Keywords: three dimensional analysis, spline finite strip, laminated composites, state space approach, plate modelling, orthotropic plates.

In this paper, a new three-dimensional spline finite strip method (spline FSM) is introduced. This is done by combining the classical spline finite strip method [1] and the state space approach. According to the traditional spline FSM, a laminated plate is divided into strips. Within each strip, the spline FSM calls for the use of simple polynomials and a continuously differentiable spline function, respectively, in the transverse and in-plane directions. In the through-thickness direction, the state space method is used to compute the distribution of displacements and stresses. The combination of the in-plane spline FSM and the out-of-plane state space formulations results in a global state space equation that is solved numerically by the precise time step integration method [2,3]. Apart from obtaining a three-dimensional solution, the new method has a unique feature that the final algebra equation system is independent of the number of material layers of a laminate.

The main aim of this work is to establish the new solution procedure and validate the method. To this end, the work reported in the paper focus on laminated plates with arbitrary boundary conditions. Thus, the spline FSM is more flexible than the FSM in imposing boundary conditions. Future development is expected to extend the solution to more practical applications.

From the numerical validation included, it can be seen clearly that the newly developed method can provide accurate three dimensional solutions for laminated composites, particularly, with continuous transverse stress distributions across material interfaces. This is normally difficult to obtain if a traditional three dimensional finite element is used, where only continuity of displacements across material boundaries are guaranteed. Apart from the above new feature, the new three-dimensional formulation always ends up with a global matrix whose dimension depends only on the number of strips and knots that a plate has been divided into, and is completely independent of the number of material layers of the plate.

1

Cheung M.S., Li W. and Chidiac S.E., Finite strip analysis of bridges. London, New York, E & FN Spon, 1996.

2

Zhong W.X., Williams F.W., "A precise time step integration method", Proc. Instn. Mech. Engrs., 208, 427-430, 1994. doi:10.1243/PIME_PROC_1994_208_148_02

3

Zhong W.X., "On precise integration method", Journal of Computational and Applied Mathematics, 163, 59-78, 2004. doi:10.1016/j.cam.2003.08.053

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