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Isogeometric analysis of size-dependent isotropic and sandwich functionally graded microplates based on modified strain gradient elasticity theory

机译：基于修正应变梯度弹性理论的尺寸相关各向同性和三明治功能梯度微板的等几何分析

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摘要

This paper presents a size-dependent four-unknown shear deformable model for static bending, free vibration and buckling analyses of isotropic and sandwich functionally graded (FG) microplates based on the modified strain gradient theory (MSGT). The MSGT requires three material length scale parameters instead of five parameters as well known in the original strain gradient theory. The material parameters of isotropic and sandwich FG microplates are directly derived from a rule of mixture. The governing equations are derived from the principle of virtual work. Since the present method contains the higher-order gradients in the weak form, NURBS-based isogeometric analysis is suitable for the solution procedure. The effects of geometrical parameters, boundary conditions, volume fraction and material length scale parameters are investigated through isotropic and sandwich FG microplate examples. Obtained results indicate that the consideration of strain gradients leads to a rise of the plate stiffness, and a reduction of displacement and an increase in natural frequency as well as critical buckling load of FG microplates are therefore remarked. Moreover, the present model can be degenerated into the modified couple stress model or classical model when a few material length-sale parameters are neglected.
机译：本文提出了一种基于尺寸的四未知剪切变形模型，用于基于改进的应变梯度理论（MSGT）的各向同性和三明治功能梯度（FG）微孔板的静态弯曲，自由振动和屈曲分析。 MSGT需要三个材料长度尺度参数，而不是原始应变梯度理论中众所周知的五个参数。各向同性和夹层FG微孔板的材料参数直接来自混合规则。控制方程式是根据虚拟功原理导出的。由于本方法包含弱形式的高阶梯度，因此基于NURBS的等几何分析适用于求解过程。通过各向同性和三明治FG微孔板实例研究了几何参数，边界条件，体积分数和材料长度比例参数的影响。获得的结果表明，考虑应变梯度会导致板刚度的增加，因此，FG微板的位移减小，固有频率的增加以及临界屈曲载荷都得到了显着体现。而且，当忽略一些材料的纵向销售参数时，本模型可以退化为改进的耦合应力模型或经典模型。

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