On a method of solving problems of bending of rods and plates of piecewise-constant stiffness
type: Item
instance of: scholarly article
title: On a method of solving problems of bending of rods and plates of piecewise-constant stiffness
zbMATH Open document ID: 0624.73060
DOI: 10.1016/0021-8928(86)90011-0
author: V. I. Travush
published in: Journal of Applied Mathematics and Mechanics
publication date: 1986-01-01T00:00:00Z
review text: By using an effective procedure expansions were constructed by \textit{Ya. Uflyand} [On certain new integral transformations and their applications to mathematical physics (1976)] of an arbitrary function in the eigenfunction integral of a boundary value problem for second-order differential equations given in an interval with different sections of stepwise-changing physical characteristics. This procedure is applied to construct the expansion of an arbitrary function in an eigenfunction series for fourth-order equations given in a finite interval with an arbitrary quantity of stepwise-varying characteristics. The finite integral transforms obtained in such a manner can be utilized in solving different bending problems for rods or plates with piecewise-varying stiffness, which enables us to formalize the procedure for solving specific problems. The need to solve differential equations given in a composite interval also arises in a study of the state of stress of layered elastic media. A general approach to the solution of problems of mechanics for layered media is proposed by \textit{G. Ya. Popov} [Izv. Akad. Nauk Arm. SSR, Mekh. 31, No.2, 34-47 (1978; Zbl 0435.73019)], and is based on extending the method of initial parameters and results in an effective calculational procedure.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 35P10
Mathematics Subject Classification ID: 35A22
zbMATH DE Number: 4014171
zbMATH Keywords: Dirichlet conditions
zbMATH Keywords: Laplace transform
zbMATH Keywords: arbitrary function
zbMATH Keywords: eigenfunction series
zbMATH Keywords: fourth-order equations
zbMATH Keywords: finite interval
zbMATH Keywords: stepwise- varying characteristics
zbMATH Keywords: finite integral transforms
zbMATH Keywords: bending problems
zbMATH Keywords: rods
zbMATH Keywords: plates
zbMATH Keywords: piecewise-varying stiffness
MaRDI profile type: Publication
full work available at URL: 0021-8928(86)90011-0
OpenAlex ID: W2071605901
cites work: Q4281155
cites work: Q3265799
cites work: Q3875434
description: scientific article; zbMATH DE number 4014171