Spline finite elements for beam and plate

Abstract

The choice of B₃-spline functions as displacement functions for beams and plates has many advantages. However, it suffers from the fact that some spline parameters are located outside the element thus making the assembly of elements and the introduction of boundary conditions difficult. Beam and plate finite elements formed by B₃-splines are developed in general finite element context. By means of boundary transformation, the spline functions are expressed in terms of physical coordinates at the boundary resulting in the required shape functions. The stiffness matrix, mass matrix and load vector of an element can similarly be related to the physical coordinates. The results converge to the exact solutions in a faster rate than the conventional finite elements using the same number of coordinates. A number of examples are given for demonstration.