## Differential Equations with Variable Coefficients in the Mechanics of Inhomogeneous Bodiesстатья

Информация о цитировании статьи получена из Scopus, Web of Science
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 10 августа 2021 г.
• Автор:
• Журнал: Mechanics of Solids
• Том: 55
• Номер: 3
• Год издания: 2020
• Издательство: Allerton Press Inc.
• Местоположение издательства: United States
• Первая страница: 396
• Последняя страница: 402
• DOI: 10.3103/S0025654420030061
• Аннотация: The paper considers differential equations in partial derivatives of an elliptic type with variables,piecewise-smooth coefficients, depending on the coordinates (initial equations). It is shownthat the solution of the original equation can be represented as an integral equation through the solutionof the accompanying equation with constant coefficients of the same type. This representationincludes a fundamental solution to the original equation. Under the assumption that the accompanyingsolution is smooth, the integral equation implies the representation of the original solution in theform of a series with respect to all possible derivatives of the related solution. The coefficients of theseries are called structural functions, since they are determined by the functional dependence of thecoefficients of the initial equations either on coordinates, or on time, or on coordinates and time.Structural functions are identically equal to zero in the case when the initial coefficients coincide withthe corresponding constant coefficients of the accompanying equation. For structural functions, systemsof recurrence equations are obtained. It is shown that in the case of a plate with non-uniformthickness, the structural functions depend only on the coordinate in the thickness of the plate, andstructural equations become ordinary differential equations that integrate in a general way. A schemefor solving the plate problem is considered.
• Добавил в систему: Горбачев Владимир Иванович

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