| Summary: | Shape functions have been derived to describe
different forms of elements, notably triangles and rectangles
in 2-D, and tetrahedrons, cuboids, and triangular
prisms in 3-D. There are generalised solutions for some regular
node configurations, and hierarchical correction algorithms
help with more difficult node distributions. But to
this point there is no single formula or set of formulae that
allows the direct determination of shape functions for any
node configuration without restrictions. This paper shows
how a general set of formulae can be derived which is applicable
to any isoparametric element type with arbitrary
node configuration. This formulation is in such a form that
it is clear and concise. The approach is based on the Lagrange
polynomial considering up to three Cartesian and
four volume coordinates. Additionally, the correction procedure
that is inherent in the formulation to guarantee an
appropriate evaluation of the generalised shape functions
and to fulfil all four isoparametric shape function criteria
is discussed. The proof of validity illustrates the correctness
of the method.
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