Justification of the Bending-Gradient Theory Through Asymptotic Expansions
In a recent work, a new plate theory for thick plates was suggested where the static unknowns are those of the Kirchhoff-Love theory, to which six components are added representing the gradient of the bending moment . This theory, called the Bending-Gradient theory, is the extension to multilayered plates of the Reissner-Mindlin theory which appears as a special case when the plate is homogeneous. This theory was derived following the ideas from Reissner  without assuming a homogeneous plate. However, it is also possible to give a justification through asymptotic expansions. In the present paper, the latter are applied one order higher than the leading order to a laminated plate following monoclinic symmetry. Using variational arguments, it is possible to derive the Bending-Gradient theory. This could explain the convergence when the thickness is small of the Bending-Gradient theory to the exact solution illustrated in . However, the question of the edge-effects and boundary conditions remains open.
KeywordsAsymptotic Expansion Transverse Shear Laminate Plate Plate Model Transverse Shear Stress
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