The Spline Finite Element Method for the Analysis of the Dynamic Response of Composite Material Plate

Abstract

Based on Kirchhoff’s classical theory and adoptation the spline finite element method, three independent displacements are interpolated into the anti-symmetric angle-ply laminated plate by the spline base of the cubic spline B function, and the stiffness array and the quality array of the composite material laminated plate are derived. By using Rayleigh-Reeds method, the damping array is established; kinetic equation is derived from Lagrange equation; the response equation is expressed; the inherent frequency of the anti-symmetric angle-ply plate is found by calculation subject to the different proportions of the length to the width, the different number of the layers of the plate and different angles; and the dynamic response problems about the anti-symmetric angle-ply laminated plate are analyzed and solved. Dynamic response problems, such as the displacement, velocity and acceleration, are solved with spline collocation method, through choosing the sample strip functions as mode shape function for various boundary conditions in several numerical examples and the results are compared with Newmark’s method. And better result can be yielded. The example calculations prove the validity of the calculating ways introduced by this paper.