• Wind and Structures
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• v.27 no.1
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• pp.59-70
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• 2018

In this paper, geometrically non-linear analysis of a functionally graded simple supported beam is investigated with porosity effect. The material properties of the beam are assumed to vary though height direction according to a prescribed power-law distributions with different porosity models. In the nonlinear kinematic model of the beam, the total Lagrangian approach is used within Timoshenko beam theory. In the solution of the nonlinear problem, the finite element method is used in conjunction with the Newton-Raphson method. In the study, the effects of material distribution such as power-law exponents, porosity coefficients, nonlinear effects on the static behavior of functionally graded beams are examined and discussed with porosity effects. The difference between the geometrically linear and nonlinear analysis of functionally graded porous beam is investigated in detail. Also, the effects of the different porosity models on the functionally graded beams are investigated both linear and nonlinear cases.

• Coupled systems mechanics
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• v.6 no.4
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• pp.399-415
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• 2017

This paper deals with the nonlinear static deflections of functionally graded (FG) porous under thermal effect. Material properties vary in both position-dependent and temperature-dependent. The considered nonlinear problem is solved by using Total Lagrangian finite element method within two-dimensional (2-D) continuum model in the Newton-Raphson iteration method. In numerical examples, the effects of material distribution, porosity parameters, temperature rising on the nonlinear large deflections of FG beams are presented and discussed with porosity effects. Also, the effects of the different porosity models on the FG beams are investigated in temperature rising.

• Steel and Composite Structures
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• v.24 no.5
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• pp.579-589
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• 2017

The objective of this work is to analyze post-buckling of functionally graded (FG) beams with porosity effect under compression load. Material properties of the beam change in the thickness direction according to power-law distributions with different porosity models. It is known that post-buckling problems are geometrically nonlinear problems. In the nonlinear kinematic model of the beam, total Lagrangian finite element model of two dimensional (2-D) continuum is used in conjunction with the Newton-Raphson method. In the study, the effects of material distribution, porosity parameters, compression loads on the post-buckling behavior of FG beams are investigated and discussed with porosity effects. Also, the effects of the different porosity models on the FG beams are investigated in post-buckling case.

• Steel and Composite Structures
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• v.49 no.6
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• pp.713-728
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• 2023

This paper aims to investigate the free vibration analysis of FG plates, taking into account the effects of even and uneven porosity. The study employs the Hellinger-Reisner functional and obtains the element's bending stress and membrane stress fields from the analytical solution of the governing equations of the thick plate and plane problem, respectively. The displacement field serves as the second independent field. While few articles on free vibration analysis of circular plates exist, this paper investigates the free vibration of both rectangular and circular plates. After validating the proposed element, the paper investigates the effects of porosity distributions on the natural frequency of the FG porous plate. The study calculates the natural frequency of thin and thick bending plates with different aspect ratios and support conditions for various porosity and volume fraction index values. The study uses three types of porosity distributions, X, V, and O, for the uneven porosity distribution case. For O and V porosity distribution modes, porosity has a minor effect on the natural frequency for both circular and rectangular plates. However, in the case of even porosity distribution or X porosity distribution, the effect of porosity on the natural frequency of circular and rectangular plates increases with an increase in the volume fraction index.

• Structural Engineering and Mechanics
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• v.71 no.1
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• pp.89-98
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• 2019

In this study, the mechanical bending behaviors of functionally graded porous nanobeams are investigated. Four types of porosity which are, the classical power porosity function, the symmetric with mid-plane cosine function, bottom surface distribution and top surface distribution are proposed in analysis of nanobeam for the first time. A comparison between four types of porosity are illustrated. The effect of nano-scale is described by the differential nonlocal continuum theory of Eringen by adding the length scale into the constitutive equations as a material parameter comprising information about nanoscopic forces and its interactions. The graded material is designated by a power function through the thickness of nanobeam. The beam is simply-supported and is assumed to be thin, and hence, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Numerical results show effects of porosity type, material graduation, and nanoscale parameters on the static deflection of nanobeam.

• Wind and Structures
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• v.32 no.1
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• pp.19-30
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• 2021

This study presents buckling analysis of a simply supported sandwich plate with functionally graded porous layers. In the kinematic relation of the plate, a hyperbolic shear displacement model is used. The governing equations of the problem are derived by using the principle of virtual work. In the solution of the governing equations, the Navier procedure is implemented. In the porosity effect, four different porosity types are used for functionally graded sandwich layers. In the numerical examples, the effects of the porosity parameters, porosity types and geometry parameters on the critical buckling of the functionally graded sandwich plates are investigated.

