this presentation let us know about the isoparametric elements

1. ISOPARMETRIC FORMULATION
By
G.MURALI MOHAN

2. The various elements so far we have seen are having straight edges. To take care of curved
boundaries refined meshes are to be used when straight edged elements are employed.
Even with refined meshes analysts were not happy with the results since unnecessary stress
concentrations are introduced. Higher order elements also do not overcome the problem of
suitably approximating curved boundaries. The isoparametric concept brought out by Taig
and latter on generalized by B.M. Irons [2] revolutionized the finite elements analysis and it
also helped in properly mapping the curved boundaries. They brought out the concept of
mapping regular triangular and rectangular elements in natural coordinate system, to
arbitrary shapes in global system . In this chapter method of coordinate transformation of
natural coordinates to global coordinate system is presented. The terms isoparametric,
super parametric and subparametrics are defined. The basic theorems on which
isoparametric concept is based are explained and need for satisfying uniqueness theorem of
mapping is presented. Assembling of stiffness matrix is illustrated. For assembling stiffness
matrix integration is to be carried out numerically. The Gaussion integration technique
which is commonly employed is explained briefly. To make the procedure clear few small
numerical problems are illustrated and lastly application to structural engineering problems
is presented.

4. 4-NODED ISOPARAMETRIC ELEMENT