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Composite Materials

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

Unit
Unit of Stiffness:
Material Properties
Material:

If the material is not in the list, please select 'Custom' and enter the data.

Material:
Young's Modulus along Fibers E1 :
Young's Modulus Normal to Fibers E2 :
Shear Modulus G12 :
Poisson's Ratio 12 :
Angle of Rotation
Rotating Angle : degree
(0 degree is the principal direction)
Stress-Strain Relations for Lamina for Principal Directions

The stiffness matrix [C] in the principal directions is

[C] =

The compliance matrix [S] in the principal direction is

[S] =
Coordinate Transformation Matrix

The coordinate transformation matrix is

[T] = T

The engineering-tensor interchange matrix [R] is

R
Stiffness and Compliance Matrices for Angled Lamina

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.

[] =