Static Analysis of Thick Laminated Beams: Two-Dimensional Elasticity Solutions via Differential Quadrature
This paper intends to present two-dimensional elasticity solutions for static problem of thick laminated composite beams using a hybrid method of state-space-based differential quadrature. The technique of differential quadrature is employed to reduce the partial differential state equations into the ordinary differential ones at all arbitrary sampling points for each individual laminate. General solution to the assembled state equation is then obtained according to the matrix theory. Taking account of the continuity conditions at the interfaces of all the adjacent lamina, a relationship between state variables at the top and bottom surfaces of the beam is established through a global transfer matrix. After incorporating the boundary conditions at these two surfaces, an eigenvalue equation for static problem is then derived. Numerical examples are presented, through which the accuracy and convergence characteristics of the present method are investigated. It is shown that the present method is of excellent efficiency for laminated composite thick beams subjected to arbitrary end supporting conditions.
Z.Y. Zhong, H. Saka, T.H. Kim, E.A. Holm, Y.F. Han and X.S. Xie
C. Lü et al., "Static Analysis of Thick Laminated Beams: Two-Dimensional Elasticity Solutions via Differential Quadrature", Materials Science Forum, Vols. 475-479, pp. 1067-1072, 2005