Underlying math and weak form of Axisymmetric elastic elements

[gxu97]

Hi, I'm using CAX8 (Axisymmetric elastic, full integration)in Abaqus for a personal project of a revolved shaft with multiple notches loaded axially. How is the mesh expanded from 2D, to account for the difference in radius? What is the weak form of this type of element? I looked through my old textbooks and it seems that Axisymmetric elements are just touched on briefly.

 

[FEA way]

There's a whole chapter about those elements in Chandrupatla's book "Introduction to Finite Elements in Engineering". Logan's book ("A First Course in the Finite Element Method") can also be useful. Then there are also books written by Hutton, Khennane and Zienkiewicz, among others.

You could check the "Axisymmetric elements" chapter of the Abaqus Theory Guide too but it's a high-level description and I would recommend the aforementioned books first.