• Steel and Composite Structures
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• 제39권3호
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• pp.275-290
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• 2021

The main purpose of this research work is to investigate the critical buckling load of functionally graded (FG) porous plates with graphene platelets (GPLs) reinforcement using generalized differential quadrature (GDQ) method at thermal condition. It is supposed that the GPL nanofillers and the porosity coefficient vary continuously along the plate thickness direction. Generally, the thermal distribution is considered to be nonlinear and the temperature changing continuously through the thickness of the nanocomposite plates according to the power-law distribution. To model closed cell FG porous material reinforced with GPLs, Halpin-Tsai micromechanical modeling in conjunction with Gaussian-Random field scheme are used, through which mechanical properties of the structures can be extracted. Based on the third order shear deformation theory (TSDT) and the Hamilton's principle, the equations of motion are established and solved for various boundary conditions (B.Cs). The fast rate of convergence and accuracy of the method are investigated through the different solved examples and validity of the present study is evaluated by comparing its numerical results with those available in the literature. A special attention is drawn to the role of GPLs weight fraction, GPLs patterns through the thickness, porosity coefficient and distribution of porosity on critical buckling load. Results reveal that the importance of thermal condition on of the critical load of FGP-GPL reinforced nanocomposite plates.

• Steel and Composite Structures
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• 제47권5호
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• pp.569-585
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• 2023

This paper proposes an efficient approach for the structural topology optimization of bi-directional functionally graded structures by incorporating popular radial basis functions (RBFs) into an implicit level set (ILS) method. Compared to traditional element density-based methods, a level set (LS) description of material boundaries produces a smoother boundary description of the design. The paper develops RBF implicit modeling with multiquadric (MQ) splines, thin-plate spline (TPS), exponential spline (ES), and Gaussians (GS) to define the ILS function with high accuracy and smoothness. The optimization problem is formulated by considering RBF-based nodal densities as design variables and minimizing the compliance objective function. A LS-RBF optimization method is proposed to transform a Hamilton-Jacobi partial differential equation (PDE) into a system of coupled non-linear ordinary differential equations (ODEs) over the entire design domain using a collocation formulation of the method of lines design variables. The paper presents detailed mathematical expressions for BiDFG beams topology optimization with two different material models: continuum functionally graded (CFG) and mechanical functionally graded (MFG). Several numerical examples are presented to verify the method's efficiency, reliability, and success in accuracy, convergence speed, and insensitivity to initial designs in the topology optimization of two-dimensional (2D) structures. Overall, the paper presents a novel and efficient approach to topology optimization that can handle bi-directional functionally graded structures with complex geometries.

• 한국소음진동공학회논문집
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• 제14권1호
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• pp.56-63
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• 2004

Exact solutions are presented for the free vibration and buckling of rectangular plates haying two opposite edges ( x=0 and a) simply supported and the other two ( y=0 and b) clamped, with the simply supported edges subjected to a linearly varying normal stress $\sigma$$_{x}$=- $N_{0}$[1-a(y/b)]/h, where h is the plate thickness. By assuming the transverse displacement ( w) to vary as sin(m$\pi$x/a), the governing partial differential equation of motion is reduced to an ordinary differential equation in y with variable coefficients. for which an exact solution is obtained as a power series (the method of Frobenius). Applying the clamped boundary conditions at y=0 and byields the frequency determinant. Buckling loads arise as the frequencies approach zero. A careful study of the convergence of the power series is made. Buckling loads are determined for loading parameters a= 0, 0.5, 1, 1.5. 2, for which a=2 is a pure in-plane bending moment. Comparisons are made with published buckling loads for a= 0, 1, 2 obtained by the method of integration of the differential equation (a=0) or the method of energy (a=1, 2). Novel results are presented for the free vibration frequencies of rectangular plates with aspect ratios a/b =0.5, 1, 2 when a=2, with load intensities $N_{0}$ / $N_{cr}$ =0, 0.5, 0.8, 0.95, 1. where $N_{cr}$ is the critical buckling load of the plate. Contour plots of buckling and free vibration mode shapes ate also shown.shown.

• 대한기계학회논문집
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• 제16권4호
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• pp.621-629
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• 1992

본 연구에서는 Kelvin의 기본해와 초기응력 증분에 의해 정식화된 경계적분방 정식을 이용하여 점차적으로 외력을 증가시켰을 때, 선형등방경화재에 국부적으로 생 기는 항복영역과 항복하중, 탄소성 응력해석등을 재료비선형문제로 해석하였다. 이 때 초기응력 증분을 결정함에 있어서 종래에는 등가 소성변형률을 수렴판정으로 해석 하였지만, 이는 구분적인 선형 경화재와 온도 의존성 문제에는 적당하지 않으므로 암 기용일등은 등가응력과 응력-변형률 선도를 이용하여 수렴판정을 하였다. 그러나 이 방법은 소성역에서의 기울기가 변화하는 곳에서는 피할 수 없는 오차가 존재한다. 따라서 여기에서는 계산된 초기응력 증분에 의한 초기 탄성변형률에너지 증분과 응력 -변형률선도로 부터 구해지는 초기 탄성변형률에너지 증분을 이용한 수렴판정으로 초 기응력증분을 결정하였다. 또한, 내부영역적분을 일부 해석적인 적분과 수치적분을 병행한 경우와 전부 수치적분방법으로 내압을 받는 실린더와 단순 인장하중이 작용하 는 양편 Ⅴ형 노치를 갖는 박판의 경우에 적용하여 해석하였으며, 그 결과를 유한요소 법 프로그램인 NISA(numerically integrated elements for system analysis)로 구한 결과치와 비교, 고찰하였다.

