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为了解释圆孔问题的尺寸效应,本文在梯度弹性理论的框架下,提出了一个弹性相关的边界条件,并求解了该条件下圆孔周围的应力、应变及位移场的分布情况.分析了弹性关联系数α对梯度解的影响:α=1时,梯度解退化为弹性解;α=0.5时,梯度解满足自洽条件;α=0时,梯度解退化为传统梯度解的形式.详细地分析了α=0.5时,即自洽条件下圆孔周围的应力、应变及位移场,研究了无量纲化内檩长度的参数敏感性.最后比较了不同边界条件下的环向应力集中系数,发现自洽条件下的梯度解可以很好地描述圆孔问题的尺寸效应且物理意义更加合理.
In order to explain the size effect of the circular hole problem, this paper proposes a boundary condition of elastic correlation under the framework of gradient elasticity theory and solves the distribution of stress, strain and displacement field around circular hole under this condition. The influence of the correlation coefficient α on the gradient solution: when α = 1, the gradient solution degenerates into the elastic solution; when α = 0.5, the gradient solution satisfies the self-consistent condition; when α = 0, the gradient solution degenerates into the traditional gradient solution The stress, strain and displacement fields around the circular hole under the condition of α = 0.5 are analyzed, and the parameter sensitivities of dimensionless internal ridges are studied.Finally, the circumferential stress concentration coefficients under different boundary conditions are compared, It is found that the gradient solution under self-consistent conditions can well describe the size effect of the circular hole problem and the physical meaning is more reasonable.