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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2016.1
- 수록면
- 15 - 33 (19page)
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In this paper, an asymptotic method is employed to formulate nano- or micro-beams based on strain gradient elasticity. Although a basic theory for the strain gradient elasticity has been well established in literature, a systematic approach is relatively rare because of its complexity and ambiguity of higher-order elasticity coefficients. In order to systematically identify the strain gradient effect, an asymptotic approach is adopted by introducing the small parameter which represents the beam geometric slenderness and/or the internal atomistic characteristic. The approach allows us to systematically split the two-dimensional strain gradient elasticity into the microscopic one-dimensional through-the-thickness analysis and the macroscopic one-dimensional beam analysis. The first-order beam problem turns out to be different from the classical elasticity in terms of the bending stiffness, which comes from the through-the-thickness strain gradient effect. This subsequently affects the second-order transverse shear stress in which the surface shear stress exists. It is demonstrated that a careful derivation of a first strain gradient elasticity embraces "Gurtin-Murdoch traction" as the surface effect of a one-dimensional Euler-Bernoulli-like beam model.
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