## Porous Fg(多孔Fg)研究综述

Porous Fg 多孔Fg - In addition, it is displayed that corresponding to different maximum deflections, the significance of the strain gradient size effect in the absence of nonlocality on the nonlinear flexural stiffness of a porous FGM microplate is more than that of the nonlocal size effect in the absence of the strain gradient size dependency.^{[1]}After computing the deflection relations, a systematic study is performed for the bending response of nanoporous FGMs in a hygro-thermal surrounding environment, with promising results for practical applications.

^{[2]}It is portrayed that for a higher value of the material gradient index, the role of surface stress type of size dependency in the thermal postbuckling of porous FGM nanoplates becomes more important.

^{[3]}Due to lack of investigations on buckling analysis of porous FGM structures and notably for spherical cap shells, we provide new buckling results for porous FGM structures with evenly and unevenly porosity distributions.

^{[4]}The current model is efficient in many applications used porous FGM, such as aerospace, nuclear, power plane sheller, and marine structures.

^{[5]}Hematoxylin and eosin staining exhibited thick and mature trabecular bone around the porous FGS in the 30% porosity FGS group, whereas thinner, more immature trabecular bone was seen around the porous FGS in the 60% porosity FGS group.

^{[6]}Results revealed that buckling and free vibration behavior of the porous FG-GPL beam are influenced by the GPLs grading pattern and the type of axially varying load.

^{[7]}The validity of the method is verified in solving the free vibration and buckling problems of the porous FGM rectangular plates with compression on four sides.

^{[8]}In the numerical examples, influences of the aggregation effect of CNTs, coupled effect of temperature and moisture, material property (graded index and porosity parameters), geometric parameters as well as the rotating conditions to the hygrothermal mechanical responses of the porous FG-CRC annular plate are studied in detail.

^{[9]}Finally, an extensive parametric study is conducted to examine the effects of the external electric potential, the nonlocal parameter, the volume fraction of nano-voids, the temperature rise on the vibration of porous FGPM cylindrical nanoshells.

^{[10]}Numerical results obtained for buckling and free vibration for porous FGM plate resting on the foundation.

^{[11]}By contrast, von Mises stress at the proximal medial cortical bone increased by about 21 % for porous titanium and porous FGM as compared to non-porous titanium and FGM stem implants.

^{[12]}In the numerical examples, influences of material property (FG index and porosity parameters), geometric structure (inner-outer thickness ratio and its change index) as well as external conditions (temperature and moisture boundary conditions) to the multi-field responses of the porous FGMEE annular plate are studied in detail.

^{[13]}

此外，表明对应于不同的最大挠度，在没有非局部性的情况下，应变梯度尺寸效应对多孔 FGM 微板的非线性弯曲刚度的显着性大于在没有非局部性的情况下的非局部尺寸效应。应变梯度大小依赖性。

^{[1]}在计算了挠度关系后，对纳米多孔FGMs在湿热环境中的弯曲响应进行了系统研究，在实际应用中取得了可喜的成果。

^{[2]}可以看出，对于较高的材料梯度指数值，尺寸依赖性的表面应力类型在多孔 FGM 纳米板的热后屈曲中的作用变得更加重要。

^{[3]}由于缺乏对多孔 FGM 结构的屈曲分析的研究，特别是对于球形帽壳，我们为具有均匀和不均匀孔隙率分布的多孔 FGM 结构提供了新的屈曲结果。

^{[4]}当前模型在许多使用多孔 FGM 的应用中都很有效，例如航空航天、核能、动力飞机脱壳机和海洋结构。

^{[5]}苏木精和伊红染色在 30% 孔隙率 FGS 组中在多孔 FGS 周围显示厚而成熟的小梁骨，而在 60% 孔隙率 FGS 组中在多孔 FGS 周围观察到更薄、更不成熟的小梁骨。

^{[6]}结果表明，多孔 FG-GPL 梁的屈曲和自由振动行为受 GPL 分级模式和轴向变化载荷类型的影响。

^{[7]}在求解四边受压多孔FGM矩形板的自由振动和屈曲问题中验证了该方法的有效性。

^{[8]}在数值例子中，碳纳米管的聚集效应、温度和水分的耦合效应、材料性能（梯度指数和孔隙率参数）、几何参数以及旋转条件对多孔 FG-CRC 环形湿热力学响应的影响板块进行了详细研究。

^{[9]}最后，进行了广泛的参数研究，以检查外部电势、非局部参数、纳米空隙的体积分数、温度升高对多孔 FGPM 圆柱形纳米壳振动的影响。

^{[10]}基础上多孔 FGM 板的屈曲和自由振动的数值结果。

^{[11]}相比之下，与无孔钛和 FGM 柄植入物相比，多孔钛和多孔 FGM 的近端内侧皮质骨处的 von Mises 应力增加了约 21%。

^{[12]}在数值例子中，材料性能（FG指数和孔隙率参数）、几何结构（内外厚度比及其变化指数）以及外部条件（温度和水分边界条件）对多场响应的影响对多孔FGMEE环形板进行了详细研究。

^{[13]}

## shear deformation theory

In order to capture the small size effects, the Eringen's nonlocal elasticity based on higher order shear deformation theory (HSDT) are used to model the porous FG nanoplates.^{[1]}Using the Hamilton's principle, the governing equations of the porous FG nanoplates using the higher order shear deformation theory are derived.

^{[2]}To reveal these effects, the thermal-mechanical coupling buckling issue of a clamped-clamped porous FGM sandwich beam is investigated in this paper by employing the high-order sinusoidal shear deformation theory.

