13.83. PLANE83 - Axisymmetric-Harmonic 8-Node Structural Solid

Matrix or Vector	Geometry	Shape Functions	Integration Points
Stiffness, Mass, and Stress Stiffness Matrices; and Thermal Load Vector	Quad	Equation 11–168, Equation 11–169, and Equation 11–170	2 x 2
	Triangle	Equation 11–157, Equation 11–158, and Equation 11–159	3
Pressure Load Vector	Same as stiffness matrix, specialized to the face		2

Load Type	Distribution
Element Temperature	Same as shape functions across element, harmonic around circumference
Nodal Temperature	Same as element temperature distribution
Pressure	Linear along each face, harmonic around circumference

Reference: Zienkiewicz([39])

13.83.1. Other Applicable Sections

Structures describes the derivation of structural element matrices and load vectors as well as stress evaluations. PLANE25 - Axisymmetric-Harmonic 4-Node Structural Solid has a discussion of temperature applicable to this element.

13.83.2. Assumptions and Restrictions

A dropped midside node implies that the edge is and remains straight.

The material properties are assumed to be constant around the entire circumference, regardless of temperature-dependent material properties or loading. For (input as MODE on MODE command) > 0, extreme values for combined stresses are obtained by computing these stresses at every 10/ degrees and selecting the extreme values.