• Steel and Composite Structures
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• 제35권1호
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• pp.77-92
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• 2020

The present paper outlined a procedure for geometrically nonlinear dynamic analysis of functionally graded graphene platelets-reinforced (GPLR-FG) nanocomposite cylinder subjected to mechanical shock loading. The governing equation of motion for large deformation problems is derived using meshless local Petrov-Galerkin (MLPG) method based on total lagrangian approach. In the MLPG method, the radial point interpolation technique is employed to construct the shape functions. A micromechanical model based on the Halpin-Tsai model and rule of mixture is used for formulation the nonlinear functionally graded distribution of GPLs in polymer matrix of composites. Energy dissipation in analyses of the structure responding to dynamic loads is considered using the Rayleigh damping. The Newmark-Newton/Raphson method which is an incremental-iterative approach is implemented to solve the nonlinear dynamic equations. The results of the proposed method for homogenous material are compared with the finite element ones. A very good agreement is achieved between the MLPG and FEM with very fine meshing. In addition, the results have demonstrated that the MLPG method is more effective method compared with the FEM for very large deformation problems due to avoiding mesh distortion issues. Finally, the effect of GPLs distribution on strength, stiffness and dynamic characteristics of the cylinder are discussed in details. The obtained results show that the distribution of GPLs changed the mechanical properties, so a classification of different types and volume fraction exponent is established. Indeed by comparing the obtained results, the best compromise of nanocomposite cylinder is determined in terms of mechanical and dynamic properties for different load patterns. All these applications have shown that the present MLPG method is very effective for geometrically nonlinear analyses of GPLR-FG nanocomposite cylinder because of vanishing mesh distortion issue in large deformation problems. In addition, since in proposed method the distributed nodes are used for discretization the problem domain (rather than the meshing), modeling the functionally graded media yields to more accurate results.

• Structural Engineering and Mechanics
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• 제74권5호
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• pp.679-698
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• 2020

In this paper, the meshless local Petrov-Galerkin (MLPG) method is developed for dynamic analysis of non-symmetric nanocomposite cylindrical shell equations of elastic wave motion with nonlinear grading patterns under shock loading. The mechanical properties of the nanocomposite cylinder are obtained based on a micro-mechanical model. In this study, four kinds of grading patterns are assumed for carbon nanotube mechanical properties. The displacements can be approximated using shape function so, the multiquadrics (MQ) Radial Basis Functions (RBF) are used as the shape function. In order to discretize the derived equations in time domains, the Newmark time approximation scheme with suitable time step is used. To demonstrate the accuracy of the present method for dynamic analysis, at the first a problem verifies with analytical solution and then the present method compares with the finite element method (FEM), finally, the present method verifies by using the element free Galerkin (EFG) method. The comparison shows the high capacity and accuracy of the present method in the dynamic analysis of cylindrical shells. The capability of the present method to dynamic analysis of non-symmetric nanocomposite cylindrical shell is demonstrated by dynamic analysis of the cylinder with different kinds of grading patterns and angle of nanocomposite reinforcements. The present method shows high accuracy, efficiency and capability to dynamic analysis of non-symmetric nanocomposite cylindrical shell, which it furnishes a ground for a more flexible design.

• International Journal of Ocean System Engineering
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• 제2권4호
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• pp.200-208
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• 2012

Surge overflow may cause damage on earthen levees. Levee strengthened on the levee crest and landward-side slope can provide protection against the erosion damage induced by surge overflow. In this paper, surge overflow of a roller compacted concrete RCC strengthened levee was studied in a purely Lagrangian and meshless approach, the smoothed particle hydrodynamics (SPH) method. After verifying the developed model with analytical solution and comparing the results with full-scale experimental data, the roughness and erosion parameters were calibrated. The water thickness, flow velocity, and erosion depth at crest, landward-side slope and toe were calculated. The characteristics of flow hydraulics and erosion on the RCC strengthened levee are given. The results indicate that the RCC strengthened levee can resist erosion damage for a long period.

