# Sign Convention

Normal Axis 3

Local axis 3 is always normal to the plane of the shell element. This axis is directed towards you when the path j1-j2-j3 appears counter-clockwise. For quadrilateral elements, the element plane is defined by the vectors that connect the mid-points of the two pairs of opposite sides.

Default Orientation

The default orientation of the local 1 and 2 axes is determined by the relationship between the local 3 axis and the global Z axis:

• The local 3-2 plane is taken to be vertical, i.e., parallel to the Z axis

• The local 2 axis is taken to have an upward (+Z) sense unless the element is horizontal, in which case the local 2 axis is taken along the global +Y direction

• The local 1 axis is horizontal, i.e., it lies in the X-Y plane

The element is considered to be horizontal if the sine of the angle between the local 3 axis and the Z axis is less than 10-3.

The local 2 axis makes the same angle with the vertical axis as the local 3 axis makes with the horizontal plane. This means that the local 2 axis points vertically upward for vertical elements.

Element Coordinate Angle

The shell element coordinate angle, ang, is used to define element orientations that are different from the default orientation. It is the angle through which the local 1 and 2 axes are rotated about the positive local 3 axis from the default orientation. The rotation for a positive angle value of ang appears counter-clockwise when the local +3 axis is pointing toward you.

For horizontal elements, ang is the angle between the local 2 axis and the horizontal +Y axis. Otherwise, ang is the angle between the local 2 axis and the vertical plane containing the local 3 axis. The following figures provide examples.    