2D Asymptotic Analysis of a Thin Elastic Beam with Density-Dependent Generalized Young’s Modulus

Erbaş, Barış; Kaplunov, Julius; Rajagopal, Kumbakonam R.

Abstract

The elastic equilibrium of a thin elastic beam is studied using asymptotic analysis starting from a 2D formulation within the context of plane elasticity. The aim of the paper is to elucidate the influence of density and hence small volume strain of Young’s modulus on the response of the beam. The adopted scaling at leading order supports the classical 1D Euler-Bernoulli beam approximation. The effect of strain-dependent Young’s modulus arises at the next order resulting in weak coupling between bending and extension deformations due to the asymmetry of the problem. The refined bending equation of interest is reduced to the form involving an explicit asymptotic correction to the prescribed transverse loading, similar to the previous considerations on the subject.

Citation

Erbaş, B., Kaplunov, J., & Rajagopal, K. R. (2023). 2D Asymptotic Analysis of a Thin Elastic Beam with Density-Dependent Generalized Young’s Modulus. In Mechanics of Heterogeneous Materials (501-513). Springer. https://doi.org/10.1007/978-3-031-28744-2_22

• Online Publication Date: Jul 13, 2023
• Publication Date: Jul 13, 2023
• Deposit Date: Jan 30, 2024
• Publisher: Springer
• Pages: 501-513
• Book Title: Mechanics of Heterogeneous Materials
• Chapter Number: 22
• ISBN: 9783031287435
• DOI: https://doi.org/10.1007/978-3-031-28744-2_22
• Publisher URL: https://link.springer.com/chapter/10.1007/978-3-031-28744-2_22
• Additional Information: First Online: 13 July 2023