• Journal of the Korean Ceramic Society
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• v.46 no.1
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• pp.35-40
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• 2009

Using zirconia and poly (methyl methacrylate-coethylene glycol dimethacrylate) (PMMA) microbeads, macroporous zirconia ceramics were fabricated by a simple pressing method. Effects of template size and content on microstructure, porosity, and flexural and compressive strengths were investigated in the processing of the macroporous zirconia ceramics. Three different sizes of microbeads (8, 20, and $50{\mu}m$) were used as a template for fabricating the macroporous ceramics. The porosity increased with increasing the template size at the same template content. The flexural and compressive strengths were primarily influenced by the porosity rather than the template size. However, the strengths increased with decreasing the template size at the same porosity. By controlling the template size and content, it was possible to produce macroporous zirconia ceramics with porosities ranging from 58% to 75%. Typical flexural and compressive strength values at 60% porosity were ${\sim}30\;MPa$ and ${\sim}75\;MPa$, respectively.

• Journal of Technologic Dentistry
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• v.22 no.1
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• pp.13-20
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• 2000

This experiment was done to find out how the length and the diameter of the sprue effects the porosity created during the moduling process, which is caused by the metal's shrinking and stretching action. the experiment was done in two groups(A and B), using experimental gold, and made 10 copings for both groups. 1. In group A, The length of the sprues were given the same, but the diameter of the sprue were 6, 8, 10, 12, 18 gauge. As a result, the porosity came out big with 12 and 18 gauge and for 10, 8, 6 gauge, the porosity was hardly seen or none was noticeable. 2. In group B, the diameter was given the sam for the sprues, but the length of the sprues were 5, 10, 15, 20, 25mm. As a result, the porosity came out big with 25, 20, 15mm the porosity was hardly seen or none was noticeable. 3. The diameter needs to be big and the length, short. 4. The appropriate sized sprue must be chosen for each individual tooth, according to it's shape and size.

• Steel and Composite Structures
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• v.42 no.6
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• pp.805-826
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• 2022

The free and live load-forced vibration behaviour of porous functionally graded (PFG) higher order nanobeams in the thermal and magnetic fields is investigated comprehensively through this work in the framework of nonlocal strain gradient theory (NLSGT). The porosity effects on the dynamic behaviour of FG nanobeams is investigated using four different porosity distribution models. These models are exploited; uniform, symmetrical, condensed upward, and condensed downward distributions. The material characteristics gradation in the thickness direction is estimated using the power-law. The magnetic field effect is incorporated using Maxwell's equations. The third order shear deformation beam theory is adopted to incorporate the shear deformation effect. The Hamilton principle is adopted to derive the coupled thermomagnetic dynamic equations of motion of the whole system and the associated boundary conditions. Navier method is used to derive the analytical solution of the governing equations. The developed methodology is verified and compared with the available results in the literature and good agreement is observed. Parametric studies are conducted to show effects of porosity parameter; porosity distribution, temperature rise, magnetic field intensity, material gradation index, non-classical parameters, and the applied moving load velocity on the vibration behavior of nanobeams. It has been showed that all the analyzed conditions have significant effects on the dynamic behavior of the nanobeams. Additionally, it has been observed that the negative effects of moving load, porosity and thermal load on the nanobeam dynamics can be reduced by the effect of the force induced from the directed magnetic field or can be kept within certain desired design limits by controlling the intensity of the magnetic field.

• Steel and Composite Structures
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• v.36 no.3
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• pp.293-305
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• 2020

This article presented a nanoscale modified continuum model to investigate the free vibration of functionally graded (FG) porous nanobeam by using finite element method. The main novelty of this manuscript is presenting effects of four different porosity models on vibration behaviors of nonlocal nanobeam structure including size effect, that not be discussed before The proposed porosity models are, uniform porosity distribution, symmetric with mid-plane, bottom surface distribution and top surface distribution. The nano-scale effect is included in modified model by using the differential nonlocal continuum theory of Eringen that adding the length scale into the constitutive equations as a material parameter constant. The graded material is distributed through the beam thickness by a generalized power law function. The beam is simply supported, and it is assumed to be thin. Therefore, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Results demonstrate effects of porosity type, material gradation, and nanoscale parameters on the free vibration of nanobeam. The proposed model is effective in vibration analysis of NEMS structure manufactured by porous functionally graded materials.