Specified models in the problems of the deformation of multilayer plates on a rigid foundations
DOI:
https://doi.org/10.32347/2410-2547.2022.109.331-341Keywords:
refined model, multilayered plate, rigid foundation, transverse shear, transverse compressionAbstract
The analysis and estimation of the stress-strain state (SSS) of multilayered plates on a rigid foundation under the action of stationary transverse loading is an urgent task. As its includes the calculations of strength and deformability of various homogeneous and multilayer coatings. This is the calculation of pavement on relatively rigid bridge structures, or on a non-deformable underlying layer, protective multilayer coatings of flat elements of structures of greater rigidity than roofing, parts and more. Combining materials with isotropic and transversely isotropic physical characteristics into a multilayer package allows you to create multifunctional structures. The SSS of such structures, due to their structural heterogeneity and relatively low transverse stiffness of the individual layers, is significantly associated with the influence of transverse shear deformations and transverse compression deformations. Therefore, the problem of refined modeling of SSS plates, which would take into account these types of deformations, is urgent. Based on the decomposition of the SSS plate into flexural and unflexuralcomponents, it is proposed to optimize the design scheme of deformation of a rectangular multilayer plate on a rigid foundation. The essence of optimization is to consider such a calculation scheme of the plate, in which the SSS of the plate would be fully described by only one component, namely the unflexural component of SSS. To do this, instead of the actual design of the multilayer plate, which is deformed without separation from the foundation, it is proposed to consider the design scheme of the plate, which is formed by symmetrical completion relative to the contact surface of the plate with the foundation. In this case, the plate will be bilaterally symmetrically loaded relative to the middle surface of the plate, and the thickness of the plate will double. SSS plate will be unflexural, which greatly simplifies its modeling. For unflexural SSS, a two-dimensional, high-degree iterative approximation, but three-dimensional models of deformation of multilayer rectangular plate on a rigid foundation with isotropic and transverse-isotropic layers are constructed in an elastic formulation.That models takes full account deformationof transverseshearand transverse compression at transverse loading of a plate. By solving the test problems of deformation of isotropic and transversely isotropic plates on a rigid foundation with sliding and rigid contact with the foundation, and comparing the solutions with the exact three-dimensional solutions of these problems obtained by known methods, the accuracy of the proposed refined models is estimated.The limits of admissible parameters of elastic characteristics of transversely isotropic plates for application of the offered models are established.
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