Example of stresses on a simplicial 2-complex (cardinality of facets =3 )

> with(linalg):

The simplicial complex has facets: 213, 143, 423, 125, 245, 415.. Bipyramid over triangle 124.

The following are chosen for the coordinates of the vertices.

> v1:=[0,0,-1]; v2:=[2,0,1]; v3:=[0,1/2,1/2]; v4:=[-2,0,1]; v5:=[0,-1/2,1/2];

> M:=transpose(array([v1,v2,v3,v4,v5]));

The following is a linear 3-stress.

> b3:=expand((1/24)*(2*x1+x2+x4)^2*(4*x1+6*x5-x2+6*x3-x4));

> g3:=grad(b3,[x1,x2,x3,x4,x5]): multiply(M,g3);

The following is a linear 2-stress, obtained by applying omega to b3.

> b2:=multiply([1,1,1,1,1],g3);

> g2:=grad(b2,[x1,x2,x3,x4,x5]): multiply(M,g2);

The following is a linear 1-stress, obtained by applying omega to b2.

> b1:=multiply([1,1,1,1,1],g2);

> g1:=grad(b1,[x1,x2,x3,x4,x5]): multiply(M,g1);

The following is a linear 0-stress, obtained by applying omega to b1.

> b0:=multiply([1,1,1,1,1],g1);

> g0:=grad(b0,[x1,x2,x3,x4,x5]): multiply(M,g0);

The following is a different linear 2-stress, obtained from b3 by using a different combination of partial derivatives.

> b2a:=multiply([1,0,3,-6,2],g3);

> g2a:=grad(b2a,[x1,x2,x3,x4,x5]): multiply(M,g2a);

The following is a more general linear 2-stress, obtained from b3 by using a general linear combination of partial derivatives.

> b2b:=expand(multiply([c1,c2,c3,c4,c5],g3));

> g2b:=grad(b2b,[x1,x2,x3,x4,x5]): multiply(M,g2b);

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