Abstract

The problem of refined modeling of ultrafine rods, which arose in connection with the need to explain the known experimental data on the significant dependence of the bending stiffness of such ultrathin structures on their thickness if the thickness becomes very small, commensurate as some authors believe with the characteristic dimensions of the material microstructure, is considered. To simulate such effects, Kirchhoff’s theory of thin rods uses gradient theories, nonlocal, micropolar elasticity theories, including scaled construction parameters. However, the obtained simulation results are very contradictory; the question of the reliability of the obtained results and the nature of the scale-dependent effect of the effective bending properties of ultrathin rods remains unresolved. It is shown in the paper that these effects for Kirchhoff and Timoshenko rods can be explained by taking into account the surface properties for ultrathin rods (plates).

中文翻译：

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弹性梯度理论中超薄梁相对弯曲刚度反常的悖论

摘要

超细杆的精细建模问题，是由于需要解释已知的实验数据，如果厚度变得很小，这种超薄结构的弯曲刚度将严重依赖于厚度，这与一些作者认为相当。考虑材料微观结构的特征尺寸。为了模拟这种效果，基尔霍夫的细杆理论使用了梯度理论，非局部微极性弹性理论，包括按比例绘制的施工参数。但是，所获得的仿真结果非常矛盾。所获得的结果的可靠性以及超薄杆的有效弯曲性能的比例依赖效应的性质仍未解决。