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FGM micro/nano-plates within modified couple stress elasticity
Composite Structures ( IF 6.3 ) Pub Date : 2020-08-01 , DOI: 10.1016/j.compstruct.2020.112294
V. Sladek , J. Sladek , M. Repka , L. Sator

Abstract A unified formulation for plate bending problems is developed within the modified couple stress theory of elasticity with incorporating the deformation assumptions of three plate bending theories, such as the Kirchhoff-Love theory, 1st and 3rd order shear deformation plate theories. The microscopic structure of material is reflected in this higher-grade continuum theory via one material coefficient called the micro-length scale parameter. Furthermore the material can be composed of two micro-constituents what is included in the employed continuum model by functional gradation of the Young modulus through the plate thickness with assuming power-law dependence of volume fractions of micro-constituents on the transversal coordinate. The boundary restrictions on the bottom and top surfaces of the plate are discussed in details together with derivation of governing equations and physical boundary conditions on the plate edges. For numerical solution a novel method is developed with using the Moving Finite Element approximation for field variables. Several numerical simulations are devoted to study the influence of micro-length scale parameter as well as the level of gradation of Young’s modulus on coupled bending and in-plane deformation response modes.

中文翻译:

修正偶应力弹性内的 FGM 微/纳米板

摘要 在修正的弹性耦合应力理论中,结合三种板弯曲理论的变形假设,如基尔霍夫-洛夫理论、一阶和三阶剪切变形板理论,开发了板弯曲问题的统一公式。材料的微观结构通过一种称为微长度尺度​​参数的材料系数反映在这种更高等级的连续介质理论中。此外,该材料可以由两种微成分组成,这些微成分包含在所采用的连续模型中,通过板厚度的杨氏模量的功能分级,并假设横向坐标上微成分的体积分数的幂律依赖性。详细讨论了板底面和顶面的边界限制以及板边缘上控制方程和物理边界条件的推导。对于数值求解,开发了一种使用场变量的移动有限元近似的新方法。几个数值模拟致力于研究微观长度尺度参数以及杨氏模量级配水平对耦合弯曲和面内变形响应模式的影响。
更新日期:2020-08-01
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