• Steel and Composite Structures
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• v.21 no.1
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• pp.123-136
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• 2016

This work focuses on the behavior of the static analysis of functionally graded plates materials (FGMs) with porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose a new refined plate theory is used in this work, it contains only four unknowns, unlike five unknowns for other theories. This new model meets the nullity of the transverse shear stress at the upper and lower surfaces of the plate. The parabolic distribution of transverse shear stresses along the thickness of the plate is taken into account in this analysis; the material properties of the FGM plate vary a power law distribution in terms of volume fraction of the constituents. The rule of mixture is modified to describe and approximate material properties of the FG plates with porosity phases. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature, the influence of material parameter, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM plate are represented by numerical examples.

• Journal of Theoretical and Applied Mechanics
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• v.2 no.1
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• pp.1-14
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• 1996

In this paper, breaking waves are generated in a 2-D wave tank and simulated by using a higher-order boundary element method. A piston-type wavemaker is operated by signals composed of elementary waves. The phase of elementary waves is determined by the linear theory such that they are focused to a prescribed position. Calculated plunging waves coincide well with experiment. A steel box with different plate thicknesses is installed at a predetermined position in the tank. Measured impulsive pressures due to breaking waves are found to be 0.8-1.2$\rho$C2, where $\rho$ corresponds to water density and C to wave celerity. The transverse displacement of the plate is described in terms of modal eigenfunctions. The natural frequencies measured by impact tests in air for thin plate coincide with the computational and theoretical values. The radiationpotential due to plate vibration is derived and the radiation force is expressed in terms of hydroelastic added mass and damping forces. Comparison of natural frequencies of plate in water proves that hydroelastic added mass and damping are properly considered. The measured strain due to regular waves supports the calculated one, but there are apparent discrepancies between theory and experiment in the impulsive case.

• Structural Engineering and Mechanics
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• v.55 no.2
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• pp.435-459
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• 2015

Parametric resonance of shear deformable composite skew plates subjected to non-uniform (parabolic) and linearly varying periodic edge loading is studied for different boundary conditions. The skew plate structural model is based on higher order shear deformation theory (HSDT), which accurately predicts the numerical results for thick skew plate. The total energy functional is derived for the skew plates from total potential energy and kinetic energy of the plate. The strain energy which is the part of total potential energy contains membrane energy, bending energy, additional bending energy due to additional change in curvature and shear energy due to shear deformation, respectively. The total energy functional is solved using Rayleigh-Ritz method in conjunction with boundary characteristics orthonormal polynomials (BCOPs) functions. The orthonormal polynomials are generated for unit square domain using Gram-Schmidt orthogonalization process. Bolotin method is followed to obtain the boundaries of parametric resonance region with higher order approximation. These boundaries are traced by the periodic solution of Mathieu-Hill equations with period T and 2T. Effect of various parameters like skew angle, span-to-thickness ratio, aspect ratio, boundary conditions, static load factor on parametric resonance of skew plate have been investigated. The investigation also includes influence of different types of linearly varying loading and parabolically varying bi-axial loading.

• Computers and Concrete
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• v.32 no.5
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• pp.439-454
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• 2023

In this article, the surface stress effects on the buckling analysis of the annular sandwich plate is developed. The proposed plate is composed of two face layers made of carbon nanotubes (CNT) reinforced composite with assuming of fully bonded to functionally graded porous core. The generalized rule of the mixture is employed to predict the mechanical properties of the microcomposite sandwich plate. The derived potentials energy based on higher order shear deformation theory (HSDT) and modified couple stress theory (MCST) is solved by employing the Ritz method. An exact analytical solution is presented to calculate the critical buckling loads of the annular sandwich plate. The predicted results are validated by carrying out the comparison studies for the buckling analysis of annular plates with those obtained by other analytical and finite element methods. The effects of various parameters such as material length scale parameter, core thickness to total thickness ratio (hc/h), surface elastic constants based on surface stress effect, various boundary condition and porosity distributions, size of the internal pores (e0), Skempton coefficient and elastic foundation on the critical buckling load have been studied. The results can be served as benchmark data for future works and also in the design of materials science, injunction high-pressure micropipe connections, nanotechnology, and smart systems.

• Steel and Composite Structures
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• v.26 no.1
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• pp.1-15
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• 2018

This study reported, the effect of random variation in system properties on bending response of single wall carbon nanotube reinforced composite (SWCNTRC) plates subjected to transverse uniform loading is examined. System parameters such as the SWCNT armchair, material properties, plate thickness and volume fraction of SWCNT are modelled as basic random variables. The basic formulation is based on higher order shear deformation theory to model the system behaviour of the SWCNTRC composite plate. A C0 finite element method in conjunction with the first order perturbation technique procedure developed earlier by the authors for the plate subjected to lateral loading is employed to obtain the mean and variance of the transverse deflection of the plate. The performance of the stochastic SWCNTRC composite model is demonstrated through a comparison of mean transverse central deflection with those results available in the literature and standard deviation of the deflection with an independent First Order perturbation Technique (FOPT), Second Order perturbation Technique (SOPT) and Monte Carlo simulation.

