Given the material properties of a unidirectional lamina, this calculator constructs the stiffness matrix [C] and the compliance matrix [S] of the lamina in the principal directions.

If the angle of rotation of the lamina is given (other than 0 degree), this calculator also constructs the stiffness matrix [] and the compliance matrix [] in the rotated directions.

Input

The stiffness matrix [C] in the principal directions is

[C]

=

The compliance matrix [S] in the principal direction is

[S]

=

The coordinate transformation matrix is

[T]

=

The engineering-tensor interchange matrix [R] is

The stiffness matrix for a lamina of arbitry orient can be expressed in terms of the stiffness matrix in the principal direction,

[]

=

The complicance matrix for a lamina of arbitry orient can be obtained in a similar manner.

[]

=