• Journal of applied mathematics & informatics
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• 제38권3_4호
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• pp.311-334
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• 2020

The solution of the elliptic partial differential equation has interface singularity at the points which are either the intersections of interfaces or the intersections of interfaces with the boundary of the domain. The singularities that arises in the elliptic interface problems are very complex. In this article we propose an exponentially accurate nonconforming spectral element method for these problems based on [7, 18]. A geometric mesh is used in the neighbourhood of the singularities and the auxiliary map of the form z = ln ξ is introduced to remove the singularities. The method is essentially a least-squares method and the solution can be obtained by solving the normal equations using the preconditioned conjugate gradient method (PCGM) without computing the mass and stiffness matrices. Numerical examples are presented to show the exponential accuracy of the method.

• Structural Engineering and Mechanics
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• 제60권2호
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• pp.271-299
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• 2016

In this article, based on the higher-order shear deformation plate theory, buckling analysis of a rectangular plate made of functionally graded piezoelectric materials and its effective parameters are investigated. Assuming the transverse distribution of electric potential to be a combination of a parabolic and a linear function of thickness coordinate, the equilibrium equations for the buckling analysis of an FGP rectangular plate are established. In addition to the Maxwell equation, all boundary conditions including the conditions on the top and bottom surfaces of the plate for closed and open circuited are satisfied. Considering double sine solution (Navier solution) for displacement field and electric potential, an analytical solution is obtained for full simply supported boundary conditions. The accurate buckling load of FGP plate is presented for both open and closed circuit conditions. It is found that the critical buckling load for open circuit is more than that of closed circuit in all loading conditions. Furthermore, it is observed that the influence of dielectric constants on the critical buckling load is more than those of others.

• Structural Engineering and Mechanics
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• 제34권1호
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• pp.85-95
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• 2010

In this paper, numerical solution of the singular integral equation for the multiple curved branch-cracks is investigated. If some quadrature rule is used, one difficult point in the problem is to balance the number of unknowns and equations in the solution. This difficult point was overcome by taking the following steps: (a) to place a point dislocation at the intersecting point of branches, (b) to use the curve length method to covert the integral on the curve to an integral on the real axis, (c) to use the semi-open quadrature rule in the integration. After taking these steps, the number of the unknowns is equal to the number of the resulting algebraic equations. This is a particular advantage of the suggested method. In addition, accurate results for the stress intensity factors (SIFs) at crack tips have been found in a numerical example. Finally, several numerical examples are given to illustrate the efficiency of the method presented.

• 호남수학학술지
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• 제45권4호
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• pp.619-628
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• 2023

In this paper, the fractional order time-varying linear dynamical systems are investigated by using a residual power series method. A residual power series method (RPSM) is constructed for this problem. The exact solution is obtained by the Laplace transform method and the analytical solution is calculated via the residual power series method (RPSM). As an application, some examples are tested to show the accuracy and efficacy of the proposed methods. The obtained result showed that the proposed methods are effective and accurate for this type of problem.

• 한국소음진동공학회논문집
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• 제22권8호
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• pp.742-747
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• 2012

A modified NDIF method using a sub-domain approach is introduced to extract highly accurate eigenvalues of two-dimensional, arbitrarily shaped acoustic cavities. The NDIF method, which was developed by the authors for the eigen-mode analysis of arbitrarily shaped acoustic cavities, has the feature that it yields highly accurate eigenvalues compared with other analytical methods or numerical methods(FEM and BEM). However, the NDIF method has the weak point that it can be applicable for only convex cavities. It was revealed that the solution of the NDIF method is very inaccurate or is not suitable for concave cavities. To overcome the weak point, the paper proposes the sub-domain method of dividing a concave domain into several convex domains. Finally, the validity of the proposed method is verified in two case studies, which indicate that eigenvalues obtained by the proposed method are more accurate compared to the exact method, the NDIF method, or FEM(ANSYS).

• 한국소음진동공학회논문집
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• 제22권9호
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• pp.830-836
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• 2012

The NDIF method based on a sub-domain technique is introduced to extract highly accurate natural frequencies of arbitrarily shaped plates with the simply-supported boundary condition. The NDIF method, which was developed by the authors for the eigen-mode analysis of arbitrarily shaped plates with various boundary conditions, has the feature that it yields highly accurate natural frequencies thanks to its effective theoretical formulation, compared with other analytical methods or numerical methods(FEM and BEM). However, the NDIF method has the weak point that it can be applicable for only convex plates. It was revealed that the NDIF method offers very inaccurate natural frequencies or no solution for concave cavities. To overcome the weak point, the paper proposes the sub-domain method of dividing a concave plate into several convex domains. Finally, the validity of the proposed method is verified in various case studies, which indicate that natural frequencies obtained by the proposed method are very accurate compared to the exact method and FEM(ANSYS).

