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首页> 外文期刊>Applied Mathematical Modelling >3D elasticity analytical solution for bending of FG microanoplates resting on elastic foundation using modified couple stress theory
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3D elasticity analytical solution for bending of FG microanoplates resting on elastic foundation using modified couple stress theory

机译：基于修正耦合应力理论的FG微/纳米板在弹性地基上弯曲的3D弹性解析解

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摘要

This paper addresses a 3D elasticity analytical solution for static deformation of a simply-supported rectangular microanoplate made of both homogeneous and functionally graded (FG) material within the framework of modified couple stress theory. The plate is assumed to be resting on a Winkler-Pasternak elastic foundation, and its modulus of elasticity is assumed to vary exponentially along thickness. By expanding displacement components in double Fourier series along in-plane coordinates and imposing relevant boundary conditions, the boundary value problem (BVP) of plate system, including its governing partial differential equations (PDEs) of equilibrium are reduced to BVP consisting only ordinary ones (ODEs). Parametric studies are conducted among displacement and stress components developed in the plate and FG material gradient index, length scale parameter, and foundation stiffnesses. From the numerical results, it is concluded that the out-of-plane shear stresses are not necessarily zero at the top and bottom surfaces of plate. The results of this investigation may serve as a benchmark to verify further bending analyses of either homogeneous or FG microanoplates on elastic foundation.
机译：本文提出了一种在变形偶应力理论框架内，用均质材料和功能梯度材料（FG）制成的简单支撑矩形微/纳米板静态变形的3D弹性解析解决方案。假定该板位于Winkler-Pasternak弹性地基上，并且假定其弹性模量沿厚度呈指数变化。通过沿平面坐标将双傅里叶级数的位移分量展开并施加相关的边界条件，板系统的边界值问题（BVP），包括其控制的平衡偏微分方程（PDE），被简化为仅包含普通方程的BVP（ ODEs）。在板中产生的位移和应力分量以及FG材料梯度指数，长度比例参数和基础刚度之间进行参数研究。从数值结果可以得出结论，板的顶面和底面的面外剪切应力不一定为零。这项研究的结果可以作为基准，以验证弹性基础上的均质或FG微型/纳米板的进一步弯曲分析。

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