Local axes orientation
The purpose of current page is to describe the convention employed in the definition of local axes within Kratos. This is designed in particular for the "structural" case, consisting in Beams, Shells and Solid elements, however the same conventions shall be employed in other fields when applicable.
The following variables, of type array_1d<double,3> are defined within the Kratos core, and shall be used in naming the axis of choice.
LOCAL_AXIS_1LOCAL_AXIS_2LOCAL_AXIS_3
For the case of a Beam, the axis LOCAL_AXIS_1 is chosen as tangent to the beam axis, oriented following the beam natural numbering (for a 2 noded beam, from node 0 towards node 1).
LOCAL_AXIS_2 is expected to be orthogonal to the direction identified by LOCAL_AXIS_1. Such axis can either be provided by the user or computed automatically. LOCAL_AXIS_3 is then computed to form an orthonormal basis with the first 2.
In this case, LOCAL_AXIS_2 is assumed to be approximatevely orthogonal to the beam axis. It will be made orhogonal and normalized as a very first step.
It shall be assigned to the element employing the GetValue/SetValue method, so that it is possible to query whether it was prescribed or not by employing the function Has().
In this case, LOCAL_AXIS_2 is computed from the inertia moment (second moment of area), remembering the definition of the inertia tensor for a beam:
The problem consists in decompose the tensor using the eigendecomposition, being the moments of inertia in the diagonal matrix the corresponding to the main moments of inertia, which in this case we will short by value. This is because we will assume that the highest one is the LOCAL_AXIS_3, because in engineering it is common for the beam to have the highest inertia moment in this direction:
Then the resulting eigenvectors will define the main axis of the beam. Then the LOCAL_AXIS_2 and LOCAL_AXIS_3 can be calculated automatically using the following formulas:
