Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transverse shear warping functions for anisotropic multilayered plates   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 involve hyperbolic trigonometric functions. They differ from the z - 4/3z3
Reddy's formula which has been found to be a limit of present warping functions
for isotropic and moderately thick plates. When the h/L and/or the G13/E1
ratios significantly differ from those of isotropic and moderately thick
plates, a difference between present warping functions and Reddy's formula can
be observed, even for the isotropic single layer plate. Finite element
simulations agree perfectly with the present warping functions in these cases.
For multilayer cross-ply configurations, the warping functions are determined
using a semi-analytical procedure. They have been compared to results of 3D
finite element simulations. They are in excellent agreement. For angle-ply
laminates, the above process gives warping functions that seem to have relevant
shapes, even if the choice for global shear values cannot be justified in this
case. No finite element comparison has been presented at this time because it
is difficult to propose boundary conditions and prescribed load that permit to
isolate the shear phenomenon.

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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn