/a)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*(36*z^2/c^2-1)/(2048.0*c)+81.0*(1-2*x/a)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*z*(1-2*z/c)/(512.0*c^2)
 (-81.0)*(1-6*x/a)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*(36*z^2/c^2-1)/(2048.0*c)+729.0*(1-6*x/a)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*z*(1-2*z/c)/(512.0*c^2)
 (-81.0)*(6*x/a+1)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*(36*z^2/c^2-1)/(2048.0*c)+729.0*(6*x/a+1)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*z*(1-2*z/c)/(512.0*c^2)
 (-81.0)*(6*x/a+1)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*(36*z^2/c^2-1)/(2048.0*c)+729.0*(6*x/a+1)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*z*(1-2*z/c)/(512.0*c^2)
 (-81.0)*(1-6*x/a)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*(36*z^2/c^2-1)/(2048.0*c)+729.0*(1-6*x/a)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*z*(1-2*z/c)/(512.0*c^2)
 (-27.0)*(1-2*x/a)*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*(1-4*z^2/c^2)/(2048.0*c)+(-9.0)*(1-2*x/a)*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*z*(1-6*z/c)/(512.0*c^2)
 (-27.0)*(2*x/a+1)*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*(1-4*z^2/c^2)/(2048.0*c)+(-9.0)*(2*x/a+1)*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*z*(1-6*z/c)/(512.0*c^2)
 (-27.0)*(2*x/a+1)*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*(1-4*z^2/c^2)/(2048.0*c)+(-9.0)*(2*x/a+1)*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*z*(1-6*z/c)/(512.0*c^2)
 (-27.0)*(1-2*x/a)*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*(1-4*z^2/c^2)/(2048.0*c)+(-9.0)*(1-2*x/a)*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*z*(1-6*z/c)/(512.0*c^2)
 (-243.0)*(1-6*x/a)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*(1-4*z^2/c^2)/(2048.0*c)+(-81.0)*(1-6*x/a)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*z*(1-6*z/c)/(512.0*c^2)
 (-243.0)*(6*x/a+1)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*(1-4*z^2/c^2)/(2048.0*c)+(-81.0)*(6*x/a+1)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*z*(1-6*z/c)/(512.0*c^2)
 (-243.0)*(2*x/a+1)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*(1-4*z^2/c^2)/(2048.0*c)+(-81.0)*(2*x/a+1)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*z*(1-6*z/c)/(512.0*c^2)
 (-243.0)*(2*x/a+1)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*(1-4*z^2/c^2)/(2048.0*c)+(-81.0)*(2*x/a+1)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*z*(1-6*z/c)/(512.0*c^2)
 (-243.0)*(6*x/a+1)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*(1-4*z^2/c^2)/(2048.0*c)+(-81.0)*(6*x/a+1)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*z*(1-6*z/c)/(512.0*c^2)
 (-243.0)*(1-6*x/a)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*(1-4*z^2/c^2)/(2048.0*c)+(-81.0)*(1-6*x/a)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*z*(1-6*z/c)/(512.0*c^2)
 (-243.0)*(1-2*x/a)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*(1-4*z^2/c^2)/(2048.0*c)+(-81.0)*(1-2*x/a)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*z*(1-6*z/c)/(512.0*c^2)
 (-243.0)*(1-2*x/a)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*(1-4*z^2/c^2)/(2048.0*c)+(-81.0)*(1-2*x/a)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*z*(1-6*z/c)/(512.0*c^2)
 (-2187.0)*(1-6*x/a)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*(1-4*z^2/c^2)/(2048.0*c)+(-729.0)*(1-6*x/a)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*z*(1-6*z/c)/(512.0*c^2)
 (-2187.0)*(6*x/a+1)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*(1-4*z^2/c^2)/(2048.0*c)+(-729.0)*(6*x/a+1)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*z*(1-6*z/c)/(512.0*c^2)
 (-2187.0)*(6*x/a+1)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*(1-4*z^2/c^2)/(2048.0*c)+(-729.0)*(6*x/a+1)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*z*(1-6*z/c)/(512.0*c^2)
 (-2187.0)*(1-6*x/a)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*(1-4*z^2/c^2)/(2048.0*c)+(-729.0)*(1-6*x/a)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*z*(1-6*z/c)/(512.0*c^2)
 27.0*(1-2*x/a)*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*(1-4*z^2/c^2)/(2048.0*c)+(-9.0)*(1-2*x/a)*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*z*(6*z/c+1)/(512.0*c^2)
 27.0*(2*x/a+1)*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*(1-4*z^2/c^2)/(2048.0*c)+(-9.0)*(2*x/a+1)*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*z*(6*z/c+1)/(512.0*c^2)
 27.0*(2*x/a+1)*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*(1-4*z^2/c^2)/(2048.0*c)+(-9.0)*(2*x/a+1)*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*z*(6*z/c+1)/(512.0*c^2)
 27.0*(1-2*x/a)*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*(1-4*z^2/c^2)/(2048.0*c)+(-9.0)*(1-2*x/a)*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*z*(6*z/c+1)/(512.0*c^2)
 243.0*(1-6*x/a)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*(1-4*z^2/c^2)/(2048.0*c)+(-81.0)*(1-6*x/a)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*z*(6*z/c+1)/(512.0*c^2)
