Use of a Cubic Spline Function in Finite Elements
A variation of the cubic spline function is used in the development of a finite element for use in thick composite plate analysis. The imposition of a cubic distribution through the thickness of the element insures that compatibility of the displacements and their first and second derivatives, and thus shear strains, are maintained from lamina to lamina. The cubic distribution is seen as a higher order approximation than has been previously employed, but because of the nature of the spline, the theory is less cumbersome and more easily implemented than parabolic theory. In addition, there is no introduction of additional degrees of freedom with the cubic theory. A family of 2-D isoparametric elements is employed in conjunction with the theory to solve a class of 3-D thick plate problems. Results are presented showing comparisons which are in good agreement with previously published work.
Abstract (c) Elsevier.
Mathematical and Computer Modelling
Hinrichsen, R. L., & Palazotto, A. N. (1988). Use of a cubic spline function in finite elements. Mathematical and Computer Modelling, 10(1), 37–47. https://doi.org/10.1016/0895-7177(88)90120-3