Search results for "warping functions"
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A multilayer anisotropic plate model with warping functions for the study of vibrations reformulated from Woodcock's work
2013
Abstract In this paper, a suitable model for static and dynamic analysis of inhomogeneous anisotropic multilayered plates is described. This model takes into account the variations of the transverse shear strains through the thickness of the plate by means of warping functions. Warping functions are determined by enforcing kinematic and static assumptions at the interfaces. This model leads to: a 10×10 stiffness matrix coupling to each other the membrane strains, the bending and torsion curvatures, and the x and y-derivatives of the transverse shear strains; and a classical 2×2 transverse shear stiffness matrix. This model has been proven to be very efficient, especially when high ratios be…
Transverse shear warping functions for anisotropic multilayered plates
2012
In this work, transverse shear warping functions for an equivalent single layer plate model are formulated from a variational approach. The part of the strain energy which involves the shear phenomenon is expressed in function of the warping functions and their derivatives. The variational calculus leads to a differential system of equations which warping functions must verify. Solving this system requires the choice of values for the (global) shear strains and their derivatives. A particular choice, which is justified for cross-ply laminates, leads to excellent results. For single layer isotropic and orthotropic plates, an analytical expression of the warping functions is given. They invol…