• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 봄 학술발표회 논문집
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• pp.497-504
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• 2002

In meshless methods, the moving least squares approximation technique is widely used to approximate a solution space because of its useful numerical characters such as non-element approximation, easily controllable smoothness, and others. In this work, a generalized version of the moving least squares method Is introduced to enhance the approximation performance through the Information converning to the derivative of the field variable. The results of numerical tests for approximation verify the improved accuracy of the generalized meshless approximation procedure compared to the conventional moving least squares method. By using this generalized moving least squares method, meshless analysis of thin beam is carried out, and its performance is investigated.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1997년도 가을 학술발표회 논문집
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• pp.16-23
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• 1997

The Reproducing Kernel Particle Method (RKPM), one of the popular meshless methods, is developed and applied to stress concentration problems. Since the meshless methods require only a set of particles (or nodes) and the description of boundaries in their formulation, the adaptivity can be implemented with much more ease than finite element method. In addition, due to its intrinsic property of multiresolution, the shape function of RKPM provides us a new criterion for adaptivity. Recently, this multiple scale Reproducing Kernel Particle Method and its adaptive procedure have been formulated for large deformation problems by the authors. They are also under development for damage materials and localization problems. In this paper the multiple scale RKPM for linear elasticity is presented and the adaptive procedure is applied to stress concentration problems. Therefore, this work may be regarded as the edition of linear elasticity in the complete framework of multiple scale RKPM and the associated adaptivity.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제1권1호
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• pp.1-34
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• 1997

In this study, various available meshless methods are briefly reviewed and the connection among them is investigated. The objective of meshless methods is to eliminate some difficulties which are originated from reliance on a mesh by constructing the approximation entirely in terms of nodes. Especially, focusing on Element Free Galerkin Method(EFGM) based on moving least square interpolants(MLSI), a new implementation is developed based on a variational principle with penalty function method were used to enforce the essential boundary condition. In addition, the weighted orthogonal basis functions are constructed to overcome disadvantage of MLSI.

• 한국자동차공학회논문집
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• 제15권2호
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• pp.101-108
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• 2007

This paper presents an efficient meshless method for analyzing cracked piezoelectric structures subjected to mechanical and electrical loading. The method employs an element free Galerkin (EFG) formulation and an enriched basic function as well as special shape functions that contain discontinuous derivatives. Based on the moving least squares (MLS) interpolation approach, The EFG method is one of the promising methods for dealing with problems involving progressive crack growth. Since the method is meshless and no element connectivity data are needed, the burdensome remeshing procedure required in the conventional finite element method (FEM) is avoided. The numerical results show that the proposed method yields an accurate near-tip stress field in an infinite piezoelectric plate containing an interior hole. Another example is to study a ceramic multilayer actuator. The proposed model was found to be accurate in the simulation of stress and electric field concentrations due to the abrupt end of an internal electrode.

• Steel and Composite Structures
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• 제27권3호
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• pp.255-271
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• 2018

This paper deals with the transient dynamic analysis and elastic wave propagation in a functionally graded graphene platelets (FGGPLs)-reinforced composite thick hollow cylinder, which is subjected to shock loading. A micromechanical model based on the Halpin-Tsai model and rule of mixture is modified for nonlinear functionally graded distributions of graphene platelets (GPLs) in polymer matrix of composites. The governing equations are derived for an axisymmetric FGGPLs-reinforced composite cylinder with a finite length and then solved using a hybrid meshless method based on the generalized finite difference (GFD) and Newmark finite difference methods. A numerical time discretization is performed for the dynamic problem using the Newmark method. The dynamic behaviors of the displacements and stresses are obtained and discussed in detail using the modified micromechanical model and meshless GFD method. The effects of the reinforcement of the composite cylinder by GPLs on the elastic wave propagations in both displacement and stress fields are obtained for various parameters. It is concluded that the proposed micromechanical model and also the meshless GFD method have a high capability to simulate the composite structures under shock loadings, which are reinforced by FGGPLs. It is shown that the modified micromechanical model and solution technique based on the meshless GFD method are accurate. Also, the time histories of the field variables are shown for various parameters.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1995년도 추계학술대회 논문집
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• pp.736-739
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• 1995

