A model of micro Euler beam containing only one internal material length scale parameter and ap-plieing to arbitrary boundary conditions was proposed based on the modified couple stress theory. Equilibri-um differential equation of micro Euler beam was deduced using the Hamiltonˊs principle,of which the form was similar to the classical model. The only difference was an additional term in bending rigidity associated with material length scale parameter. The equation could be used directly to analyze and explain multi-scale problems. Therefore,a strategy reducing modulus was proposed to solve the problems such as bending,vibra-tion and buckling of micro beams by classical beam elements. The numerical results show that the bending rigidity of the Euler beam in a micro scale is higher than that in a macro scale,indicating that model presen-ted in this paper can capture the scale effects. It is found that the geometric size is a significant factor of the scale effects.%基于修正偶应力理论建立了仅含一个尺度参数且适用于各种边界条件的微尺度欧拉梁模型。基于哈密顿原理推导了微尺度欧拉梁的平衡微分方程,该方程与经典梁的平衡微分方程具有相似的形式,只是在弯曲刚度中多了一项与尺度效应有关的项,可直接用于分析和解释多尺度问题。提出了一种模量折算策略,从而利用经典梁单元即可完成对微细观尺度下的梁的弯曲、动力和稳定问题的求解。算例结果表明,在微细观尺度下梁结构将表现出比宏观状态下更强的抗弯刚度,即本文模型能捕捉到尺度效应。进一步的研究则指出,几何尺寸的大小是尺度效应的决定性因素。
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机译:通过仔细观察微观/纳米尺度的有机/矿物协会,可以更好地理解考古学的骨骼变化现象。来自法国汝拉Chalain Lake Site 19的新石器时代样本的初步结果:通过在微观和纳米尺度上详细观察有机矿物组合,可以更好地了解考古骨骼的变化现象。从法国汝拉州Lac de Chalain站19的新石器时代样本获得的初步结果