stress tensor transformation

tricha122

Hi all,

I have been reading up about continuum mechanics recently, and have a question regarding the reduction in stiffness coefficients in the stiffness matrix.

I am aware of how the stiffness matrix is reduced to 21 coefficients. However, in order to reduce it from 21 to 13, one has to assume 1 plane of material symmetry.

When doing so, (say x1 = 0 is the plane of symmetry), in order to reduce the # of coefficients, you have to look at sigma = C*epsilon, and sigma' = C'*epsilon'

where C = C' for 1 symmetric plane.

Transforming sigma and epsilon from OX1X2X3 to OX1'X2X3 you can get the "boundary conditions" you need to zero out certain coefficients of the stiffness matrix and result with 13 (from 21).

My problem is O-X1-X2-X3 to O-X1'-X2-X3 is changing from a RH coordinate system to a LH coordinate system.

a RH to RH system would look like this: O-X1-X2-X3 to O-X1'-X2'-X3.

However, when i attempt the same reduction with that transformation the math doesnt work out correctly.

SHould it work out? Does one always use a RH->LH transformation when using planes of symmetry?

Any help would be greatly appreciated.

Thanks