How to calculate volume of a hex ( brick ) element?
How to calculate volume of a hex ( brick ) element?
(OP)
Anyone know offhand the formula for calculating the volume of an 8-noded brick element. I have got all the nodal coordinates but not sure what the formula is? I realize it may not be a simple answer, but will likely involve some vector math..
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RE: How to calculate volume of a hex ( brick ) element?
RE: How to calculate volume of a hex ( brick ) element?
x=sum(X(i)*N(i))=X(1)*N(1)+....X(8)*N(8),..X(i) are the
x coordinates of the nodes.
y=sum(Y(i)*N(i)), z=sum(Z(i)*N(i)). The shape functions N(i) are a function of the parent element coordinates, xi, eta, zeta.
Volume=integral(1*dx*dy*dz)=integral(J*dxi*deta*dzeta), where J is the Jacobian, the determinant of a 3 x 3 matrix, first row are the derivatives dx/dxi, dy/dxi, and dz/dxi, second row are the derivates with respect to eta, third row zeta. The derivatives are easy to compute:
dx/dxi=sum(X(i)*dN(i)/dxi)=X(1)*dN(1)/dxi+X(2)*dN(2)/dxi+...X(8)*dN(8)/dxi, same for the other 8 derivatives.
Once you compute those derivatives, compute the Jacobian, the integral(J*dxi*deta*dzeta) you can do by hand I think. Even if not, you may be able to write a small VBA in Excel to compute the integral numerically.
RE: How to calculate volume of a hex ( brick ) element?
RE: How to calculate volume of a hex ( brick ) element?
RE: How to calculate volume of a hex ( brick ) element?
If the solid has planar sides then it'll reduce to a prizmatic portion and some (maximum of 6?) pyramids ??
RE: How to calculate volume of a hex ( brick ) element?
Cheers
Greg Locock
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