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

Matrix or VectorGeometryShape Functions Integration Points
Stiffness, Mass, and Stress Stiffness Matrices; and Thermal Load VectorQuad 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 face2
Load TypeDistribution
Element TemperatureSame as shape functions across element, harmonic around circumference
Nodal TemperatureSame as element temperature distribution
PressureLinear 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.

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