Expansion of the one-dimensional and two-dimensional elements

Typical one-dimensional elements are beams, typical two-dimensional elements are shells, plane stress elements, plane strain elements and axisymmetric elements. Their dimension in thickness direction (for two-dimensional elements) or orthogonal to their axis (for beam elements) is much smaller than in the other directions. In CalculiX these elements are expanded to volume elements. Only quadratic shape functions are accepted.

The expansion of the elements requires several steps:

• cataloguing the elements belonging to one and the same node
• calculating the normals in the nodes
• generating the expanded volume elements
• taking care of the connection of 1D/2D elements with genuine 3D elements
• applying the SPC's to the expanded structure
• applying the MPC's to the expanded structure
• applying the temperatures and temperature gradients
• applying nodal forces to the expanded structure