A multilayer anisotropic plate model with warping functions for the study of vibrations reformulated from Woodcock's work

Abstract

In this paper, a plate model suitable for static and dynamic analysis of inhomogeneous anisotropic multilayered plates is described. This model takes transverse shear variation through the thickness of the plate into account by means of warping functions which are determined by enforcing kinematic and static assumptions at the layers interfaces. This model leads to a 10 x 10 behavior matrix in which membrane strains, bending curvatures, and transverse shear x and y-derivatives are coupled, and to a classical 2 x 2 shear behavior matrix. This model has been proven to be very efficient, especially when high ratios -up to 10E5- between the stiffnesses of layers are present. This work is related to Woodcock's model, so it can be seen as a reformulation of his work. However, it propose several enhancements: the displacement field is made explicit; it is reformulated with commonly used plate notations; laminate equations of motion are fully detailed; the place of this model relatively to other plate models is now easy to see and is discussed; the link between this formulation and the original one is completely written with all necessary proofs; misses and errors have been found in the energy coefficients of the original work, and then have been corrected; it is now easy to improve or to adapt the model for specific applications with the choice of refined or specific warping functions.