| Abstract: | A method is presented for the polynomial approximation of shape function gradients based solely on the geometry of finite 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 finite elements. The method is applicable to a broad class of problems such as connecting dissimilar meshes, mesh adaptivity and transitioning, and the construction of finite 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, higher‐order 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. Copyright © 2001 John Wiley & Sons, Ltd. |
