# Axisymmetric shell element allowing asymmetric loading

 The Abaqus/Standard element library includes a family of nonlinear thin shell elements with axisymmetric reference geometry that allow asymmetric loading and deformation (SAXA1N and SAXA2N). This section provides their theoretical formulation. These elements encompass a broad range of practical applications from the bending/ovalization of variable diameter pipes to the bending of circular plates. The theoretical formulation of these elements is similar to the general finite-strain shell element described in Finite-strain shell element formulation. Furthermore, this formulation is the shell counterpart to the continuum axisymmetric bending elements described in Axisymmetric elements allowing nonlinear bending. The following topics are discussed:
 Related Topics In Other Guides Axisymmetric shell elements with nonlinear, asymmetric deformation

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As with the continuum axisymmetric bending formulation, the restriction is made that a plane of symmetry exists in the rz plane at $θ=0$. Hence in-plane bending of the model is permitted, while deformations such as torsion about the axis of symmetry are precluded. The symmetries of the undeformed configuration and of the deformation are exploited through the assumption of particular displacement and rotation interpolations around the circumference of the shell. Specifically, Fourier series expansions are used in the $θ$ or circumferential direction that preserve the plane of symmetry.