Development of a new finite element for plate and shell analysis by application of generalized approach to patch test

A triangular flat finite element with three nodes in the corners has been developed for analysis of Kirchhoff plates and shells within the framework of the extended interpretation of the Irons patch test. The condition of the bending displacements continuity in the case of non-constant strains is supposed to be violated not only on the boundaries but inside the area of an element as well. In general the typical approximations of the finite element method are implemented here in the limit of the infinitesimal elements. Thus it is possible to obtain the relatively simple but quite effective finite elements. The numerical results based on the classical tests demonstrate the high accuracy and quick convergence of the solutions obtained with the help of the presented finite element.