• Structural Engineering and Mechanics
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• v.70 no.6
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• pp.711-722
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• 2019

Considering stress singularities at point support locations, buckling solutions for plates with arbitrary number of point supports are hard to obtain. Thus, new Hp-Cloud shape functions with Kronecker delta property (HPCK) were developed in the present paper to examine elastic buckling of point-supported thin plates in various shapes. Having the Kronecker delta property, this specific Hp-Cloud shape functions were constructed through selecting particular quantities for influence radii of nodal points as well as proposing appropriate enrichment functions. Since the given quantities for influence radii of nodal points could bring about poor quality of interpolation for plates with sharp corners, the radii were increased and the method of Lagrange multiplier was used for the purpose of applying boundary conditions. To demonstrate the capability of the new Hp-Cloud shape functions in the domain of analyzing plates in different geometry shapes, various test cases were correspondingly investigated and the obtained findings were compared with those available in the related literature. Such results concerning these new Hp-Cloud shape functions revealed a significant consistency with those reported by other researchers.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11a
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• pp.155-160
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• 2001

Actual engineering structure is frequently very complex, and parts of structure are designed independently by different engineers. Also each structure contains so many degree of freedom. For these reason, methods have been developed which permits the structure to be divided into components or substructures, with analysis being done on a small substructure in order to obtain a full structural system. In such case, because of different mesh size among finite element model (FEM) or different matching points among FEM models and experimentally obtained models, their interfacing points may be non-matching. Solving this non-matching problem is useful to other application such as structural dynamic modification or model updating. In this work, virtual node concept is introduced. Lagrange multipliers are used to enforce the interface compatibility constraint, and interface displacement is approximated by polynomial presentation. The governing equation of whole structure is derived using hybrid variational principle. The eigenvalue of whole structure are calculated using the determinant search method. The number of degree of freedom in the eigenvalue problem can be drastically reduced to just the number of interface degree of freedom. Some numerical simulation is performed to show usefulness of synthesis method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.666-671
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• 2002

For a large structure, substructure based SDM(structural dynamics modification) method is very effective to raise its dynamic characteristics. Dividing into smaller substructures has a major advantage in the aspect of computation especially for getting sensitivities, which are in the core of SDM process. But quite often, non-matching nodes problem occurs in the process of synthesizing substructures. The reason is that, in general, each substructure is modelled separately, then later combined together to form a entire structure model under interface constraint conditions. Without solving the non-matching nodes problem, the substructure based SDM can not be processed. In this work, virtual node concept is introduced. Lagrange multipliers are used to enforce the interface compatibility constraint. The governing equation of whole structure is derived using hybrid variational principle. The eigenvalues of whole structure are calculated using determinant search method. The number of degrees of freedom of the eigenvalue problem can be drastically reduced to just the number of interface degree of freedom. Thus, the eigenvalue sensitivities can be easily calculated, and further SDM can be efficiently performed. Some numerical problems are tested to show the effectiveness of handling non-matching nodes.

• Tribology and Lubricants
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• v.36 no.5
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• pp.262-266
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• 2020

Herein, we present a numerical investigation of wear analysis of sliding systems with a constant speed subjected to Archard's wear law. For this investigation, we compared two methods: eigen-wear analysis and adaptive meshing technique. The eigen-wear analysis is advantageous to predict the evolution of contact pressure due to wear using the initial contact pressure and contact stiffness. The adaptive meshing technique in finite element analysis is employed to obtain transient wear behavior, which needs significant computational resources. From the eigen-wear analysis, we can determine the appropriate element size required for finite element analysis and the time increment required for wear evolution by a dimensionless variable above a certain value. Since the prediction of wear depends on the maximum contact pressure, the finite element model should have a reasonable representation of the maximum contact pressure. The maximum contact pressure and wear amount according to this dimensionless variable shows that the number of fine meshes in the contact area contributes more to the accuracy of the wear analysis, and the time increment is less sensitive when the number of contact nodes is significantly larger. The results derived from a two-dimensional wear model can be applied to a three-dimensional wear model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.3
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• pp.125-142
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• 2017

In this paper, development of the three-dimensional structural analysis is performed by applying FETI-local method. In the FETI-local method, the penalty term is added as a preconditioner. The OPT-DKT shell element is used in the present structural analysis. Newmark-${\beta}$ method is employed to conduct the dynamic analysis. The three-dimensional FETI-local static structural analysis is conducted. The contour and the displacement of the results are compared following the different number of sub-domains. The computational time and memory usage are compared with respect to the number of CPUs used. The three-dimensional dynamic structural analysis is conducted while applying FETI-local method. The present results show appropriate scalability in terms of the computational time and memory usage. It is expected to improve the computational efficiency by combining the advantages of the original FETI method, i.e., FETI-mixed using the mixed local-global Lagrange multiplier.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.77-81
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• 2003

