New Spline Finite Element for Plate Bending

Abstract

This paper presents a spline finite element for bending analysis of thin‐plate structures. A new set of B‐spline shape functions is developed for the interpolation of displacements. The element has nine nodes, in the shape of an arbitrary quadrilateral with biquadratic Lagrangian shape functions for geometric interpolation. The classical Kirchhoffs plate theory is used, and the element is formulated through standard displacement approach. Although in recent years, the use of Reissner‐Mindlin plate theory is more popular among researchers, it is believed that for thin‐plate problems, elements based on Kirchhoff's plate theory is more efficient and reliable. The comparison of numerical results of present element with some highly successful Mindlin‐plate elements have favored the argument. The accuracy and validity of the element have also been investigated through the analysis of a representative set of test problems. It is shown that the use of B‐spline shape functions in general two‐dimensional finite element analysis is promising, and the potentialities of