^{[3]}

为了捕捉小尺寸效应，基于高阶剪切变形理论 (HSDT) 的 Eringen 非局部弹性用于模拟多孔 FG 纳米板。

^{[1]}利用汉密尔顿原理，导出了使用高阶剪切变形理论的多孔FG纳米板的控制方程。

^{[2]}nan

^{[3]}

## modified power law 修正幂律

Material properties of porous FG nanoplate are defined by a modified power-law function, and two types of distribution for porosity are used.^{[1]}The material properties of the porous FGM pipe are assumed to vary continuously and smoothly along the radial direction based on the modified power-law distribution.

^{[2]}

多孔 FG 纳米板的材料特性由修正的幂律函数定义，并使用两种类型的孔隙率分布。

^{[1]}基于修正的幂律分布，假设多孔 FGM 管的材料特性沿径向连续平滑地变化。

^{[2]}

## order shear deformation 阶剪切变形

In the present paper, the wave propagation analysis of porous FG plates with clamped ends in thermal environments based on first order shear deformation theory are presented.^{[1]}

在本文中，基于一阶剪切变形理论，提出了在热环境中具有夹紧端部的多孔FG板的波传播分析。

^{[1]}

## porous fg nanoplate

Material properties of porous FG nanoplate are defined by a modified power-law function, and two types of distribution for porosity are used.^{[1]}An analytical approach for simply-supported and clamped bilayer porous FG nanoplates is implemented.

^{[2]}In order to capture the small size effects, the Eringen's nonlocal elasticity based on higher order shear deformation theory (HSDT) are used to model the porous FG nanoplates.

^{[3]}Using the Hamilton's principle, the governing equations of the porous FG nanoplates using the higher order shear deformation theory are derived.

^{[4]}Modified power-law function is developed to show the effective material properties of the porous FG nanoplate that change uniformly from one surface to another.

^{[5]}ABSTRACTA quasi-3D refined plate theory is presented with the nonlocal strain gradient theory to investigate the wave propagation in bi-layer porous FG nanoplates surrounded by an elastic medium.

^{[6]}

多孔 FG 纳米板的材料特性由修正的幂律函数定义，并使用两种类型的孔隙率分布。

^{[1]}实施了一种用于简单支撑和夹紧的双层多孔 FG 纳米板的分析方法。

^{[2]}为了捕捉小尺寸效应，基于高阶剪切变形理论 (HSDT) 的 Eringen 非局部弹性用于模拟多孔 FG 纳米板。

^{[3]}利用汉密尔顿原理，导出了使用高阶剪切变形理论的多孔FG纳米板的控制方程。

^{[4]}nan

^{[5]}nan

^{[6]}

## porous fg plate 多孔板

In the present paper, the wave propagation analysis of porous FG plates with clamped ends in thermal environments based on first order shear deformation theory are presented.^{[1]}The effect of the porosity parameter, the power-law exponent, side-thickness ratio, and aspect ratio on the static and buckling responses of the porous FG plate is evaluated.

^{[2]}Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction.

^{[3]}The equilibrium equations according to the porous FG plates are derived.

^{[4]}An analytical solution approach is utilized to get the natural frequencies of embedded porous FG plate with FG-CNTRC core subjected to magneto-electrical field.

^{[5]}

在本文中，基于一阶剪切变形理论，提出了在热环境中具有夹紧端部的多孔FG板的波传播分析。

^{[1]}评估了孔隙率参数、幂律指数、边厚比和纵横比对多孔 FG 板的静态和屈曲响应的影响。

^{[2]}多孔 FG 板的材料特性由混合物规则定义，并在厚度方向上附加了孔隙率项。

^{[3]}导出了根据多孔 FG 板的平衡方程。

^{[4]}nan

^{[5]}

## porous fg nanobeam

Hygro-thermal buckling of the porous FG nanobeam incorporating the surface effect is investigated.^{[1]}Based on the results of this study, a porous FG nanobeam has higher thermal buckling resistance and natural frequencies compared to a perfect FG nanobeam.

^{[2]}Once the validity of presented methodology is proved, a set of parametric studies are adopted to emphasize the role of each variant on the wave dispersion behaviors of porous FG nanobeams.

^{[3]}Navier's solution as well as Bolotin's approach are utilized to obtain the dynamic instability region of viscoelastic porous FG nanobeam.

^{[4]}

研究了结合表面效应的多孔FG纳米束的湿热屈曲。

^{[1]}根据这项研究的结果，与完美的 FG 纳米梁相比，多孔 FG 纳米梁具有更高的热屈曲阻力和固有频率。

^{[2]}一旦证明了所提出方法的有效性，就采用了一组参数研究来强调每个变体对多孔 FG 纳米束的波色散行为的作用。

^{[3]}nan

^{[4]}

## porous fg beam 多孔 Fg 梁

Furthermore, the Artificial Neural Networks (ANNs) technique is used to predict the effects of porosity distributions, porosity coefficient, slenderness ratio and boundary conditions on natural frequency variations of porous FG beam.^{[1]}For the analytical solution, Navier method is used to solve the governing equations for simply supported porous FG beams.

^{[2]}Mechanical properties of porous FG beams are supposed to vary through the thickness direction and are modeled via the modified power-law.

^{[3]}

此外，人工神经网络 (ANNs) 技术用于预测孔隙率分布、孔隙率系数、长细比和边界条件对多孔 FG 梁的固有频率变化的影响。

^{[1]}对于解析解，Navier 方法用于求解简支多孔 FG 梁的控制方程。

^{[2]}nan

^{[3]}