The approximate closed-form solution to the problem on a circular multilayer (sandwich) constant-thickness plate bending on an elastic foundation with a complicated structure is obtained. The plate is bent under the axisymmetric distributed load, and the foundation reaction. The elastic foundation is a uniformly irregular in thickness layer (coating) based on a homogeneous half-space (substrate). Young’s modulus value at the interface of the coating and the substrate has a significant leap. Two different cases of the boundary conditions are considered for the plate: fixed and free edge conditions. The constructed approximate analytical solution to the problem is effective for a wide range of both geometric (the inhomogeneous layer thickness and the plate radius) and physical parameters (plate flexibility, and elastic properties of the coating and the substrate). The contact problem is reduced to the system of the integro-differential equation solution through the integral transformation method. The obtained formulas can be used for calculating the contact interaction characteristics between a multilayer plate and a foundation with a complex structure in various cases of the boundary conditions, and various loads applied to the plate.
inhomogeneous materials, sandwich plate, functionally-graded coating, axisymmetric problem, analytical methods, approximate analytical solution.
УДК 539.3
Осесимметричный изгиб круглой многослойной пластины на упругом основании сложной структуры[1]
С. М. Айзикович, С. С. Волков, А. В. Мелконян
Получено в аналитическом виде приближенное решение задачи об изгибе круглой многослойной пластины постоянной толщины, лежащей на упругом основании сложной структуры. Пластина изгибается под действием осесимметричной распределенной нагрузки и реакции со стороны основания. Упругое основание представляет собой непрерывно-неоднородный по толщине слой (покрытие), лежащий на однородном полупространстве (подложке). Модуль Юнга в зоне сопряжения покрытия и подложки имеет существенный скачок.Для пластины рассмотрены два случая граничных условий: условия закрепленного и свободного края. Построенное приближенное аналитическое решение задачи эффективно в широком диапазоне как геометрических параметров (толщина неоднородного слоя и радиус пластины), так и физических параметров (гибкость пластины и упругие свойства покрытия и подложки). Методом интегральных преобразований контактная задача сводится к решению системы интегро-дифференциальных уравнений. Полученные формулы могут быть использованы для расчета характеристик контактного взаимодействия многослойной пластины с основанием сложной структуры в зависимости от граничных условий ихарактера нагрузки на пластину.
[1] Результаты работы получены при выполнении проекта, поддержанного грантом РФФИ № 13-08-90916-мол_ин_нр
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