User Element: 3-node shell element (US3)

Figure 80: Definition of the US3 element

The US3 shell element has six degrees of freedom per node - three translations and three rotations (Figure 80). The discrete shear gap approach together with the cell smoothing technique is implemented for the treatment of shear locking. The membrane behavior is resolved by means of the assumed natural deviatoric strains formulation with certain adjustments implemented to accommodate for shell behavior. A detailed description of the formulation is given in [81]. In that reference the accuracy and convergence rate were tested on a chosen set of well-known challenging benchmark problems, and the results were compared with those yielded by the Abaqus $\copyright$ S3 element. The element shows a very good performance in the static linear elastic analysis compared to the Abaqus $\copyright$ S3 element.

The shell formulation is implemented as element “US3” in CalculiX and can be used for static and dynamic linear elastic (small deformations) calculations under the consideration of isotropic material properties. Simpson's rule (three points) is provided to calculate the cross-sectional behavior of the shell. For a homogeneous section this integration scheme is exact for linear problems and should be sufficient for routine thermal-stress calculations. Following loadings are implemented:

• Concentrated forces and moments.
• Nodal temperatures with temperature gradients through shell thickness.
• Element face pressure loads.