Substructure recovery with The nodal Transformation

In all the analyses a local coordinate system is defined at two adjacent nodes of a 1.0 × 1.0 planar substructure. Displacement boundary conditions are prescribed at these nodes such that the net effect is pure extension in the global x-direction. In the first and third analyses a local Cartesian coordinate system is defined at an angle of 45° with the global Cartesian system; in the second analysis a local cylindrical coordinate system is defined such that the axis of the cylindrical system is parallel to the global z-axis; and in the fourth analysis a local spherical coordinate system is defined such that the polar axis is parallel to the global z-axis. The center of the spherical system is defined such that the radial direction at all the nodes coincides with the global x-direction.