• Steel and Composite Structures
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• 제34권2호
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• pp.215-226
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• 2020

The aim of this study is to investigate free vibration of functionally graded porous nanocomposite rectangular plates where the internal pores and graphene platelets (GPLs) are distributed in the matrix either uniformly or non-uniformly according to three different patterns. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. The GPL-reinforced plate is modeled using a semi-analytic approach composed of generalized differential quadrature method (GDQM) and series solution adopted to solve the equations of motion. The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and those reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. New results reveal the importance of porosity coefficient, porosity distribution, graphene platelets (GPLs) distribution, geometrical and boundary conditions on vibration behavior of porous nanocomposite plates. It is observed that the maximum vibration frequency obtained in the case of symmetric porosity and GPL distribution, while the minimum vibration frequency is obtained using uniform porosity distribution.

• Composites Research
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• 제24권4호
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• pp.41-47
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• 2011

본 연구는 사출 성형 공정을 통하여 제작되는 단섬유강화 플라스틱 복합재료의 구조해석 기법에 관한 내용으로 소재의 이방성 기계물성을 예측하고 이를 구조해석에 적용하도록 하였다. 사출 성형 공정을 통하여 제작되는 단섬유강화 플라스틱 복합재료의 구조해석에 있어서 기존의 경우는 일반적으로 소재의 기계적 물성을 균질 등방성 탄성 모델로 이용하여 왔으나, 실제 부품 파손 모드와 크게 상이한 경우가 많다. 이러한 점을 극복하고자 사출 성형 g,름 해석, 일방향성 복합재료의 Halpin-Tsai 식과 배향 평균 모델을 도입하여 단섬유강화 플라스틱 복합재료의 섬유배향 효과가 고려되도록 새로운 구조해석 시스템을 개발하였다. 해석의 정확도는 시편시험 결과와의 비교를 통하여 검증하였으며, 섬유 배향 및 웰드라인 영향 및 섬유 함량에 따른 변화가 해석에 장 반영됨을 확인하였다. 또한 자동차 부품에 개발된 해석 시스템을 적용하여 균질 등방 모델과 달리 부품의 위치별로 다른 기계적 성능이 반영되고, 사출 게이트 위치에 따라 유리섬유 배향이 변화하여 부품의 성능이 달라짐을 확인하였다.

• Advances in nano research
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• 제15권2호
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• pp.141-153
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• 2023

The main objective of this paper is to develop the finite element study on the nonlinear free vibration of functionally graded nanocomposite spherical shells reinforced with graphene platelets under the first-order shear deformation shell theory and von Kármán nonlinear kinematic relations. The governing equations are presented by introducing the full asymmetric nonlinear strain-displacement relations followed by the constitutive relations and energy functional. The extended Halpin-Tsai model is utilized to specify the overall Young's modulus of the nanocomposite. Then, the finite element formulation is derived and the quadrilateral 8-node shell element is implemented for finite element discretization. The nonlinear sets of dynamic equations are solved by the use of the harmonic balance technique and iterative method to find the nonlinear frequency response. Several numerical examples are represented to highlight the impact of involved factors on the large-amplitude vibration responses of nanocomposite spherical shells. One of the main findings is that for some geometrical and material parameters, the fundamental vibrational mode shape is asymmetric and the axisymmetric formulation cannot be appropriately employed to model the nonlinear dynamic behavior of nanocomposite spherical shells.

• Steel and Composite Structures
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• 제37권1호
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• pp.27-35
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• 2020

This study examines the wave propagation of the functionally graded polymer composite (FG-PC) nanoplates reinforced with graphene nanoplatelets (GNPs) resting on elastic foundations in the framework of the nonlocal strain gradient theory incorporating both stiffness hardening and softening mechanisms of nanostructures. To this end, the material properties are based on the Halpin-Tsai model, and the expressions for the classical and higher-order stresses and strains are consistently derived employing the second-order shear deformation theory. The equations of motion are then consistently derived using Hamilton's principle of variation. These governing equations are solved with the help of Trial function method. Extensive numerical discussions are conducted for wave propagation of the nanoplates and the influences of different parameters, such as the nonlocal parameter, strain gradient parameter, weight fraction of GNPs, uniform and non-uniform distributions of GNPs, elastic foundation parameters as well as wave number.

• Computers and Concrete
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• 제22권6호
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• pp.501-514
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• 2018

The paper presents the thermo-mechanically induced non-linear response of multiwall carbon nanotube reinforced laminated composite beam (MWCNTRCB) supported by elastic foundation using higher order shear deformation theory and von-Karman non-linear kinematics. The elastic properties of MWCNT reinforced composites are evaluated using Halpin-Tsai model by considering MWCNT reinforced polymer matrix as new matrix by dispersing in it and then reinforced with E-glass fiber in an orthotropic manner. The laminated beam is supported by Pasternak elastic foundation with Winkler cubic nonlinearity. A generalized static analysis is formulated using finite element method (FEM) through principle of minimum potential energy approach.

