Mumbai University > Mechanical Engineering > Sem 6 > Finite Element Analysis

Marks: 5M

Year: may 2016

Subparametric, Isoparametric and Superparametric Elements

Consider quadrilateral element ABCD in x-y axis and equaivalent square element in transformed natural coordinates as shown in fig (a) and (b) . As we have to deal with curved edges as shown in fig (a) we have taken eight nodes. Coordinates of any point P(x,y) are interpolated as

$x = \sum N_i x_i$ and $y = \sum N_i y_i$

Here we can take just four vertices and use linear interpolation or use full eight nodes to take care of curved edges.

Displacements of point P(u,v) are also interpolated from nodal deflections using the same shape functions i.e

$u = \sum \phi_j u_j$ and $v = \sum \phi_j v_j$

Three posibilities arise in such problems.

1. First possibility refers to subparametric elements where i < j. This is useful when geometry is simply polygonal but field variations are not known.
2. Second possibility refers to isoparametric elements where i - j. This is useful when geometry consists of curved edges and there are quadratic variations in displacements.
3. The third possibility refers to superparametric category where i > j. This is useful when geometry has curved features but is in low stress region.