Decay rates of Saint-Venant type for a functionally graded heat-conducting hollowed cylinder. (May 2019)

• Record Type: Journal Article
• Authors: Leseduarte, Mari Carme; Quintanilla, Ramon
• Is Part Of: Mathematics and mechanics of solids. Volume 24:Number 5(2019)
• Page Start: 1368
• Page End: 1386
• Publication Date: 2019-05
• Subjects: Functionally graded materials -- heat conduction -- spatial decay estimates -- Saint-Venant's principle -- inhomogeneity; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/1081286518796474
• Languages: English
• ISSNs: 1081-2865

Abstract

In this paper we consider the case of a functionally graded heat-conducting hollowed cylinder. Our purpose is to investigate the consequences of the material inhomogeneity on the decay of Saint-Venant end effects in the case of linear isotropic rigid solids. The mathematical issues involve the implications of spatial inhomogeneity on the decay rates of solutions to Dirichlet boundary-value problems. The rate of decay is characterized in terms of the smallest eigenvalue of a Sturm–Liouville problem. We first consider the case where the inhomogeneity depends on the radius of the cross-section, but later we also consider the case where the inhomogeneity also depends on the axial variable. The last section considers the case where the cross-section is increasing. Some tables and figures illustrate our estimates.