Polynomial approximation of shape function gradients from element geometries

A method is presented for the polynomial approximation of shape function gradients based solely on the geometry of 7nite element boundaries. The method is founded on a least squares approach which leads to an integration scheme satisfying a necessary condition for convergence. In its simplest form the method reduces to the well-known uniform strain approach for 7nite elements. The method is applicable to a broad class of problems such as connecting dissimilar meshes, mesh adaptivity and transitioning, and the construction of 7nite elements with variable topologies. Finite elements based on the polynomial approximations are shown to pass patch tests of various orders. In contrast to standard elements, higherorder patch tests are passed without the need for nodes internal to element boundaries. Less sensitivity to volumetric locking under plane strain conditions is demonstrated through comparisons with a standard element formulation