The meshless adaptive method based on multiple scale analysis is developed to simulate large deformation problems. In the procedure, new particles are simply added to the orginal particle distribution because meshless methods do not require mesh structures in the formulations. The high scale component of the approximated solution detects the localized region where a refinement is needed. The high scale component of the second invariant od Green-Lagrangian strain tensor is suggested as the new high gradient detector for adaptive procedures. The feasibility of the proposed theory is demonstrated by a numerical experiment for the large deformation of hyperelastic materials.

• 대한기계학회논문집A
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• 제24권11호
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• pp.2705-2712
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• 2000

In meshless methods some techniques to impose essential boundary conditions have been developed since the approximations do not satisfy Kronecker delta properties at nodal points. In this study, new scheme for imposing essential boundary conditions is developed. Weight functions are modified by multiplying with auxiliary weight functions and the resulting shape functions satisfy Kronecker delta property on the bound ary nodes. In addition, the resulting shape functions possess and interpolation features on the boundary segments where essential boundary conditions are prescribed. Therefore the essential boundary conditions can be exactly satisfied with the new method. More importantly, the impositions of essential boundary conditions using the present method is relatively easy as in finite element method. Numerical examples show that the method also retains high convergence rate comparable to Lagrange multiplier method.

• Structural Engineering and Mechanics
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• 제89권2호
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• pp.135-153
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• 2024

In this study, the impact response of a nanobeam with a moving nanoparticle is investigated. Timoshenko beam theory is used to model the nanobeam behavior and nonlocal elasticity theory is used to consider the effects of small dimensions. The interaction between the nanoparticle and nanobeam has been described using Lennard-Jones potential theory and the equations are discretized by the radial basis meshless method and a mathematical model is presented for the nanobeam-nanoparticle system. Validation of the proposed model is achieved by comparing the obtained natural frequencies with reference values, demonstrating good agreement. Dimensionless frequency analysis reveals a decrease with increasing nonlocal parameter, pointing out a toughening effect in nanobeam. The dynamic response of the nanobeam and nanoparticle is obtained by time integration of equations of motion using Newmark and Wilson-𝜃 methods. A comparative analysis of the two methods is conducted to determine the most suitable approach for this study. As a distinctive aspect in this study, the analysis incorporates the deformation of the nanobeam resulting from the nanoparticle-nanobeam interaction when calculating the Lennard-Jones force in the nanobeam-nanoparticle system. The numerical findings explore the impact of various factors, including the nonlocal parameter, initial velocity, nanoparticle mass, and boundary conditions.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2006년도 정기 학술대회 논문집
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• pp.357-364
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• 2006

The meshfree method is extended by the local partition of unity method to model the cohesive cracks in two dimensional continuum The shape function of a particle whose domain of influence is completely cut by a crack is enriched by the step enrichment function. If the domain of influence contains a crack tip inside, it is enriched by the branch enrichment function without the stress singularity. It is found that this method is more accurate and converges faster than the meshless methods for LEFM cracks based on the visibility concept Several staic and dynamic examples are solved to verify the method.

• Steel and Composite Structures
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• 제22권1호
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• pp.161-182
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• 2016

A state space differential reproducing kernel (DRK) method is developed for the three-dimensional (3D) analysis of functionally graded material (FGM) axisymmetric circular plates with simply-supported and clamped edges. The strong formulation of this 3D elasticity axisymmetric problem is derived on the basis of the Reissner mixed variational theorem (RMVT), which consists of the Euler-Lagrange equations of this problem and its associated boundary conditions. The primary field variables are naturally independent of the circumferential coordinate, then interpolated in the radial coordinate using the early proposed DRK interpolation functions, and finally the state space equations of this problem are obtained, which represent a system of ordinary differential equations in the thickness coordinate. The state space DRK solutions can then be obtained by means of the transfer matrix method. The accuracy and convergence of this method are examined by comparing their solutions with the accurate ones available in the literature.