• Journal of Positioning, Navigation, and Timing
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• 제5권1호
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• pp.1-9
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• 2016

Range-based wireless localization system must measure accurate range between a mobile node (MN) and reference nodes. However, non-line-of-sight (NLOS) error caused by the spatial structures disturbs the localization system obtaining the accurate range measurements. Localization methods using the range measurements including NLOS error yield large localization error. But filter-based localization methods can provide comparatively accurate location solution. Motivated by the accuracy of the filter-based localization method, a filter residual-based NLOS error estimation method is presented in this paper. Range measurement-based residual contains NLOS error. By considering this factor with NLOS error properties, NLOS error is mitigated. Also a process noise covariance matrix tuning method is presented to reduce the time-delay estimation error caused by the single dynamic model-based filter when the speed or moving direction of a MN changes, that is the used dynamic model is not fit the current dynamic of a MN. The presented methods are evaluated by simulation allowing direct comparison between different localization methods. The simulation results show that the presented filter is more accurate than the iterative least squares- and extended Kalman filter-based localization methods.

• Bulletin of the Korean Chemical Society
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• 제25권2호
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• pp.233-236
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• 2004

Total impurity analysis of a primary standard solution is one of the essential procedures to determine an accurate concentration of the standard solution by the gravimetry. Bi impurity is determined in Pb standard solutions by inductively coupled plasma mass spectrometry (ICP-MS). The direct nebulization of the Pb standard solution produces a significant amount of the Pb matrix-induced molecular ions which give rise to a serious spectral interference to the Bi determination. In order to avoid the spectral interference from the interferent $^{208}PbH^+$, the hydride generation method is employed for the matrix separation. The Bi hydride vapor is generated by reaction of the sample solution with 1% sodium borohydride solution. The vapor is then directed by argon carrier gas into the ICP after separation from the mixture solution in a liquid-gas separator made of a polytetrafluoroethylene membrane tube. The presence of 1000 ${\mu}$g/mL Pb matrix caused reduction of the bismuthine generation efficiency by about 40%. The standard addition method is used to overcome the chemical interference from the Pb matrix. Optimum conditions are investigated for the hydride-generation ICPMS. The detection limit of this method is 0.5 pg/mL for the sample solutions containing 1000 ${\mu}$g/mL Pb matrix.

• Structural Engineering and Mechanics
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• 제35권2호
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• pp.205-215
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• 2010

Recently, earthquake proof technology has been widely applied to both new and existing structures and bridges. The analysis of bridge systems equipped with structural control devices, which possess large degrees of freedom and nonlinear characteristics, is a result in time-consuming task. Therefore, a piecewise exact solution is proposed in this study to simplify the seismic mitigation analysis process for bridge systems equipped with sliding-type isolators. In this study, the simplified system having two degrees of freedom, to reasonably represent the large number of degrees of freedom of a bridge, and is modeled to obtain a piecewise exact solution for system responses during earthquakes. Simultaneously, we used the nonlinear finite element computer program to analyze the bridge responses and verify the accuracy of the proposed piecewise exact solution for bridge systems equipped with sliding-type isolators. The conclusions derived by comparing the results obtained from the piecewise exact solution and nonlinear finite element analysis reveal that the proposed solution not only simplifies the calculation process but also provides highly accurate seismic responses of isolated bridges under earthquakes.

• Computers and Concrete
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• 제18권1호
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• pp.17-37
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• 2016

This paper compares the arc-length and explicit dynamic solution methods for nonlinear finite element analysis of prestressed concrete members subjected to monotonically increasing loads. The investigations have been conducted using an L-shaped, prestressed concrete spandrel beam, selected as a highly nonlinear problem from the literature to give insight into the advantages and disadvantages of these two solution methods. Convergence problems, computational effort, and quality of the results were investigated using the commercial finite element package ABAQUS. The work in this paper demonstrates that a static analysis procedure, based on the arc-length method, provides more accurate results if it is able to converge on the solution. However, it experiences convergence problems depending upon the choice of mesh configuration and the selection of concrete post-cracking response parameters. The explicit dynamic solution procedure appears to be more robust than the arc-length method in the sense that it provides acceptable solutions in cases when the arc-length approach fails, however solution accuracy may be slightly lower and computational effort may be significantly larger. Furthermore, prestressing forces must be introduced into the finite element model in different ways for the explicit dynamic and arc-length solution procedures.