SDM (Structural Dynamics Modification) is a tool to improve dynamic characteristics of a structure, more specifically of a base structure, by adding or deleting auxiliary (modifying) structures. In this paper, the goal of the optimal SDM is set to maximize the natural frequency of a base plate structure by attaching serially-connected beam stiffeners. The design variables are chosen as positions of the attaching beam stiffeners, where the number of stiffeners is considered as a design space. The problem of non-matching interface nodes between the base plate and beam stiffeners is solved by using localized Lagrange multipliers, which act to glue the two structures with non-matching interface nodes. As fer the cases of non-matching interface nodes problem, the governing equation of motion of a structure can be considered from the viewpoint of a topological modification, which involves the change of the number of structural members and DOFs. Consequently, the eigenpairs of the beam-stiffened plate structure are obtained by using an eigen reanalysis technique of topological modifications. Evolution Strategies (ES), which is a probabilistic population-based optimization technique that mimics the principles from biological evolution in nature, is utilized as a mean for the optimization.

• Geomechanics and Engineering
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• v.33 no.4
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• pp.381-391
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• 2023

The aim of this work is to analyze and predict the wave propagation behavior of the carbon nanotube reinforced composites (CNTRC) beams within the framework of various higher order shear deformation beam theory. Using the Euler-Lagrange principle, the wave equations for CNTRC beams are derived, where the determining factor is to make the determinant equal to zero. Based on the eigenvalue method, the relationship between wave number and circular frequency is obtained. Furthermore, the phase and group velocities during wave propagation are obtained as a function of wave number, and the material properties of CNTRC beams are estimated by the mixture rule. In this paper, various higher order shear beam theory including Euler beam theory, Timoshenko beam theory and other beam theories are mainly adopted to analyze the wave propagation problem of the CNTRC beams, and by this way, we conduct a comparative analysis to verify the correctness of this paper. The mathematical model provided in this paper is verified numerically by comparing it with some existing results. We further investigate the effects of different enhancement modes of CNTs, volume fraction of CNTs, spring factor and other aspects on the wave propagation behaviors of the CNTRC beams.

• Journal of the Institute of Electronics and Information Engineers
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• v.52 no.8
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• pp.3-9
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• 2015

Under the maximum transmit power constraint and the minimum rate constraint, we propose the optimal number of transmit antennas and transmit power which maximize energy-efficiency (EE) in multi-user multiple-input multiple-output (MIMO) downlink system with the maximal ratio transmission (MRT) precoding. Because the optimization problem for the instantaneous channel is difficult to solve, we use independence of individual channel, average channel gain and path loss to approximate the objective function. Since the approximated EE optimization problem is two-dimensional search problem, we find the optimal number of transmit antennas and transmit power using Lagrange multipliers and our proposed algorithm. Simulation results show that the number of transmit antennas and power obtained by proposed algorithm are almost identical to the value by the exhaustive search.

• Smart Structures and Systems
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• v.16 no.5
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• pp.781-806
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• 2015

A unified formulation of finite layer methods (FLMs), based on the Reissner mixed variational theorem (RMVT), is developed for the three-dimensional (3D) coupled electro-elastic analysis of simply-supported, functionally graded piezoelectric material (FGPM) plates with open- and closed-circuit surface conditions and under electro-mechanical loads. In this formulation, the material properties of the plate are assumed to obey an exponent-law varying exponentially through the thickness coordinate, and the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the primary field variables of each individual layer, respectively, such as the elastic displacement, transverse shear and normal stress, electric potential, and normal electric displacement components. The relevant orders used for expanding these variables in the thickness coordinate can be freely chosen as the linear, quadratic and cubic orders. Four different mechanical/electrical loading conditions applied on the top and bottom surfaces of the plate are considered, and the corresponding coupled electro-elastic analysis of the loaded FGPM plates is undertaken. The accuracy and convergence rate of the RMVT-based FLMs are assessed by comparing their solutions with the exact 3D piezoelectricity ones available in the literature.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.1
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• pp.20-39
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• 2020

This paper considers a downlink multi-carrier cooperative non-orthogonal multiple access (NOMA) transmission, where no direct link exists between the far user and the base station (BS), and the communication between them only relies on the assist of the near user. Firstly, the BS sends a superimposed signal of the far and the near user to the near user, and then the near user adopts simultaneous wireless information and power transfer (SWIPT) to split the received superimposed signal into two portions for energy harvesting and information decoding respectively. Afterwards, the near user forwards the signal of the far user by utilizing the harvested energy. A minimum data is required to ensure the quality of service (QoS) of the far user. We jointly optimize power allocation, subcarrier allocation, time allocation, the power allocation (PA) coefficient and the power splitting (PS) ratio to maximize the number of data bits received at the near user under the energy causality constraint, the minimum data constraint and the transmission power constraint. The block-coordinate descent method and the Lagrange duality method are used to obtain a suboptimal solution of this optimization problem. In the final simulation results, the superiority of the proposed NOMA scheme is confirmed compared with the benchmark NOMA schemes and the orthogonal multiple access (OMA) scheme.