基于修正偶应力理论的功能梯度微板等几何分析
Isogeometric analysis for functionally graded microplates based on modified couple stress theory
摘要：
本文研究了功能梯度微板的静弯曲、自由振动和屈曲特性。其主要思想是将等几何分析与新型四变量精化板理论和准三维理论相结合。更重要的是，修正的偶应力理论，只有一个材料长度尺度参数，有效地捕捉内的微板的尺寸依赖性的影响。同时，基于一种新的七阶剪切变形四元精化板理论建立的准三维理论能够同时考虑剪切变形和厚度拉伸效应，且不需要剪切修正因子。该方法结合了基于NURBS的等几何分析，精确描述了几何形状，并近似计算了具有高阶导数和连续性要求的未知场。收敛性和验证表明，该方法的有效性和效率与现有的文献相比。进一步应用该方法研究了矩形和圆形功能梯度微板在各种边界条件下的静弯曲、自由振动和屈曲响应。还进行了一些调查，以说明材料的长度尺度，材料指数，和长度与厚度的比例上的响应的微板的效果。
英文摘要：
Analysis of static bending, free vibration and buckling behaviours of functionally graded microplates is investigated in this study. The main idea is to use the isogeometric analysis in associated with novel four-variable refined plate theory and quasi-3D theory. More importantly, the modified couple stress theory with only one material length scale parameter is employed to effectively capture the size-dependent effects within the microplates. Meanwhile, the quasi-3D theory which is constructed from a novel seventh-order shear deformation refined plate theory with four unknowns is able to consider both shear deformations and thickness stretching effect without requiring shear correction factors. The NURBS-based isogeometric analysis is integrated to exactly describe the geometry and approximately calculate the unknown fields with higher-order derivative and continuity requirements. The convergence and verification show the validity and efficiency of this proposed computational approach in comparison with those existing in the literature. It is further applied to study the static bending, free vibration and buckling responses of rectangular and circular functionally graded microplates with various types of boundary conditions. A number of investigations are also conducted to illustrate the effects of the material length scale, material index, and length-to-thickness ratios on the responses of the microplates.
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