An inhomogeneous problem for an elastic half-strip: An exact solution. (November 2021)

• Record Type: Journal Article
• Authors: Kovalenko, Mikhail D; Menshova, Irina V; Kerzhaev, Alexander P; Yu, Guangming
• Is Part Of: Mathematics and mechanics of solids. Volume 26:Number 11(2021)
• Page Start: 1565
• Page End: 1580
• Publication Date: 2021-11
• Subjects: Half-strip -- inhomogeneous boundary value problem -- Papkovich–Fadle eigenfunctions -- Papkovich orthogonality relation -- exact solution; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/1081286521996418
• Languages: English
• ISSNs: 1081-2865

Abstract

We construct exact solutions of two inhomogeneous boundary value problems in the theory of elasticity for a half-strip with free long sides in the form of series in Papkovich–Fadle eigenfunctions: (a) the half-strip end is free and (b) the half-strip end is firmly clamped. Initially, we construct a solution of the inhomogeneous problem for an infinite strip. Subsequently, the corresponding solutions for a half-strip are added to this solution, whereby the boundary conditions at the end are satisfied. The Papkovich orthogonality relation is used to solve the inhomogeneous problem in a strip.