An Exact Elasticity Solution for Monoclinic Functionally Graded Beams

• Published in: Arabian journal for science and engineering (2011) Vol. 46; no. 5; pp. 5135 - 5155
• Main Authors: Çömez, İsa, Aribas, Umit N., Kutlu, Akif, Omurtag, Mehmet H.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2021; Springer Nature B.V
• Subjects: Axial stress; Beam theory (structures); Beams (structural); Elasticity; Engineering; Euler-Bernoulli beams; Exact solutions; Functionally gradient materials; Humanities and Social Sciences; Material properties; multidisciplinary; Research Article-Civil Engineering; Science; Shear stress; Stress concentration; Thickness ratio; Functionally graded beam; Elasticity solution; Monoclinic material; Heterogeneous beam; Exact solution
• ISSN: 2193-567X; 1319-8025; 2191-4281
• DOI: 10.1007/s13369-021-05434-9

In this study, an elasticity solution is presented for monoclinic functionally graded beams subject to a transverse pressure distributed sinusoidally. Monoclinic material properties are assumed to vary exponentially throughout the thickness of the beam’s layers. An analytical formulation based on the classical Euler–Bernoulli beam theory is also derived for comparison purposes of simply supported monoclinic functionally graded beams. In benchmark examples, the numerical results of normal stresses, transverse shear stress, as well as axial and vertical displacements are presented. The effect of material grading, fiber angle, and beam length to thickness ratio on the stress and displacement distributions is comprehensively investigated. The proposed elasticity-based analytical solution and presented numerical results can be used for verification or comparison purposes of numerical procedures.