Formulation of the element matrices and vectors for elasticity problem > Finite element types

There are eight nodes for this element, four corner nodes and four mid-side nodes (Fig.22). In the natural coordinate system (ξ, η), the eight shape functions are:

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(49)

The displacement field is given by:

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(50)

which are quadratic functions over the element. Strains and stresses over a quadratic quadrilateral element are linear functions that are better representations.

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Fig.22. Quadratic quadrilateral element (Q8).