Some Two-dimensional Non-classical Models of Anisotropic Plates

Alexander K. Belyaev, Nikita F. Morozov, Peter E. Tovstik, Tatyana P. Tovstik

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийглава/разделнаучнаярецензирование

Аннотация

Thin elastic plates made of an anisotropic material (with 21 elastic moduli) and heterogeneous in the thickness direction (in partial, multilayered) are considered. A short overview of various 2D models describing deformations and vibrations of a plate is given. The classical Kirchhoff–Love and the Timoshenko–Reissner models are discussed and compared in cases of isotropic and transversely isotropic materials. A correspondence of boundary conditions of these models is established. A multilayered plate with alternating soft and hard layers is considered. By using an asymptotic expansion of the solution in a series in small thickness parameter, the 2D equations of second-order accuracy are delivered. From these equations the correct choice of parameters of the single-layered Timoshenko–Reissner model is derived, which is equivalent to a given multilayered plate. In the case of general anisotropy, a model of second-order accuracy is presented as well, and the main properties of the harmonic solutions for static problems and for free vibrations of a plate are briefly described.
Язык оригиналаанглийский
Название основной публикацииAnalysis of Plates, Shells and Beams
Подзаголовок основной публикацииA State of the Art Report
РедакторыHolm Altenbach, Natalia Chinchaladze, Reinhold Kienzler, Wolfgang H. Müller
ИздательSpringer Nature
Глава5
Страницы75-94
Том134
ISBN (электронное издание)9783030474911
ISBN (печатное издание)9783030474904
СостояниеОпубликовано - 2020

Серия публикаций

НазваниеAdvanced Structured Materials
Том134

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