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Photograph supplied by Michael Nemeth, NASA Langley Research Center, Hampton, Virginia
From the report:
Michael P. Nemeth, "A treatise on equivalent-plate stiffnesses for stiffeneed laminated composite plates and plate-like lattices", NASA/TP-2011-21682 , January 2011
SUMMARY: A survey of studies conducted since 1914 on the use of equivalent-plate stiffnesses in modeling the overall, stiffness-critical response of stiffened plates and shells is presented. Two detailed, comprehensive derivations of first-approximation equivalent-plate stiffnesses are also presented that are based on the Reissner-Mindlin-type, first-order transverse-shear deformation theory for anisotropic plates. First, a derivation based purely on static and kinematic equivalence between a stiffened plate and its homogenized equivalent is presented, followed by a derivation based on equivalence of the strain-energy density. In both derivations, the stiffener members are modelled as beams that are shear deformable within and transverse to the plane of the plate, consistent with the classical continuum mechanics representation of solids. Additionally, each stiffener is presumed to be constructed, at most, in a nonhomogeneous manner from orthotropic materials with one axis aligned with the stiffener axis and the other two axes aligned with the cross-sectional axes. This presumption allows the computation of equivalent-plate stiffnesses for stiffened panels such as those in which the stiffener caps are reinforced with high-strength, pultruded rods. Consistent with a first-approximation analysis, inplane bending of the stiffeners and total compatibility between the plate skin and the stiffeners are neglected.
Equivalent-plate stiffness expressions, and a corresponding symbolic manipulation computer program, are also presented for several different stiffener configurations. These expressions are very general and exhibit the full range of anisotropies permitted by the Reissner-Mindlin-type, first-order transverse-shear deformation theory for anisotropic plates. The expressions presented in the present study were also compared with available, previously published results. For the most part, the previously published results are for special cases of the general expressions presented herein and are almost in complete agreement. Analysis is also presented that extends the use of the equivalent-plate stiffness expressions to sandwich plates with nonidentical, anisotropic face plates, and expressions for equivalent-plate thicknesses are presented.
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