Implementation relies on elements located exclusively in x,y plane. The coordinate x corresponds to radius, y is the axis of rotation. Approximation of displacement functions u,v is carried out on a particular finite element. Nonzero strains read
Implementation of triangular threenode finite element for axisymmetric continuum. Each node has 2 degrees of freedom. Node numbering and edge position is the same as in Fig. 7. The element features are summarized in Table 30.
Keyword  Axisymm3d 
Description  Triangular axisymmetric linear element 
Specific parameters  [NIP #(in)] [NIPfish #(in)] 
Parameters  NIP: allows to set the number of integration points (possible completions are 1 (default), 4 and 7 point integration rule). 
Unknowns  Two dofs (udisplacement, vdisplacement) are required in each node. 
Approximation  Linear approximation of displacement and geometry. 
Integration  The integration can be altered using NIP paramter (default is 1 point integration). 
Features   
CS properties   
Loads  Boundary and body loads are supported. 
Nlgeo  0. 
Status   
Implementation of quadratic isoparametric eightnode quadrilateral  finite element for axisymmetric 3d continuum. Each node has 2 degrees of freedom. The element features are summarized in Table 31.
Keyword  Q4axisymm 
Description  Quadratic isoparametric eightnode quadrilateral for axisymmetric analysis 
Specific parameters  [NIP #(in)] [NIPfish #(in)] 
Parameters  NIP: allows to set the number of integration points for integration of terms corresponding to ε_{x} and ε_{y} strains (possible completions are 1, 4 (default), 9, and 16). 
NIPfish: allows to set the number of integration points for integration of remain terms (corresponding to ε_{θ} and γ_{rz}) (Supported values include 1 (default), 4, 9, and 16 integration point formula). 

Unknowns  Two dofs (udisplacement, vdisplacement) are required in each node. 
Approximation  Quadratic approximation of displacement and geometry. 
Integration  The integration of terms corresponding to ε_{x} and ε_{y} strains can be altered using NIP parameter (default is 4 point formula). The remaining terms (creesponding to ε_{θ} and γ_{rz}) are integrated by default using 1 point formula (see NIPfish parameter). 
Features   
CS properties   
Loads  No boundary and body loads are supported. 
Nlgeo  0. 
Status   
Implementation of isoparametric fournode quadrilateral axisymmetric finite element with linear interpolations of displacements u,v. Node numbering and edge position is the same as in Fig. 5. The element features are summarized in Table 32.
Keyword  L4axisymm 
Description  Isoparametric fournode quadrilateral element for axisymmetric analysis 
Specific parameters  [NIP #(in)] 
Parameters  NIP: allows to set the number of integration points for integration of terms corresponding to ε_{x} and ε_{y} strains (possible completions are 1, 4 (default), 9, and 16). 
Unknowns  Two dofs (udisplacement, vdisplacement) are required in each node. 
Approximation  Linear approximation of displacement and geometry. 
Integration  The integration of ε_{x} and ε_{y} strains can be altered using NIP parameter (possible completions are 1, 4 (default), 9 or 16 point integration rule). The remaining strain components (ε_{θ} and γ_{rz}) are integrated using one point integration formula. 
Features   
CS properties   
Loads  Boundary and body loads supported. 
Nlgeo  0. 
Status   