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Nonlinear finite element analysis of temperature-dependent functionally graded porous micro-plates under thermal and mechanical loads

机译：温度依赖性功能梯度多孔微板的非线性有限元分析

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摘要

In the present study, a displacement based nonlinear finite element model for functionally graded porous micro-plates is developed based on the general third-order shear deformation plate theory and the modified couple stress theory. The developed finite element model accounts for von Karman nonlinear strains, a power-law variation of two material constituents through the plate thickness, and different distributions of porosity with a constant volume of voids on static bending of micro-plates are analyzed. The length scale dependency is captured using a single parameter of the modified couple stress theory. A power-law distribution is assumed to model the variation of the two material constituents, while the porosity distributions vary according to cosine functions. The temperature-dependent properties are obtained using a cubic-spline interpolation from experimental data. A one-dimensional steady-state heat conduction problem is solved using the effective thermal conductivity of the porous material based on the Maxwell-Eucken model to obtain temperature distribution through the plate thickness. The Newton-Raphson iteration scheme is used to solve the nonlinear system of equations. A parametric study is conducted to demonstrate the effects of material and porosity parameters, temperature and length scale dependencies, and boundary conditions on the deflections and stress distributions.
机译：在本研究中，基于一般的三阶剪切变形板理论和改进的夫妇应力理论，开发了一种用于功能梯度多孔微板的基于位移的非线性有限元模型。分析了von Karman非线性菌株的开发有限元模型，分析了通过板厚度的两种材料成分的动力律变化，以及在微板的静态弯曲上具有恒定空隙的恒定空隙的不同孔隙率分布。使用修改的夫妇应力理论的单个参数捕获长度级依赖性。假设动力法分布模拟两种材料成分的变型，而孔隙分布变化根据余弦功能。使用实验数据的立方样条插值获得温度依赖性性质。使用基于Maxwell-eChen模型的多孔材料的有效导热率来解决一维稳态导热问题，以通过板厚度获得温度分布。 Newton-Raphson迭代方案用于解决方程的非线性系统。进行参数研究以展示材料和孔隙率参数，温度和长度尺度依赖性的影响，以及偏转和应力分布的边界条件。

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