This section contains shape functions for axisymmetric harmonic solid elements. These elements are available in a number of configurations, including certain combinations of the following features:
triangular or quadrilateral.
- if quadrilateral, with or without extra shape functions (ESF).
with or without midside nodes.
The shape functions of this section use the quantities sin
β and cos
β (where
= input as MODE on the MODE command). sin
β and cos
β are interchanged if Is = -1 (where Is = input as ISYM on the MODE command). If
= 0, sin
β = cos
β = 1.0.
These shape functions are for the 3-node axisymmetric triangular solid elements, such as PLANE25 with only 3 nodes input:
 | (11–156) |
 | (11–157) |
 | (11–158) |
 | (11–159) |
These shape functions are for the 6-node axisymmetric triangular solids elements, such as PLANE83 input as a triangle:
 | (11–160) |
 | (11–161) |
 | (11–162) |
 | (11–163) |
These shape functions are for the 4-node axisymmetric harmonic quadrilateral solid elements without extra shape functions, such as PLANE25 with KEYOPT(2) = 1, or PLANE75:
 | (11–164) |
 | (11–165) |
 | (11–166) |
 | (11–167) |
These shape functions are for the 4-node axisymmetric harmonic quadrilateral elements with extra shape functions, such as PLANE25 with KEYOPT(2) = 0.
 | (11–168) |
 | (11–169) |
 | (11–170) |
Unless
(MODE) = 1, u1 or u2 and w1 or w2 motions are suppressed for elements
near the centerline.
