INVESTIGATION OF A THREE-LAYERED HINGE-SUPPORTED PLATE SUPPORTED BY ONE LONGITUDINAL RIB OF RIGIDITY
DOI:
https://doi.org/10.32851/tnv-tech.2021.3.16Keywords:
three-layer plate, lightweight aggregate, rigidity, stability, rigidity of the plate, rigidity of the ribs, shear parameter, rigidity parameter, stability equation of a three-layer plate, boundary conditionsAbstract
The article considers the problem of stability of a three-layer plate of symmetrical structure in thickness with a light transversely isotropic filler, supported by one longitudinal rigidity rib taking into account the action of longitudinal forces in the middle planes of the outer layers and in the edge. The urgency of the question of the stability of the reinforced three-layer plates, which are insufficiently studied, is substantiated. The lack of practical and theoretical bases for parametric studies of the stability of these plates is noted. It is noted that the equations of motion of a three-layer plate of symmetrical structure supported by stiffening ribs in two mutually perpendicular directions taking into account the action of longitudinal forces in the middle planes of outer layers and ribs, boundary conditions and conditions along ribs are obtained using the Ostrogradsky-Hamilton variational principle. In deriving the equations, it was assumed that the filler is light, and the edges have the same stiffness in one direction and are located at equal distances. The Kirchhoff-Lev hypotheses were accepted for the outer bearing layers, and the linear law of change of tangential displacements in thickness was accepted for the aggregate and edges, and the bending of the edges in the vertical plane was taken into account. Differential equations of stability of the section of the plate, which is closed between the edge and the edges of the plate, without taking into account the bending stiffness of the outer layers. By means of the boundary transition, the conditions on the sides of the plate and the rib line are obtained in the presence of diaphragms on the bearing edges without taking into account the torsional stiffness of the ribs. The equation of stability of a three-layer plate of symmetrical structure with a light transversely isotropic filler, supported by one longitudinal stiffening rib, is obtained. Equations are obtained to determine the stiffness parameter and the critical force parameter. The forms of loss of stability of the specified plate are analyzed.
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