Mathematical model for elastic beams with longitudinally variable depth

Article type: Research Article

Authors: Alvarez‐Vázquez, L.J.^; | Samartín, A. | Viaño, J.M.

Affiliations: Departamento de Matemática Aplicada, ETSI Telecomunicaciones, Universidad de Vigo, 36200 Vigo, Spain | Departamento de Mecánica Estructural, ETSI Caminos, Canales y Puertos, Universidad Politécnica de Madrid, 28040 Madrid, Spain | Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15706 Santiago de Compostela, Spain

Note: [] Corresponding author. E‐mail: lino@dma.uvigo.es

Abstract: In this work we introduce a new mathematical model for elastic beams with a cross‐section of constant width and longitudinally variable depth, obtained from the classical three‐dimensional linear elasticity problem by using an asymptotic expansion method. We characterize the first‐ and second‐order displacements and the first‐order stress field, giving results related to existence, uniqueness and convergence for the limit model solution. Finally, we present the computations for a classical example.

Keywords: beam, longitudinally variable depth, asymptotic analysis, linear elasticity, limit model

Journal: Asymptotic Analysis, vol. 27, no. 1, pp. 75-93, 2001