13.159. SURF159 - General Axisymmetric Surface with 2 or 3 Nodes

Matrix or Vector	Midside Nodes [1]	Shape Functions	Integration Points[2]
Mass Matrix	With midside nodes	Equation 11–46 through Equation 11–48	3 x N_c
Mass Matrix	Without midside nodes	Equation 11–43 through Equation 11–45	2 x N_c
Stress Stiffness Matrix	With midside nodes	Same as mass matrix.	2 x N_c
Stress Stiffness Matrix	Without midside nodes	Same as mass matrix.	2 x N_c
Pressure Load Vector	With midside nodes	Same as mass matrix.	2 x N_c
	Without midside nodes	Same as mass matrix.	2 x N_c

Midside node setting is controlled by KEYOPT(4).
N_c = the number of node planes in the circumferential direction. The N_c integration points are circumferentially located at:
the nodal planes, and
midway between the nodal planes (that is, at the integration planes)
so that N_c = (2 * N_np), where N_np = number of nodal planes (KEYOPT(2)).
Exception: If KEYOPT(2) = 1, then N_c = 1.

Load Type	Distribution
Pressure	Linear along each face in both directions.

13.159.1. Other Applicable Sections

General Element Formulations gives the general element formulations used by this element.

13.159.2. Assumptions and Restrictions

Although the elements are initially axisymmetric, the loads and deformation can be general in nonaxisymmetric 3-D. The displacements are interpolated in elemental coordinate system by interpolation functions, but the user can define the nodal displacements in any direction.