## 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. 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。

Porosity-dependent nonlinear transient responses of functionally graded nanoplates using isogeometric analysis

## Using the Hamilton's principle, the governing equations of the porous FG nanoplates using the higher order shear deformation theory are derived. 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。

An isogeometric approach of static and free vibration analyses for porous FG nanoplates

## Material properties of porous FG nanoplate are defined by a modified power-law function, and two types of distribution for porosity are used. 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。

Influence of initial geometric imperfection on static and free vibration analyses of porous FG nanoplate using an isogeometric approach

## 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. 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。

Static and dynamic characteristics of the post-buckling of fluid-conveying porous functionally graded pipes with geometric imperfections

## Material properties of porous FG nanoplate are defined by a modified power-law function, and two types of distribution for porosity are used. 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。

Influence of initial geometric imperfection on static and free vibration analyses of porous FG nanoplate using an isogeometric approach

## An analytical approach for simply-supported and clamped bilayer porous FG nanoplates is implemented. 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。

Porosity and inhomogeneity effects on the buckling and vibration of double-FGM nanoplates via a quasi-3D refined theory

## 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. 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。

Influence of porosity distribution on static and buckling responses of porous functionally graded plates

## Hygro-thermal buckling of the porous FG nanobeam incorporating the surface effect is investigated. 研究了结合表面效应的多孔FG纳米束的湿热屈曲。

Hygro-thermal buckling of porous FG nanobeams considering surface effects

## 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. 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。

A finite element model for the thermo-elastic analysis of functionally graded porous nanobeams

## 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. 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。

Free vibration analysis of open-cell FG porous beams: analytical, numerical and ANN approaches

## For the analytical solution, Navier method is used to solve the governing equations for simply supported porous FG beams. 对于解析解，Navier 方法用于求解简支多孔 FG 梁的控制方程。

Investigation on the dynamic response of porous FGM beams resting on variable foundation using a new higher order shear deformation theory

10.1007/s00366-021-01303-z

## 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. 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。

Size-dependent nonlinear bending behavior of porous FGM quasi-3D microplates with a central cutout based on nonlocal strain gradient isogeometric finite element modelling

10.1016/J.COMPSTRUCT.2020.112925

## 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. 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。

Nonlocal elasticity analysis of moderately thick porous functionally graded plates in a hygro-thermal environment

10.1016/J.COMPSTRUCT.2021.113604

## 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. 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。

Isogeometric thermal postbuckling analysis of porous FGM quasi-3D nanoplates having cutouts with different shapes based upon surface stress elasticity

10.1016/J.COMPSTRUCT.2021.114313

## 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. 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。

Buckling responses of porous structural components with gradient power-based and sigmoid material variations under different types of compression loads

10.12989/GAE.2021.24.1.091

## The current model is efficient in many applications used porous FGM, such as aerospace, nuclear, power plane sheller, and marine structures. 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。

Forced vibration of a functionally graded porous beam resting on viscoelastic foundation

10.1016/j.jot.2021.01.002

## 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. 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。

Effect of porosity of a functionally-graded scaffold for the treatment of corticosteroid-associated osteonecrosis of the femoral head in rabbits

10.1007/s00366-021-01478-5

## 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. 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。

Stability and dynamic behavior of porous FGM beam: influence of graded porosity, graphene platelets, and axially varying loads

10.1051/JNWPU/20213920317

## 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. 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。

Analysis on free vibration and critical buckling load of a FGM porous rectangular plate

10.1016/J.COMPSTRUCT.2019.02.061

## 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. 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。

Hygrothermal mechanical behaviors of a porous FG-CRC annular plate with variable thickness considering aggregation of CNTs

## 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. 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。

Thermo-Electro-Mechanical Vibrations of Porous Functionally Graded Piezoelectric Nanoshells

## Numerical results obtained for buckling and free vibration for porous FGM plate resting on the foundation. 基础上多孔 FGM 板的屈曲和自由振动的数值结果。

Meshfree approach on buckling and free vibration analysis of porous FGM plate with proposed IHHSDT resting on the foundation

## 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. 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%。

Stress shielding reduction via graded porosity of a femoral stem implant

10.1016/J.COMPSTRUCT.2018.11.077

## 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. 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。

Multi-field mechanical behavior of a rotating porous FGMEE circular disk with variable thickness under hygrothermal environment