• Structural Engineering and Mechanics
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• v.39 no.4
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• pp.579-598
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• 2011

The present work mainly reports a significant development of a novel efficient meshfree method for vibration and buckling analysis of orthotropic plates. The plate theory with orthotropic materials is followed the Kirchhoff''s assumption in which the only deflection is field variable and approximated by the moving Kriging interpolation approach, a new technique used for constructing the shape functions. The moving Kriging technique holds the Kronecker delta property, thus it makes the method efficiently in imposing the essential boundary conditions and no special techniques are required. Assessment of numerical results is to accurately illustrate the applicability and the effectiveness of the proposed method in the class of eigenvalue problems.

• Interaction and multiscale mechanics
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• v.7 no.1
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• pp.525-542
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• 2014

The state-based peridynamics is considered a nonlocal method in which the equations of motion utilize integral form as opposed to the partial differential equations in the classical continuum mechanics. As a result, the enforcement of boundary conditions in solid mechanics analyses cannot follow the standard way as in a classical continuum theory. In this paper, a new approach for the boundary condition enforcement in the state-based peridynamic formulation is presented. The new method is first formulated based on a convex kernel approximation to restore the Kronecker-delta property on the boundary in 1-D case. The convex kernel approximation is further localized near the boundary to meet the condition that recovers the correct boundary particle forces. The new formulation is extended to the two-dimensional problem and is shown to reserve the conservation of linear momentum and angular momentum. Three numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed approach.

• 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.

• Wind and Structures
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• v.27 no.4
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• pp.235-245
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• 2018

In this study the stress analysis of orthotropic thin plate with arbitrary shapes for different boundary conditionsis investigated. Meshfreemethod is applied to static analysis of thin plates with various geometries based on the Kirchhoff classical plate theory. According to the meshfree method the domain of the plates are expressed through a set of nodes without using mesh. In this method, a set of nodes are defined in a standard rectangular domain, then via a third order map, these nodes are transferred to the main domain of the original geometry; therefore the analysis of the plates can be done. Herein, Meshless local Petrov-Galerkin (MLPG) as a meshfree numerical method is utilized. The MLS function in MLPG does not satisfy essential boundary conditions using Delta Kronecker. In the MLPG method, direct interpolation of the boundary conditions can be applied due to constructing node by node of the system equations. The detailed parametric study is conducted, focusing on the arbitrary geometries of the thin plates. Results show that the meshfree method provides better accuracy rather than finite element method. Also, it is found that trend of the figures have good agreement with relevant published papers.

• Interaction and multiscale mechanics
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• v.6 no.2
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• pp.237-255
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• 2013

In this paper, a meshfree-enriched finite element method (ME-FEM) is introduced for the large deformation analysis of nonlinear path-dependent problems involving contact. In linear ME-FEM, the element formulation is established by introducing a meshfree convex approximation into the linear triangular element in 2D and linear tetrahedron element in 3D along with an enriched meshfree node. In nonlinear formulation, the area-weighted smoothing scheme for deformation gradient is then developed in conjunction with the meshfree-enriched element interpolation functions to yield a discrete divergence-free property at the integration points, which is essential to enhance the stress calculation in the stage of plastic deformation. A modified variational formulation using the smoothed deformation gradient is developed for path-dependent material analysis. In the industrial metal forming problems, the mortar contact algorithm is implemented in the explicit formulation. Since the meshfree-enriched element shape functions are constructed using the meshfree convex approximation, they pose the desired Kronecker-delta property at the element edge thus requires no special treatments in the enforcement of essential boundary condition as well as the contact conditions. As a result, this approach can be easily incorporated into a conventional displacement-based finite element code. Two elasto-plastic problems are studied and the numerical results indicated that ME-FEM is capable of delivering a volumetric locking-free and pressure oscillation-free solutions for the large deformation problems in metal forming analysis.

