• Proceedings of the KSME Conference
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• 2008.11a
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• pp.418-423
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• 2008

Among various sensitivity evaluation techniques, semi-analytical method is quite popular since this method is more advantageous than analytical method and global finite difference method. However, SAM reveals severe inaccuracy problem when relatively large rigid body motions are identified for individual elements. Such errors result from the numerical differentiation of the pseudo load vector calculated by the finite difference scheme. In the present study, the adjoint variable method combined with complex variable is proposed to obtain the shape and size sensitivity for structural optimization. The complex variable can present accurate results regardless of the perturbation size as well as easy to be implemented. Through a few numerical examples of the static problem for the structural sensitivity, the efficiency and reliability of the adjoint variable method combined with complex variable is demonstrated.

• Structural Engineering and Mechanics
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• v.45 no.4
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• pp.495-519
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• 2013

This paper investigates properties of integral operators in complex variable boundary integral equation in plane elasticity, which is derived from the Somigliana identity in the complex variable form. The generalized Sokhotski-Plemelj's formulae are used to obtain the BIE in complex variable. The properties of some integral operators in the interior problem are studied in detail. The Neumann and Dirichlet problems are analyzed. The prior condition for solution is studied. The solvability of the formulated problems is addressed. Similar analysis is carried out for the exterior problem. It is found that the properties of some integral operators in the exterior boundary value problem (BVP) are quite different from their counterparts in the interior BVP.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.3
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• pp.243-250
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• 2009

The adjoint variable method can reduce computation time and save computer resources because it can selectively provide the sensitivity information for the positions that designers wish to measure. However, the adjoint variable method commonly employs exact analytical differentiation with respect to the design variables. It can be cumbersome to precisely differentiate every given type of finite element. This trouble can be overcome only if the numerical differentiation scheme can replace this exact manner of differentiation. But, the numerical differentiation scheme causes of severe inaccuracy due to the perturbation size dilemma. For assuring the accurate sensitivity without any dependency of perturbation size, this paper employs a complex variable that has been mainly used for computational fluid dynamics problems. The adjoint variable method combined with complex variables is applied to obtain the shape and size sensitivity for structural optimization. Numerical examples demonstrate that the proposed method can predict stable sensitivity results and that its accuracy is remarkably superior to traditional sensitivity evaluation methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.1 no.1
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• pp.65-74
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• 1997

For two dimensional elasticity, we suggest a new complex variable method using the Navier's displacement equation. This method gives alternative displacement and stress formulae to those resulting from the Muskhelishvili's complex function method.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.183-198
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• 2003

We highlight the alternative presentation of the Cauchy-Riemann conditions for the analyticity of a complex variable function and consider plane equilibrium problem for an elastic transversely isotropic layer, in finite deformation. We state the fundamental problems and consider traction boundary value problem, as an example of fundamental problem-one. A simple solution of“Lame's problem”for an infinite layer is obtained. The profile of the deformed contour is given; and this depends on the order of the term used in the power series specification for the complex potential and on the material constants of the medium.

• International Journal of Advanced Culture Technology
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• v.6 no.3
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• pp.163-172
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• 2018

The power train of hydro-mechanical continuously variable transmission(HMCVT) for the middle class forklift makes use of an hydro-static unit, hydraulic multi-wet disc brake & clutches and complex helical & planetary gears. The complex helical & planetary gears are a very important part of the transmission because of strength problems. The helical & planetary gears belong to the very important part of the HMCVT's power train where strength problems are the main concerns including the gear bending stress, the gear compressive stress and scoring failures. The present study, calculates specifications of the complex helical & planetary gear train and analyzes the gear bending and compressive stresses of the gears. It is necessary to analyze gear bending and compressive stresses confidently for an optimal design of the complex helical & planetary gears in respect of cost and reliability. This paper not only analyzes actual gear bending and compressive stresses of complex helical & planetary gears using Lewes & Hertz equation, but also verifies the calculated specifications of the complex helical & planetary gears by evaluating the results with the data of allowable bending and compressive stress from the Stress - No. of cycles curves of gears. In addition, this paper explains actual gear scoring and evaluates the possibility of scoring failure of complex helical & planetary gear train of hydro-mechanical continuously variable transmission for the forklift.

• Journal of Drive and Control
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• v.13 no.4
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• pp.45-51
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• 2016

The power train of a hydro-mechanical, continuously variable transmission for forklifts makes use of hydro-static units, hydraulic multi-wet disc brakes & clutches, and complex helical & planetary gears. The complex helical & planetary gears are very important parts of the transmission because of a strength problem. In the present study, we calculated the specifications of the complex helical & planetary gear train, and analyzed the gear bending and compressive stresses of the gears. It is necessary to analyze the gear bending and compressive stresses thoroughly for optimal design of the complex helical & planetary gears with respect to cost and reliability. In this paper, we analyze the actual gear bending and compressive stresses of complex helical & planetary gears using the Lewes & Hertz equation, and we also verify the calculated specifications of the complex helical & planetary gears by evaluating the results of the data of allowable bending and compressive stress using the Stress vrs Number of Cycles curves of gears.

• Journal of the Korean Statistical Society
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• v.29 no.4
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• pp.489-499
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• 2000

We propose a new instrumental variable estimator of the complex parameter of a class of univariate complex-valued diffusion processes defined by the possibly non-stationary and/or nonlinear stochastic differential equations. On the basis of the exact finite sample distribution of the pivotal quantity, we construct the exact confidence intervals and the exact tests for the parameter. Monte-Carlo simulation suggests that the new estimator seems to provide a viable alternative to the maximum likelihood estimator (MLE) for nonlinear and/or non-stationary processes.

• Interaction and multiscale mechanics
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• v.3 no.3
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• pp.277-298
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• 2010

The complex variable reproducing kernel particle method (CVRKPM) and the FEM are coupled in this paper to analyze the two-dimensional potential problems. The coupled method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, resulting in improved computational efficiency. A hybrid approximation function is applied to combine the CVRKPM with the FEM. Formulations of the coupled method are presented in detail. Three numerical examples of the two-dimensional potential problems are presented to demonstrate the effectiveness of the new method.

• Structural Engineering and Mechanics
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• v.77 no.2
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• pp.245-259
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• 2021

In this research, the influence of the laminate stacking sequence on thermal stress distribution in symmetric composite plates with a quasi-square cutout subjected to uniform heat flux is examined analytically using the complex variable technique. The analytical solution is obtained based on the thermo-elastic theory and the Lekhnitskii's method. Furthermore, by employing a suitable mapping function, the solution of symmetric laminates containing a circular cutout is extended to the quasi-square cutout. The effect of important parameters including the stacking sequence of laminates, the angular position, the bluntness, the aspect ratio of cutout, the flux angle and the composite material are examined on the thermal stress distribution. It is found out that the circular shape for cutout may not necessarily be the optimum geometry for all stacking sequences. The finite element analysis results are used to validate the analytical solution.