Orthotropic linear elastic material - OrthoLE

Local coordinate system
can also be specified using *scs* parameter. Then local coordinate
system is specified in so called ``shell''
coordinate system, which is defined locally on each particular element
and its definition is as follows: principal z-axis is perpendicular to
shell mid-section, x-axis is perpendicular to z-axis and normal to
user specified vector (so x-axis is parallel to plane, with being
normal to this plane) and y-axis is perpendicular both to x and z
axes. This definition of coordinate system can be used only with plates
and shells elements.
When vector is parallel to z-axis an error occurs. The *scs* array contain three numbers
defining direction vector . If no local coordinate system is
specified, by default a global coordinate system is used.

For 3D case the material compliance matrix has the following form

(1) |

By inversion, the material stiffness matrix has the form

(2) |

where and

(3) | |||

(4) | |||

(5) | |||

(6) | |||

(7) | |||

(8) |

is Young's modulus in the -th direction, is the shear modulus in plane, is the major Poisson ratio, and is the minor Poisson ratio. Assuming that , etc., then is referred to as the major Poisson ratio, while is referred as the minor Poisson ratio. Note that there are only nine independent material parameters, because of symmetry conditions. The symmetry condition yields

2018-01-02