C1 conforming quadrilateral finite elements with complete second-order derivatives on vertices and its application to Kirchhoff plates

Abstract

The classical problem of the construction of C 1 conforming single-patch quadrilateral finite elements has been solved in this investigation by using the blending function interpolation method. In order to achieve the C 1 conformity on the interfaces of quadrilateral elements, complete second-order derivatives are used at the element vertices, and the information of geometrical mapping is also considered into the construction of shape functions. It is found that the shape functions and the polynomial spaces of the present elements vary with element shapes. However, the developed quadrilateral elements are at least third order for general quadrilateral shapes and fifth order for rectangular shapes. Therefore, very fast convergence can be achieved. A promising feature of the present elements is that they can be used in cooperation with those high-precision rectangular and triangular elements. Since the present elements are over conforming on element vertices, an approach for handling problems of material discontinuity is also proposed. Numerical examples of Kirchhoff plates are employed to demonstrate the computational performance of the present elements.