• Transactions of the Korean Society of Automotive Engineers
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• v.7 no.5
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• pp.141-153
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• 1999

A finite element procedure for the analysis of rubber-like hyperelastic material is developed. The volumetric incompressiblity conditions of the rubber deformation is included in the formulation by using penalty method. In this paper, the behavior of the rubber deformation is represented by hyperelastic constitutive relations based on a generalized Mooney-Rivlin model. The principle of virtual work is used to derive nonlinear finite element equation for the large displacement problem and presented in total-Lagrangian description. The finite element procedure using analytic differentiation resulted in very close solution to the result of the well known commercial packages NISAII AND ABAQUS. Numerical tests show that the results from the numerical differentiation method coincide very well with those from the analytic method and the well known commercial packages in static analysis. The convergency of rubber usingν iteration method is also discussed.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.627-645
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• 2017

In this paper, we characterize the boundedness, compactness and essential norm of products of differentiation and composition operators from the Bloch space and weighted Dirichlet spaces to analytic Morrey type spaces.

• Geophysics and Geophysical Exploration
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• v.25 no.4
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• pp.242-251
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• 2022

Automatic differentiation automatically calculates the derivatives of a function using the chain rule once the forward operation of a function is defined. Given the recent development of computing libraries that support automatic differentiation, many researchers have adopted automatic differentiation techniques to solve geophysical inverse problems. We analyzed the advantages, disadvantages, and performances of automatic differentiation techniques using the gradient calculations of seismic full waveform inversion objective functions. The gradients of objective functions can be expressed as multiplications of the derivatives of the model parameters, wavefields, and objective functions using the chain rule. Using numerical examples, we demonstrated the speed of analytic differentiation and the convenience of complex gradient calculations for automatic differentiation. We calculated derivatives of model parameters and objective functions using automatic differentiation and derivatives of wavefields using analytic differentiation.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.5
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• pp.1458-1467
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• 1996

A direct differentiationmethod is presented for the shape design sensitivity analysis of axisymmeetric elastic solids. Based on the exisymmetric boundary integralequaiton formulation, a new boundary ntegral equatio for sensitivity analysis is derived by taking meterial derivative to the same integral identity that was used in the adjoint variable melthod. Numerical implementation is performed to show the applicaiton of the theoretical formulation. For a simple example with analytic solution, the sensitivities by present method are compared with analytic sensitivities. As an application to the shape optimization, an optimal shape of a gas turbine disc toinimize the weight under stress constraints is found by incorporating the sensitivity analysis algorithm in an optimizatio program.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.4
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• pp.585-592
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• 2003

Among various sensitivity evaluation techniques, semi-analytical method(SAM) is quite popular since this method is more advantageous than analytical method(AM) and global finite difference method(FDM). However, SAM reveals severe inaccuracy problem when relatively large rigid body motions are identified fur individual elements. Such errors result from the numerical differentiation of the pseudo load vector calculated by the finite difference scheme. In the present study, an iterative method combined with mode decomposition technique is proposed to compute reliable semi-analytical design sensitivities. The improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes and the error of SAM caused by numerical difference scheme is alleviated by using a Von Neumann series approximation considering the higher order terms for the sensitivity derivatives.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.99-111
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• 2024

In this paper, a new seven-parameter Mittag-Leffler function of a single complex variable is proposed as a generalization of the standard Mittag-Leffler function, certain generalizations of Mittag-Leffler function, hypergeometric function and confluent hypergeometric function. Certain essential analytic properties are mainly discussed, such as radius of convergence, order, type, differentiation, Mellin-Barnes integral representation and Euler transform in the complex plane. Its relation to Fox-Wright function and H-function is also developed.

