• Structural Engineering and Mechanics
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• v.51 no.6
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• pp.893-907
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• 2014

Meshless local collocation method produces much better conditioned matrices than meshless global collocation methods. In this paper, the meshless local collocation method based on thin plate spline radial basis function and first-order shear deformation theory are used to calculate the natural frequencies and mode shapes of laminated composite shells. Through numerical experiments, the accuracy and efficiency of present method are demonstrated.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.04a
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• pp.3-10
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• 1997

Meshless particle method is a numerical technique which does not use the concept of element. This method can easily handle special engineering problems which cause difficulty in the use of finite element method, however it has a drawback that essential boundary condition is not satisfied. In this paper, several studies for satisfying essential boundary conditions and enhancing the accuracy of solutions are discussed. Particular emphasis is placed on a new numerical technique in which finite elements are used on the boundaries to satisfy the essential boundary conditions and meshless particle method is used in the interior domain. For coupling of the two methods interface elements are introduced into the zone between the subdomains using meshless particle method and finite element method. The shape functions and the approximated displacement functions of the interface element are derived with the ramp function based on the shape function of finite elements. The whole numerical procedures are formulated by Galerkin method. Several numerical examples for enhancing the accuracy of solution in the meshless particle method and a new coupling method are presented.

• Structural Engineering and Mechanics
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• v.17 no.5
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• pp.671-690
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• 2004

A meshless method with novel variation of point collocation by finite mixture approximation is developed in this paper, termed the meshless finite mixture (MFM) method. It is based on the finite mixture theorem and consists of two or more existing meshless techniques for exploitation of their respective merits for the numerical solution of partial differential boundary value (PDBV) problems. In this representation, the classical reproducing kernel particle and differential quadrature techniques are mixed in a point collocation framework. The least-square method is used to optimize the value of the weight coefficient to construct the final finite mixture approximation with higher accuracy and numerical stability. In order to validate the developed MFM method, several one- and two-dimensional PDBV problems are studied with different mixed boundary conditions. From the numerical results, it is observed that the optimized MFM weight coefficient can improve significantly the numerical stability and accuracy of the newly developed MFM method for the various PDBV problems.

• Structural Engineering and Mechanics
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• v.23 no.3
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• pp.217-232
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• 2006

A crack model for the fracture in concrete based on meshless method is proposed in this paper. The cracks in concrete are classified into micro-cracks or macro-cracks respectively according to their widths, and different numerical approaches are adopted for them. The micro-cracks are represented with smeared crack approach whilst the macro-cracks are represented with discrete cracks that are made up with additional nodes and boundaries. The widely used meshless method, Element-free Galerkin method, is adopted instead of finite element method to model the concrete, so that the discrete crack approach is easier to be implemented with the convenience of arranging node distribution in the meshless method. Rotating-Crack-Model is proved to be preferred over Fixed-Crack-Model for the smeared cracks of this composite crack model due to its better performance on mesh bias. Numerical examples show that this composite crack model can take advantage of the positive characteristics in the smeared and discrete approaches, and overcome some of their disadvantages.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.732-735
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• 1995

A meshless method which is the new computational method being developed recently, is applied to the simulation of large deformation problems. Among the many types of meshless methods, the Reproducing Kernel particle method (RKPM) is used and the nearly incompressible hyperelastic materials are employed in simulations. The meshless methods can avoid metsh distortions and mesh entanglements that may frequently happen when the mesh-based methods like finite element method are used for the simulations of largely deformed materials. A general features of meshless methods are reviewed and the formulation of RKPM is presented. Next, the performance of explicit RKPM is demonstrated by examples.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.36 no.1
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• pp.67-74
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• 2023

A meshless technique using the geometric conservation least-squares method (GC-LSM) was devised to discretize the governing equation of linear elasticity. Although the finite-element method is widely used for structural analysis, a meshless method was developed because of its advantages in a moving grid system. This work is the preliminary phase for developing a fully meshless-based fluid-structure interaction solver. In this study, Cauchy's momentum equation was discretized in strong form using GC-LSM for the structural domain, and the Newmark beta method was used for time integration. The solver was validated in 1D, 2D, and 3D benchmarking problems. Static and dynamic results were obtained. The results are more accurate than those of analytic solutions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.9
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• pp.1376-1383
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• 2001

Meshless methods, developed in various ways over the past decade, have been attractive as new computational methods in that they do not need mesh generation in analyzing procedure. But most of these methods were not truly meshless methods because background meshes were required for the spatial integration of a weak form. Accordingly, in this paper, nodal integration for truly meshless methods has been studied, and an improvement scheme is proposed. To improve stabilization and accuracy, which are the weak points in previous nodal integration methods, the integration area is transformed to circle and then numerically integrated. This method does not need any adding term for stabilization in the variational formulation and then simplifies the integration procedure. Numerical test results show that the proposed method is more accurate, stable, and reasonable than the existed nodal integration methods.

• 연구논문집
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• s.29
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• pp.69-82
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• 1999

Numerical techniques for the simulations of crack propagation are reviewed. This paper highlights the meshless methods as a potential method for the simulations. thus they are reviewed deeply. Especially the theoretical aspects of meshless methods are discussed. and it is shown that all meshless methods are based on the PUM and unified in GFEM even though they are originated from different sources.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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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.

• Structural Engineering and Mechanics
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• v.81 no.5
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• pp.607-616
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• 2022

In this work, the free vibration problem of a rotating Rayleigh beam is solved using the meshless Petrov-Galerkin method which is a truly meshless method. The Rayleigh beam includes rotatory inertia in addition to Euler-Bernoulli beam theory. The radial basis functions, which satisfy the Kronecker delta property, are used for the interpolation. The essential boundary conditions can be easily applied with radial basis functions. The results are obtained using six nodes within a subdomain. The results accurately match with the published literature. Also, the results with Euler-Bernoulli are obtained to compare the change in higher natural frequencies with change in the slenderness ratio (${\sqrt{A_0R^2/I_0}}$). The mass and stiffness matrices are derived where we get two stiffness matrices for the node and boundary respectively. The non-dimensional form is discussed as well.