• Computers and Concrete
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• 제27권4호
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• pp.369-383
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• 2021

This article deals with the frequency analysis of viscoelastic sandwich disk with graphene nano-platelets (GPLs) reinforced viscoelastic concrete (GPLRVC) face sheets and honeycomb core. The honeycomb core is made of aluminum due to its low weight and high stiffness. The rule of the mixture and modified Halpin-Tsai model are engaged to provide the effective material constant of the concrete. By employing Hamilton's principle, the governing equations of the structure are derived and solved with the aid of the Generalize Differential Quadrature Method (GDQM). In this paper, viscoelastic properties are modeled according to Kelvin-Voigt viscoelasticity. The deflection as the function of time can be solved by the fourth-order Runge-Kutta numerical method. Afterward, a parametric study is carried out to investigate the effects of the outer to inner radius ratio, hexagonal core angle, thickness to length ratio of the concrete, the weight fraction of GPLs into concrete, and the thickness of honeycomb core to inner radius ratio on the frequency of the viscoelastic sandwich disk with honeycomb core and FG-GPLRVC face sheet.

• Advances in nano research
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• 제13권3호
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• pp.233-245
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• 2022

Resently, the use of smart structures has been heightened up rapidly. For this issue, vibration analysis related to a graphene nanoplatelet composite (GPLRC) nanodisk which is attached to a piezoelectric layer and is subjected to thermal loads is explored in the current paper. The formulation of this study is obtained through the energy method and nonlocal strain gradient theory, and then it is solved employing generalized differential quadrature method (GDQM). Halpin-Tsai model in addition to the mixture's rule are utilized to capture the material properties related to the reinforced composite layer. The compatibility conditions are presented for exhibiting the perfect bounding between two layers. The results of this study are validated by employing the other published articles. The impact of such parameters as external voltage, the radius ratio, temperature difference, and nonlocality on the vibrational frequency of the system is investigated in detail.

• Steel and Composite Structures
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• 제46권5호
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• pp.611-619
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• 2023

In the present work, the flutter characteristics of porous nanocomposite cylindrical shells, reinforced with graphene platelets (GPLs) in supersonic airflow, have been investigated. Different distributions for GPLs and porosities have been considered which are named uniform and non-uniform distributions thorough the shell's thickness. The effective material properties have been determined via Halpin-Tsai micromechanical model. The cylindrical shell formulation considering supersonic airflow has been developed in the context of first-order shell and first-order piston theories. The governing equations have been solved using Galerkin's method to find the frequency-pressure plots. It will be seen that the flutter points of the shell are dependent on the both amount and distribution of porosities and GPLs and also shell geometrical parameters.

• Steel and Composite Structures
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• 제48권3호
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• pp.263-273
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• 2023

This paper investigates dynamic characteristics of a graphene nanoplatelets reinforced composite (GNPRC) sandwich doubly curved shell based on the first-order shear deformation theory (FSDT) and Hamilton's principle. The sandwich doubly curved shell is fabricated from a core made of honeycomb materials sandwiched by composite GNPs reinforced face-sheets. Effective materials properties of composite face-sheets are assumed to vary based on Halpin-Tsai micromechanical models and rule of mixture. Furthermore, the material properties of honeycomb core are estimated using Gibson's formula. The fundamental frequencies of the shell are computed with changes of main geometrical and material properties such as amount and distribution type of graphene nanoplatelets, side length ratio, thickness to length ratio of and side length ratio of honeycomb. The Navier's technique is presented to obtain responses. Accuracy and trueness of the present model and analytical solution is confirmed through comparison of the results with available results in literature. It is concluded that an increase in thickness to length ratio yields a softer core with lower natural frequencies. Furthermore, increase in height to length ratio leads to significant decrease in natural frequencies.

• Steel and Composite Structures
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• 제46권2호
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• pp.203-210
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• 2023

In the present research, dynamic deflections of a sandwich beam having functionally graded (FG) porous core have been investigated assuming that the sandwich beam is exposed to a pulse load of blast type. The two layers of sandwich beam have been made of a polymeric matrix reinforced by graphene oxide powder (GOP). The micromechanical formulation of the layers has been done via Halpin-Tsai model. The solution method is chosen to be Ritz method which is an efficient method to solve the system of equations of beams modeled based on a higher-order theory. To derive the time history of sandwich beam under pulse load, Laplace method has been used. The porosity content of the core, the GOP content of the layers, thickness of the layer and also duration of the applied load have great influences of the responses of sandwich beam.