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首页> 外文期刊>Applied Mathematical Modelling >Influence of homogenization models on size-dependent nonlinear bending and postbuckling of bi-directional functionally graded microano-beams
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Influence of homogenization models on size-dependent nonlinear bending and postbuckling of bi-directional functionally graded microano-beams

机译：均质化模型对双向功能梯度微束/纳米束尺寸相关的非线性弯曲和后屈曲的影响

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摘要

In this work, different homogenization schemes are employed to analyze both size-dependent postbuckling and nonlinear bending behavior of microano-beams, made of a bi-directional functionally graded material (BDFGM), under external axial compression and distributed load. To such different homogenization models, including Reuss, Voigt, Mori-Tanaka, and Hashin-Shtrikman bounds schemes, together with nonlocal strain gradient elasticity theory are adopted within the framework of refined exponential shear deformation beam theory, to develop a comprehensive size-dependent BDFGM beam model. Deviation of associated physical neutral plane, from mid-plane counterpart, is also considered. Nonlocal strain gradient load-deflection responses of BDFGM microano-beam are obtained by numerical solution methodology for both nonlinear bending and postbuckling behaviors corresponding to different values of the lateral and longitudinal material property indices and various small scale parameters. We observed that by decreasing the values of material property gradient indices, associated with BDFGM, difference between the estimations of various homogenization schemes is raised. We also indicated that increasing maximum deflection, decreasing the significance of nonlocal size effect on the bending strength of BDFGM microano-beams, whereas strain gradient size effect becomes more important. In addition, we found that at lower material property gradient indices, bending strength reduction in BDFGM microano-beams, causes by the axial gradient property is higher than lateral gradient property. At higher values of these indices, however, the trend is opposite.
机译：在这项工作中，采用不同的均质化方案来分析由双向功能梯度材料（BDFGM）制成的微/纳米梁在外部轴向压缩和分布载荷下的尺寸相关的后屈曲和非线性弯曲行为。针对这种不同的均质模型，包括Reuss，Voigt，Mori-Tanaka和Hashin-Shtrikman边界方案，并在精细的指数剪切变形梁理论的框架内，结合非局部应变梯度弹性理论，开发了一种与尺寸有关的综合BDFGM梁模型。还考虑了相关联的物理中性平面相对于中平面的偏离。通过数值求解方法获得了BDFGM微/纳米梁的非局部应变梯度载荷-挠度响应，该方法分别对应于横向和纵向材料性能指标的不同值以及各种小尺寸参数，针对非线性弯曲和后屈曲行为。我们观察到，通过降低与BDFGM相关的材料特性梯度指数的值，可以提高各种均化方案的估计之间的差异。我们还表明，增加最大挠度，降低非局部尺寸对BDFGM微/纳米梁抗弯强度的影响，而应变梯度尺寸效应则变得更为重要。此外，我们发现，在较低的材料性能梯度指数下，BDFGM微/纳米梁的弯曲强度降低是由轴向梯度特性引起的，而其比侧向梯度特性要高。但是，如果这些指数的值较高，则趋势相反。

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