Explicit stiffness matric'es of the serendipity rectangular elements for linear plane elastic continuum

Abstract

The analytical integration formulae for the products of shape function local derivatives of parabolic and cubic elements over the square region first obtained. By means of a transformation from global to local coordinates, the analytical integration formulae Of the products of shape function global derivatives over the rectangular region are then established These results are then illustrated with reference to the evaluation of stiffness matrices in terms of explicit expressions for the parabolic and cubic elements of the serendipity family in rectangular shapes under the assumptions of linear plane elasticity.