bug in hinges about anastruct HOT 1 CLOSED

Okay, I think I'm pinning this down finally.

Key fact: In the above script, if instead of setting the hinge at node 2 of element 1, you set it at node 1 of element 2, then the asymmetry of the results exactly switches. (i.e. higher reaction on the right node rather than left node)

Digging in: When a hinge is added to a specific element, then the constitutive matrix for that element is modified to remove stiffness due to that end of the beam (effectively creating a constitutive matrix for a cantilevered beam). It does nothing, however, for the neighbouring element, which still has a constitutive matrix that assumes stiffnesses for a fixed beam. That means that when the global stiffness matrix is assembled, the free rotation of node 2 is incorrectly taken as affecting the moment and shear of the unreleased neighbouring element.

The Solution: I think we need to modify the ensure_single_hinge() function to, rather than ensuring at least one element has a moment connection to a node, instead ensuring that every element is hinged and adding a rotation-only support at the affected node (to prevent a singular stiffness matrix). I'll work on that.

This is the correct solution, if I set a hinge on both elements and then manually delete the rotational dof for node 2 from the system_displacement_vector (effectively adding a rotation-only support there):

And for reference, these are the incorrect results from the above script:

from anastruct.