• Journal of the Society of Disaster Information
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• v.16 no.4
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• pp.832-841
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• 2020

Purpose: This study attempts at analyzing mechanical response of functionally graded material (FGM) plates in bending. An accurate and effective numerical approach based on isogeometric analysis (IGA) combined with higher-order shear deformation plate theory to predict the nonlinear flexural behavior is developed. Method: A higher-order shear deformation theory(HSDT) which accounts for the geometric nonlinearity in the von Karman sense is presented and used to derive the equilibrium and governing equations for FGM plate in bending. The nonlinear equations are solved by the modified Newton-Raphson iterative technique. Result: The volume fraction, plate length-to-thickness ratio and boundary condition have signifiant effects on the nonlinear flexural behavior of FGM plates. Conclusion: The proposed IGA method can be used as an accurate and effective numerical tool for analyzing the mechanical responses of FGM plates in flexure.

• Advances in nano research
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• v.7 no.5
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• pp.293-310
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• 2019

In this paper, thermal-buckling behavior of the functionally graded (FG) nanocomposite plates reinforced with graphene oxide powder (GOP) is studied under three types of thermal loading once the plate is supposed to be rested on a two-parameter elastic foundation. The effective material properties of the nanocomposite plate are considered to be graded continuously through the thickness according to the Halpin-Tsai micromechanical scheme. Four types of GOPs' distribution namely uniform (U), X, V and O, are considered in a comparative way in order to find out the most efficient model of GOPs' distribution for the purpose of improving the stability limit of the structure. The governing equations of the plate have been derived based on a refined higher-order shear deformation plate theory incorporated with Hamilton's principle and solved analytically via Navier's solution for a simply supported GOP reinforced (GOPR) nanocomposite plate. Some new results are obtained by applying different thermal loadings to the plate according to the GOPs' negative coefficient of thermal expansion and considering both Winkler-type and Pasternak-type foundation models. Besides, detailed parametric studies have been carried out to reveal the influences of the different types of thermal loading, weight fraction of GOP, aspect and length-to-thickness ratios, distribution type, elastic foundation constants and so on, on the critical buckling load of nanocomposite plates. Moreover, the effects of thermal loadings with various types of temperature rise are investigated comparatively according to the graphical results. It is explicitly shown that the buckling behavior of an FG nanocomposite plate is significantly influenced by these effects.

• Steel and Composite Structures
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• v.35 no.1
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• pp.1-12
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• 2020

This article deals with the buckling analysis in the plates containing carbon nanotubes (CNTs) subject to axial load. In order to control the plate smartly, a piezoelectric layer covered the plate. The plate is located in elastic medium which is modeled by spring elements. The Mori-Tanaka low is utilized for calculating the equivalent mechanical characteristics of the plate. The structure is modeled by a thick plate and the governing equations are deduced using Hamilton's principle under the assumption of higher-order shear deformation theory (HSDT). The Navier method is applied to obtain the bulking load. The effects of the applied voltage to the smart layer, agglomeration and volume percent of CNT nanoparticles, geometrical parameters and elastic medium of the structure are assessed on the buckling response. It has been demonstrated that by applying a negative voltage, the buckling load is increased significantly.

• Steel and Composite Structures
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• v.24 no.5
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• pp.603-613
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• 2017

In this research, the free vibration response of laminated composite plates is investigated using a novel and simple higher order shear deformation plate theory. The model considers a non-linear distribution of the transverse shear strains, and verifies the zero traction boundary conditions on the surfaces of the plate without introducing shear correction coefficient. The developed kinematic uses undetermined integral terms with only four unknowns. Equations of motion are obtained from the Hamilton's principle and the Navier method is used to determine the closed-form solutions of antisymmetric cross-ply and angle-ply laminates. Numerical examples studied using the present formulation is compared with three-dimensional elasticity solutions and those calculated using the first-order and the other higher-order theories. It can be concluded that the present model is not only accurate but also efficient and simple in studying the free vibration response of laminated composite plates.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.2
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• pp.129-136
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• 2011

The aim of this paper is to present the method of identifying the impact location on the plate. This basic research has the future purpose to achieve the human-interaction technology based on the signal processing, piezoelectric materials, and wave propagation. The present work concerning the location identification of a single impact on the plate simulated the waveform numerically generated by impact force and applied the SWFOM(sliced Wigner higher fourth order moment) to the waveform to get the arrival time differences due to impact force between three sensors attached to the plate. The simulated signal is useful to get the information for time interval for the only direct wave. This information is used the source localization by using experimental work. The measured signal is also used for source localization of a single impact based on the higher order time frequency as a novel work.