• 대한기계학회논문집A
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• 제26권6호
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• pp.1169-1177
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• 2002

A study of fee vibration of circular Mindlin plates is presented. The analysis is based on the pseudospctral method, which uses Chebyshev polynomials and Fourier series as basis functions. It Is demonstrated that rapid convergence and accuracy as well as the conceptual simplicity could be achieved when the pseudospectral method was apt)lied to the solution of eigenvalue problems. Numerical examples of circular Mindlin plates with clamped and simply supported boundary conditions are provided for various thickness-to-radius ratios.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.495-500
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• 2007

A Meshfree is a method used to establish algebraic equations of system for the whole problem domain without the use of a predefined mesh for the domain discretization. A point interpolation method is based on combining radial and polynomial basis functions. Involvement of radial basis functions overcomes possible singularity. Furthermore, the interpolation function passes through all scattered points in an influence domain and thus shape functions are of delta function property. This makes the implementation of essential boundary conditions much easier than the meshfree methods based on the moving least-squares approximation. This study aims to investigate a stress analysis of structural element between a meshfree method and the finite element method. Examples on cantilever type plate and stress concentration problems show that the accuracy and convergence rate of the meshfree methods are high.

• 열처리공학회지
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• 제32권1호
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• pp.1-11
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• 2019

In this study, microstructure evolution and crystallographic orientation are investigated under various deformation conditions in M1 magnesium alloy. M1 magnesium ingot was rolled at 673 K with the rolling reduction of 30%. The compression test specimens were machined out from rolled plate, and then the specimens were annealed at 823 K for 1h. Uniaxial compression tests were conducted at 723 K and under the strain rate ranging from $5.0{\times}10^{-4}s^{-1}$ to $5.0{\times}10^{-2}s^{-1}$ up to a true strain of -1.0. For observation of crystal orientation distribution, EBSD measurement was performed. Occurrence of the dynamic recrystallization and grain boundary migration were confirmed in all case of the specimens. The distribution of the grains is not uniformed in the experimental conditions.

• 한국산업융합학회 논문집
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• 제20권2호
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• pp.133-140
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• 2017

This paper is a study of the central structural unit model of the sandwich core structure. The applied model is based on the honeycomb structure formed by the truss, the H-shaped honeycomb structure formed by adding the truss of H shape to the space of the center portion, and the honeycomb structure formed by the plate. Applied material property is AISI 304 stainless steel, which has cost effectiveness and easy to get near place. The truss diameter of the model is three different type: 1mm, 2mm and 3mm. ABAQUS software is obtained to do the analysis and applied test is quasi-static loading. Boundary conditions for the analysis are that vertical direction loading at top place without any rotation and bottom surface is fixed. The test results show that the H-truss model has the highest stiffness and yield strength. Therefore, it is hoped that more and more researching for the development of a unit model in sandwich core structure has been investigating and that the developed sandwich core model can be applied into various industrial fields such as mechanical or aerospace industries.

• 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.

• 자원환경지질
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• 제45권2호
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• pp.145-156
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• 2012

해저열수시스템은 중앙해령이나 후열도확장대와 같은 해저화산대를 따라 생성된다. 해저열수시스템은 지각-맨틀과 해양의 에너지와 물질이 교환되는 장으로 이를 통해 지각과 해수의 조성이 변화하며, 해저면에 열수분출구를 침전시켜 열수생태계를 형성하고 금속광상이 만들어진다. 상대적으로 단순한 중앙해령과 달리 지판소멸지역의 해저열수시스템은 섭입되는 물질의 재순환과정에서 다양한 특성이 나타난다. 황동위원소 조성은 이러한 열수시스템의 다양성을 평가하는데 유용하다. 이 논문에서는 서태평양의 지판소멸대에서 발견된 열수분출 지역에서 채취된 열수분출구 시료의 황동위원소 조성변화를 살펴보고 이들 환경에서 열수생성의 다양성을 일으키는 요인을 고찰하였다. 지판소멸대의 열수분출구는 황화광물과 황산염광물 모두 낮은 황동위원소 조성을 갖는 것이 특징이며, 이는 마그마로부터 공급된 $SO_2$ 기체의 유입으로 해석된다. 황동위원소 조성 변화를 포함한 열수시스템의 다양성은 열수시스템 생성과정에서 마그마의 적극적인 역할을 지시한다.