Table 1: Shape functions N and their derivatives with respect to r, s and t of a tetrahedron T4 element

Table 1: Shape functions N and their derivatives with respect to r, s and t of a tetrahedron T4 element

Node Number	Shape Function N
0	r	1.0	0.0	0.0
1	s	0.0	1.0	0.0
2	t	0.0	0.0	1.0
3	u	-1.0	-1.0	-1.0

u = 1-r-s-t

// ----------------------------------------------------------------

// 4-noded linear tetrahedral

FemVector *T4Shape::shape_functions(const double r,

const double s,

const double t) const

{

double u = 1.0 - r - s - t ;

FemVector *shape = new FemVector(4) ;

shape->at(0) = r ;

shape->at(1) = s ;

shape->at(2) = t ;

shape->at(3) = u ;

return(shape) ;

}

FemMatrix *T4Shape::shape_derivatives(const double r,

const double s,

const double t) const

{

double u = 1.0 - r - s - t ;

FemMatrix *deriv = new FemMatrix(3,4) ;

deriv->at(0,0) = 1.0 ;

deriv->at(0,1) = 0.0 ;

deriv->at(0,2) = 0.0 ;

deriv->at(0,3) = -1.0 ;

deriv->at(1,0) = 0.0 ;

deriv->at(1,1) = 1.0 ;

deriv->at(1,2) = 0.0 ;

deriv->at(1,3) = -1.0 ;

deriv->at(2,0) = 0.0 ;

deriv->at(2,1) = 0.0 ;

deriv->at(2,2) = 1.0 ;

deriv->at(2,3) = -1.0 ;

return(deriv) ;

}

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).