On Limits of Application of Kirchhoff's Hypothesis in the Theory of Viscoelastic Fibrous Composite Plates
This paper contains the discussion on the application of Kirchhoff's hypothesis to viscoelastic fibrous composite plates based on the example of buckling of a plate strip. lt has been assumed, that the plate is made of a fibrous composite, and a simplified two-phase continua! model introduced by HOLNICKI-SZULC  and ŚWITKA [9, 10] is used. To describe the displacements of the phase I (matrix), the VLASOV'S , Hencky-Bolle's and Kirchhoff's kinematic hypotheses were adopted. The matrix material is viscoelastic, while the fibers (phase II) are made of material which satisfies the Hooke's law. Buckling of a plate strip was analyzed within the range of linear theory of stability, by assuming the equilibrium equations in a classical form, that is, in accordance with Hencky-Bolle's assumptions. The results obtained include closed-form analytical solutions for the immediate and sustained critical loads applied to a. simply supported plate which was reinforced by fibrous meshes symmetrically distributed across the plate cross-section. A parametric analysis was performed on the obtained solutions, with respect to the plate strip geometry shape and with respect to the properties of the strip material. The analysis made enabled the author to draw some conclusions pointing to the limits of applicability of the Kirchhoff's hypothesis.
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