• 대한기계학회논문집A
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• 제26권11호
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• pp.2312-2321
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• 2002

The first-order least-squares meshfree method for linear elasticity is presented. The conventional and the compatibility-imposed least-squares formulations are studied on the convergence behavior of the solution and the robustness to integration error. Since the least-squares formulation is a type of mixed formulation and induces positive-definite system matrix, by using shape functions of same order for both primal and dual variables, higher rate of convergence is obtained for dual variables than Galerkin formulation. Numerical examples also show that the presented formulations do not exhibit any volumetric locking for the incompressible materials.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 춘계학술대회 논문집 전기기기 및 에너지변환시스템부문
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• pp.59-61
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• 2003

The natural element method is a kind of meshless Galerkin method. The shape function is derived from the natural neighbor coordinates interpolation scheme. Natural neighbor shape functions are $C^0$ everywhere, except the nodes where they are $C^0$. The numerical integration is carried out using the Delaunay triangles as the background cells. The method is applied to the test problems and simulation results show that the natural element method can give accurate solutions for the electromagnetic field problems.

• Journal of Electrical Engineering and Technology
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• 제4권2호
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• pp.272-276
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• 2009

In this paper, the arc region of a gas circuit breaker (GCB) is analyzed using the fast moving least square reproducing kernel method (FMLSRKM) which can simultaneously calculate an approximated solution and its derivatives. For this problem, an axisymmetric and inhomogeneous formulation of the FMLSRKM is used and applied. The field distribution obtained by the FMLSRKM is compared to that of the finite element method. Then, a whole breaking period of a GCB is simulated, including analysis of the arc gas flow by finite volume fluid in the cell, and the electric field of the arc region using the FMLSRKM.

• Structural Engineering and Mechanics
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• 제30권1호
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• pp.119-129
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• 2008

A small strain and elastoplastic formulation of Polygonal Element Method (PEM) is developed for efficient analysis of elastoplastic solids. In this work, the polygonal elements are constructed based on traditional triangular finite meshes. The construction method of polygonal mesh can directly utilize the sophisticated triangularization algorithm and reduce the difficulty in generating polygonal elements. The Wachspress rational finite element basis function is used to construct the approximations of polygonal elements. The incremental variational form and a von Mises type model are used for non-linear elastoplastic analysis. Several small strain elastoplastic numerical examples are presented to verify the advantages and the accuracy of the numerical formulation.

• Korea-Australia Rheology Journal
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• 제21권1호
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• pp.1-12
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• 2009

This paper reports the suitability of a domain decomposition technique for the hybrid simulation of dilute polymer solution flows using Eulerian Brownian dynamics and Radial Basis Function Networks (RBFN) based methods. The Brownian Configuration Fields (BCF) and RBFN method incorporates the features of the BCF scheme (which render both closed form constitutive equations and a particle tracking process unnecessary) and a mesh-less method (which eliminates element-based discretisation of domains). However, when dealing with large scale problems, there appear several difficulties: the high computational time associated with the Stochastic Simulation Technique (SST), and the ill-condition of the system matrix associated with the RBFN. One way to overcome these disadvantages is to use parallel domain decomposition (DD) techniques. This approach makes the BCF-RBFN method more suitable for large scale problems.

• 대한기계학회논문집A
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• 제26권9호
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• pp.1849-1858
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• 2002

An h-adaptive scheme of first-order least-squares meshfree method is presented. A posteriori error estimates, which can be readily computed from the residual, are also presented. For elliptic problem the error indicators are further improved by applying the Aubin-Nitsche method. In the proposed refinement scheme, Voronoi cells are utilized to insert nodes at appropriate positions. Through numerical examples, it is demonstrated that the error indicators reveal good correlations with the actual errors and the adaptive first-order least-squares meshfree method is effectively applied to the localized problems such as the shock formation in fluid dynamics.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2006년도 정기 학술대회 논문집
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• pp.365-372
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• 2006

A new meshfree formulation is developed for material discontinuity problems. A local interfacial jump function which is defined as hyperplane function is embedded in the meshless approximation and the approximation accurately models functions with jumps in the displacement and the derivative fields. Diffuse derivative technique copes with difficulty due to complexity of derivative computation of meshfree approximation. Collocation method with diffuse derivative accelerates computing speed for numerical solution. By solving inclusion and composite material problems, the robustness and effectiveness of the method are verified.