• Structural Engineering and Mechanics
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• v.18 no.2
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• pp.247-262
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• 2004

In the earlier application of the spline finite strip method(FSM), the uniform B3-spline functions were used in the longitudinal direction while the conventional interpolation functions were used in the transverse direction to construct the displacement filed in a strip. To overcome the shortcoming of the uniform B3-spline, non-periodic B-spline was developed as the displacement function. The use of non-periodic B3-spline function requires no tangential vectors at both ends to interpolate the geometry of shell and the Kronecker delta property is also satisfied at the end boundaries. Recently, non-periodic spline FSM which was modified to have a multiple knots at the boundary was developed for the shell analysis and applied to the analysis of bridges. In the formulation of a non-symmetric spline finite strip method, the concepts of non-periodic B3-spline and a stress-resultant finite strip with drilling degrees of freedom for a shell are used. The introduction of non-symmetrically spaced knots in the longitudinal direction allows the selective local refinement to improve the accuracy of solution at the connections or at the location of concentrated load. A number of numerical tests were performed to prove the accuracy and efficiency of the present study.

• Proceedings of the Korea Society of Information Technology Applications Conference
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• 2002.11a
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• pp.407-411
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• 2002

Ternary sequences are digital codes consisting of discrete values -1, 0, and 1 only. They are advantageous in that the correlation can be carried out using additions only. Also, they feature an ideal circular autocorrelation function, but in channel characterization tasks, the usual requirement is that the linear autocorrelation function be ideal, i.e., a Kronecker delta function. In this article, we consider two approaches to improving their linear autocorrelation or crosscorrelation properties: one is an inverse filtering method with thresholding, and the other is a singular value decomposition (SVD) method. Both methods are simulated under noisy circumstances. The inverse filtering method resulted in an improvement in peak sidelobe level of about 11 dB at an SNR of 30 dB, and the SVD method showed similar performances, albeit more sensitive to noise depending on the singular value selection strategy.

• Proceedings of the Korea Society for Industrial Systems Conference
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• 2002.11a
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• pp.407-411
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• 2002

Ternary sequences are digital codes consisting of discrete values -1, 0, and 1 only. They are advantageous in that the correlation can be carried out using additions only Also, they feature an ideal circular autocorrelation function, but in channel characterization tasks, the usual requirement is that the linear autocorrelation function be ideal, i.e., a Kronecker delta function. In this article, we consider two approaches to improving their linear autocorrelation or crosscorrelation properties: one is an inverse filtering method with theresholding and the other is a singular value decomposition (SVD) method. Both methods are simulated under noisy circumstances. The inverse filtering method resulted in an improvement in peak sidelobe level of about 1㏈ at an SNR of 30㏈, and the SVD method showed similar performances, albeit more sensitive to noise depending on the singular value selection strategy.

• The Journal of the Korea institute of electronic communication sciences
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• v.12 no.6
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• pp.1027-1034
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• 2017

In this paper, we propose a new function embedding method that can measure mathematical projections of probability amplitude, probability, average expectation and matrix elements of stationary-state unit matrix at all control operation points of quantum gates. The function embedding method in this paper is to embed orthogonal normalization condition of probability amplitude for each control operating point into a binary scalar operator by using Dirac symbol and Kronecker delta symbol. Such a function embedding method is a very effective means of controlling the arithmetic power function of a unitary gate in a unitary transformation which expresses a quantum gate function as a tensor product of a single quantum. We present the results of evolutionary operation and projective measurement when we apply the proposed function embedding method to the ternary 2-qutrit cNOT gate and compare it with the existing methods.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.4
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• pp.335-341
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• 2009

In this paper, review of developed MLS-based finite elements and a proposal for their applications are described. The shape functions and their derivatives of MLS-based finite elements are constructed using Moving-Least Square approximation. In MLS-based finite element, using the adequate influence domain of weight function used in MLS approximation, kronecker delta condition could be satisfied at the element boundary. Moreover, because of the characteristics of MLS approximation, we could easily add extra nodes at an arbitrary position in MLS-based finite elements. For these reasons, until now, several variable-node elements(2D variable element for linear case and quadratic case and 3D variable-node elements) and finite crack elements are developed using MLS-based finite elements concept. MLS-based finite elements could be extended to 2D variable-node triangle element, 2D finite crack triangle element, variable-node shell element, finite crack shell element, and 3D polyhedron element. In this paper, we showed the feasibility of 3D polyhedron element at the case of femur meshing.