Differential Equations with Variable Coefficients in the Mechanics of Inhomogeneous Bodies

Gorbachev, V.I.

Автор: Gorbachev V.I.
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
Переводные версии: ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ С ПЕРЕМЕННЫМИ КОЭФФИЦИЕНТАМИ В МЕХАНИКЕ НЕОДНОРОДНЫХ ТЕЛ
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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Differential Equations with Variable Coefficients in the Mechanics of Inhomogeneous Bodiesстатья

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