• Proceedings of the KSME Conference
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• 2001.06a
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• pp.686-691
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• 2001

Structural optimization often require the evaluation of design sensitivities. The Semi Analytic method(SAM) is popular for shape optimization because this method has several advantages. But when relatively large rigid body motions are identified for individual elements, the SA method shows severe inaccuracy. In this paper, the improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes. Moreover, the error of the SA method caused by numerical difference scheme is alleviated by using a series approximation for the sensitivity derivatives and considering the higher order terms.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.4
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• pp.593-600
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• 2003

Structural optimization often requires the evaluation of design sensitivities. The Semi Analytic Method(SAM) fur computing sensitivity is popular in shape optimization because this method has several advantages. But when relatively large rigid body motions are identified for individual elements. the SAM shows severe inaccuracy. In this study, the improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes. Moreover. the error of the SAM caused by numerical difference scheme is alleviated by using a series approximation for the sensitivity derivatives and considering the higher order terms. Finally the present study shows that the refined SAM including the iterative method improves the results of sensitivity analysis in dynamic problems.

• Biomedical Engineering Letters
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• v.8 no.4
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• pp.383-392
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• 2018

For prompt gamma ray imaging for biomedical applications and environmental radiation monitoring, we propose herein a multiple-scattering Compton camera (MSCC). MSCC consists of three or more semiconductor layers with good energy resolution, and has potential for simultaneous detection and differentiation of multiple radio-isotopes based on the measured energies, as well as three-dimensional (3D) imaging of the radio-isotope distribution. In this study, we developed an analytic simulator and a 3D image generator for a MSCC, including the physical models of the radiation source emission and detection processes that can be utilized for geometry and performance prediction prior to the construction of a real system. The analytic simulator for a MSCC records coincidence detections of successive interactions in multiple detector layers. In the successive interaction processes, the emission direction of the incident gamma ray, the scattering angle, and the changed traveling path after the Compton scattering interaction in each detector, were determined by a conical surface uniform random number generator (RNG), and by a Klein-Nishina RNG. The 3D image generator has two functions: the recovery of the initial source energy spectrum and the 3D spatial distribution of the source. We evaluated the analytic simulator and image generator with two different energetic point radiation sources (Cs-137 and Co-60) and with an MSCC comprising three detector layers. The recovered initial energies of the incident radiations were well differentiated from the generated MSCC events. Correspondingly, we could obtain a multi-tracer image that combined the two differentiated images. The developed analytic simulator in this study emulated the randomness of the detection process of a multiple-scattering Compton camera, including the inherent degradation factors of the detectors, such as the limited spatial and energy resolutions. The Doppler-broadening effect owing to the momentum distribution of electrons in Compton scattering was not considered in the detection process because most interested isotopes for biomedical and environmental applications have high energies that are less sensitive to Doppler broadening. The analytic simulator and image generator for MSCC can be utilized to determine the optimal geometrical parameters, such as the distances between detectors and detector size, thus affecting the imaging performance of the Compton camera prior to the development of a real system.

• The Journal of Internal Korean Medicine
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• v.28 no.4
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• pp.791-796
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• 2007

Objective : This study was conducted to find the relationship between syndrome-differentiation and Sasang-constitution in chronic fatigue patients. Methods : The subjects were 72 adults with chronic fatigue who visited Dunsan Oriental Hospital of Daejeon University between March 2007 and April 2007. Their main complaint was fatigue for longer than 6 months and they did not have any physical or mental problems. We measured their fatigue degree by using Chalder fatigue scale and health habits. To evaluate relationship between syndrome-differentiation with sasang-constitution, The patients were divided into four syndrome-differentiations, such as liver and kidney asthenia of Yin, spleen and kidney deficiency of Yang, deficiency of lung and spleen qi, and deficiency of heart and spleen blood. We also diagnosed Sasang-constitution by using Questionnaire for Sasang Constitution Classification II (QSCCII). Results : Among the 72 patients, 41.4%, 34.5% and 24.1% of belonged in Soyangin, Soeumin and Taeumin respectively. Interestingly, we found a meaningful correlation between syndrome-differentiation and physiological function by Sasang-constitution. Conclusion : The result may help Oriental medicine understanding and treatment of chronic fatigue-related diseases and patients.