TY - JOUR

T1 - Gradient elasticity solutions of 2D nano-beams

AU - Özer, Teoman

N1 - Publisher Copyright:
© 2023

PY - 2023/9

Y1 - 2023/9

N2 - In this study, the exact analytical solutions of a two-dimensional linear homogeneous isotropic nano-beam in gradient elasticity are studied. Four different types of two-dimensional cantilever beams and related boundary conditions are considered. The cases are a cantilever beam under a concentrated force at the end, a cantilever beam under a uniform load, a propped cantilever beam under a uniform load, and a fixed-end beam under a uniform load. The two-dimensional stress gradient fields are investigated and obtained from the analytical solutions of a linear second-order partial differential equation written in terms of the classical and the gradient Airy stress functions. Additionally, the micro-size effects in the displacement components for different loads and support conditions for the two-dimensional cantilever beams by using strain gradient elasticity theory are investigated. Furthermore, for one-dimensional Euler–Bernoulli beam model, the associated stress and strain elasticity solutions are obtained from two-dimensional analytical solutions. The graphical presentations of the exact closed-form solutions are provided and discussed.

AB - In this study, the exact analytical solutions of a two-dimensional linear homogeneous isotropic nano-beam in gradient elasticity are studied. Four different types of two-dimensional cantilever beams and related boundary conditions are considered. The cases are a cantilever beam under a concentrated force at the end, a cantilever beam under a uniform load, a propped cantilever beam under a uniform load, and a fixed-end beam under a uniform load. The two-dimensional stress gradient fields are investigated and obtained from the analytical solutions of a linear second-order partial differential equation written in terms of the classical and the gradient Airy stress functions. Additionally, the micro-size effects in the displacement components for different loads and support conditions for the two-dimensional cantilever beams by using strain gradient elasticity theory are investigated. Furthermore, for one-dimensional Euler–Bernoulli beam model, the associated stress and strain elasticity solutions are obtained from two-dimensional analytical solutions. The graphical presentations of the exact closed-form solutions are provided and discussed.

KW - Analytical solutions

KW - Bi-harmonic differential equations

KW - Cantilever beams

KW - Micro-size effects

KW - Nonlocal elasticity

KW - One and two-dimensional nano-beams

KW - Stress and strain gradient elasticity

UR - http://www.scopus.com/inward/record.url?scp=85168974849&partnerID=8YFLogxK

U2 - 10.1016/j.apples.2023.100140

DO - 10.1016/j.apples.2023.100140

M3 - Article

AN - SCOPUS:85168974849

SN - 2666-4968

VL - 15

JO - Applications in Engineering Science

JF - Applications in Engineering Science

M1 - 100140

ER -