 243.0*(6*x/a+1)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*(1-4*z^2/c^2)/(2048.0*c)+(-81.0)*(6*x/a+1)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*z*(6*z/c+1)/(512.0*c^2)
 243.0*(2*x/a+1)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*(1-4*z^2/c^2)/(2048.0*c)+(-81.0)*(2*x/a+1)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*z*(6*z/c+1)/(512.0*c^2)
 243.0*(2*x/a+1)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*(1-4*z^2/c^2)/(2048.0*c)+(-81.0)*(2*x/a+1)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*z*(6*z/c+1)/(512.0*c^2)
 243.0*(6*x/a+1)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*(1-4*z^2/c^2)/(2048.0*c)+(-81.0)*(6*x/a+1)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*z*(6*z/c+1)/(512.0*c^2)
 243.0*(1-6*x/a)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*(1-4*z^2/c^2)/(2048.0*c)+(-81.0)*(1-6*x/a)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*z*(6*z/c+1)/(512.0*c^2)
 243.0*(1-2*x/a)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*(1-4*z^2/c^2)/(2048.0*c)+(-81.0)*(1-2*x/a)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*z*(6*z/c+1)/(512.0*c^2)
 243.0*(1-2*x/a)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*(1-4*z^2/c^2)/(2048.0*c)+(-81.0)*(1-2*x/a)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*z*(6*z/c+1)/(512.0*c^2)
 2187.0*(1-6*x/a)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*(1-4*z^2/c^2)/(2048.0*c)+(-729.0)*(1-6*x/a)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*z*(6*z/c+1)/(512.0*c^2)
 2187.0*(6*x/a+1)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*(1-4*z^2/c^2)/(2048.0*c)+(-729.0)*(6*x/a+1)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*z*(6*z/c+1)/(512.0*c^2)
 2187.0*(6*x/a+1)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*(1-4*z^2/c^2)/(2048.0*c)+(-729.0)*(6*x/a+1)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*z*(6*z/c+1)/(512.0*c^2)
 2187.0*(1-6*x/a)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*(1-4*z^2/c^2)/(2048.0*c)+(-729.0)*(1-6*x/a)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*z*(6*z/c+1)/(512.0*c^2)
 (1-2*x/a)*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*(36*z^2/c^2-1)/c/2048.0+9.0*(1-2*x/a)*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*z*(2*z/c+1)/(512.0*c^2)
 (2*x/a+1)*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*(36*z^2/c^2-1)/c/2048.0+9.0*(2*x/a+1)*(36*x^2/a^2-1)*(1-2*y/b)*(36*y^2/b^2-1)*z*(2*z/c+1)/(512.0*c^2)
 (2*x/a+1)*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*(36*z^2/c^2-1)/c/2048.0+9.0*(2*x/a+1)*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*z*(2*z/c+1)/(512.0*c^2)
 (1-2*x/a)*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*(36*z^2/c^2-1)/c/2048.0+9.0*(1-2*x/a)*(36*x^2/a^2-1)*(2*y/b+1)*(36*y^2/b^2-1)*z*(2*z/c+1)/(512.0*c^2)
 9.0*(1-6*x/a)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*(36*z^2/c^2-1)/(2048.0*c)+81.0*(1-6*x/a)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*z*(2*z/c+1)/(512.0*c^2)
 9.0*(6*x/a+1)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*(36*z^2/c^2-1)/(2048.0*c)+81.0*(6*x/a+1)*(1-4*x^2/a^2)*(1-2*y/b)*(36*y^2/b^2-1)*z*(2*z/c+1)/(512.0*c^2)
 9.0*(2*x/a+1)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*(36*z^2/c^2-1)/(2048.0*c)+81.0*(2*x/a+1)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*z*(2*z/c+1)/(512.0*c^2)
 9.0*(2*x/a+1)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*(36*z^2/c^2-1)/(2048.0*c)+81.0*(2*x/a+1)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*z*(2*z/c+1)/(512.0*c^2)
 9.0*(6*x/a+1)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*(36*z^2/c^2-1)/(2048.0*c)+81.0*(6*x/a+1)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*z*(2*z/c+1)/(512.0*c^2)
 9.0*(1-6*x/a)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*(36*z^2/c^2-1)/(2048.0*c)+81.0*(1-6*x/a)*(1-4*x^2/a^2)*(2*y/b+1)*(36*y^2/b^2-1)*z*(2*z/c+1)/(512.0*c^2)
 9.0*(1-2*x/a)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*(36*z^2/c^2-1)/(2048.0*c)+81.0*(1-2*x/a)*(36*x^2/a^2-1)*(6*y/b+1)*(1-4*y^2/b^2)*z*(2*z/c+1)/(512.0*c^2)
 9.0*(1-2*x/a)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*(36*z^2/c^2-1)/(2048.0*c)+81.0*(1-2*x/a)*(36*x^2/a^2-1)*(1-6*y/b)*(1-4*y^2/b^2)*z*(2*z/c+1)/(512.0*c^2)
 81.0*(1-6*x/a)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*(36*z^2/c^2-1)/(2048.0*c)+729.0*(1-6*x/a)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*z*(2*z/c+1)/(512.0*c^2)
 81.0*(6*x/a+1)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*(36*z^2/c^2-1)/(2048.0*c)+729.0*(6*x/a+1)*(1-4*x^2/a^2)*(1-6*y/b)*(1-4*y^2/b^2)*z*(2*z/c+1)/(512.0*c^2)
 81.0*(6*x/a+1)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*(36*z^2/c^2-1)/(2048.0*c)+729.0*(6*x/a+1)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*z*(2*z/c+1)/(512.0*c^2)
 81.0*(1-6*x/a)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*(36*z^2/c^2-1)/(2048.0*c)+729.0*(1-6*x/a)*(1-4*x^2/a^2)*(6*y/b+1)*(1-4*y^2/b^2)*z*(2*z/c+1)/(512.0*c^2)];
Highlights from Parametric Hexahedral Solid FEMs

Highlights from
Parametric Hexahedral Solid FEMs
