This document discusses axisymmetric elements for finite element analysis. It covers the conditions required for a problem to be axisymmetric, including symmetry about the axis of revolution. It also discusses the derivation of shape functions for axisymmetric elements, such as the three node axisymmetric triangular element, and covers strain-displacement matrices, stress-strain relationships, and assembling the element stiffness matrix for axisymmetric elements.

2. SHAPE FUNCTION DERIVATION FOR
EIGHT NODED RECTANGULAR ELEMENT

4. SHAPE FUNCTION DERIVATION FOR THE
SIX NODED TRIANGULAR ELEMENT

6. UNIT – IV
TWO DIMENSIONAL VECTOR VARIABLE
PROBLEMS
Axisymmetric Elements
In previous chapters, we have been concerned with one
dimensional elements and two dimensional elements. In this
chapter, we consider a special two dimensional element
called the axisymmetric element.

7. The required conditions for a problem to
be axisymmetric are as follows
 The problem domain must be symmetric about the axis of
revolution, which is conventionally taken as the z axis.
 All boundary conditions must be symmetric about the axis of
revolution.
 All loading conditions must be symmetric about the axis of
revolution.

8. Three node axisymmetric triangular
element

9. Axis symmetric formulation

13. Derivation of shape function for
axisymmetric element

15. Strain displacement matrix for
axisymmetric triangular element

16. Stress-strain relationship matrix for
axisymmetric triangular element.

17. Assemblage of element stiffness matrix

18. STRESSES

19. STRAINS