I have a FEM program for shell elements implemented through the direct stiffness method. Using this program corner displacements of shell elements due to external loading are obtained through the inversion of a global stiffness matrix. Once the displacements are known, computing forces and moments acting on the corner of each shell element is quite straightforward.
The shell element employed in this program has 4 corner nodes, and therefore it has 24 degrees of freedom in total; 6 degrees of freedom for each node (at each corner):
- 2 dofs for membrane/axial
- 1 dof for shear
- 3 dofs for bending
The issue here, I would like to compute the angles of the principal stress for each plate element. However most literature on the topic is referring to a convention where stresses are computed using forces and moments observed on the sides of the element (see picture). My question is, how to compute (or rather, estimate) forces and moments acting on the sides of a rectangular shell element when corner forces and moments are known? Can it be done through simple averaging? (I have a hunch that averaging is not the way to go)