• Structural Engineering and Mechanics
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• v.73 no.1
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• pp.75-82
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• 2020

In this study, the problem of torsion of bars with open cross section surrounded by corrugated boundaries is analyzed. An approximate analytical solution is given using perturbation technique. First, the stress analysis for circular open cross-section for arbitrary opening angle is formulated and the problem is analytically solved. Second, the open cross-section with corrugated cross section is analyzed using perturbation method. First order contributions to the stresses and the torques have been added. The results have been exemplified and compared by considering special examples.

• Proceedings of the KIEE Conference
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• 2007.04a
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• pp.92-94
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• 2007

This paper considers an optimal control problem for a remote control to an electrical drive system with a DC motor. Since it is a linear control system with time-delay subject to unknown but bounded disturbance, we construct a worst-case feedback control policy. This policy can guarantee that, for all admissible uncertain disturbances, the real system state should be in a prescribed neighborhood of a desired value, and the cost functional takes the best guarantee value. The worst-case feedback control policy is allowed to be corrected at one correction point between the initial to the final time, which is equivalent to solving a 1-level min-max problem. Since the min-max problem at the stage does not yield a simple analytical solution, we consider an approximate control policy, which is equivalent and can be solved explicitly m the numerical experiments.

• Structural Engineering and Mechanics
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• v.3 no.1
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• pp.61-74
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• 1995

A linearly tapered, doubly symmetric thin-walled closed member, such as power-transmission towers and tourist towers, are often characterized by local variation in mass and/or rigidity, due to additional mass and rigidity. On the preliminary stage of design the closed-form solution is more effective than the finite element method. In order to propose approximate solutions, the discontinuous and local variation in mass and/or rigidity is treated continuously by means of a usable function proposed by Takabatake(1988, 1991, 1993). Thus, a simplified analytical method and approximate solutions for the free and forced transverse vibrations in linear elasticity are demonstrated in general by means of the Galerkin method. The solutions proposed here are examined from the results obtained using the Galerkin method and Wilson-${\theta}$ method and from the results obtained using NASTRAN.

• Solar Energy
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• v.15 no.2
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• pp.25-37
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• 1995

This paper presents an approximate analytical solution to one-dimensional model of the charging process for stratified thermal storage tanks, in which variation of the inlet temperature as well as the momemtum-induced mixing is taken into accout. The mixing is incorporated into the model as a constant-depth perfectly mixed layer above the plug flow region. Based on the superposition principle, the variable inlet temperature is approximated by a number of step functions. Temperature distributions for the thermocline corresponding to three types of interfacial condition arr successfully derived in terms of well-defined functions, so that a linear combination of them constitutes the final solution. Validity and utility of this work is examined through the comparison of the approximate solution with an exact solution available for the case of linearly increasing inlet temperature. With increasing the number of steps, the present solution asymptotically approaches to the exact one. Even with a limited number of steps, the present results favorably agree with those by the exact solution for a wide range of the mixing depth. Also, it is revealed that fewer steps are needed for meaningful predictions as the mixing. depth becomes larger.

• Steel and Composite Structures
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• v.29 no.4
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• pp.483-491
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• 2018

Timoshenko beam model is widely exploited in the literature to examine the mechanical behavior of stubby beam-like components. Timoshenko beam theory is well-known to require the shear correction factor in order to recognize the nonuniform shear distribution at a section. While a variety of shear correction factors are appeared in the literature so far, there is still no consensus on the most appropriate form of the shear correction factor. The Saint-Venant's flexure problem is first revisited in the frame work of the classical theory of elasticity and a highly accurate approximate closed-form solution is presented employing the extended Kantorovich method. The resulted approximate solution for the elasticity field is then employed to introduce two shear correction factors consistent with the Cowper's and energy approaches. The mathematical form of the proposed shear correction factors are then simplified and compared with the results available in the literature over an extended range of Poisson's and aspect ratios. The proposed shear correction factors do not exhibit implausible issue of negative values and do not result in numerical instabilities too. Based on the comprehensive discussion on the shear correction factors, a piecewise definition of shear correction factor is introduced for rectangular cross-sections having excellent agreement with the numerical results in the literature for both shallow and deep cross-sections.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.1
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• pp.16-22
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• 1998

This paper addresses a method which can be used for analyzing thermal stresses of a functionally graded material(FGM) using semi-analytical approach. FGM is a nonhomogeneous material whose composition is changed continuously from a metal surface to a ceramic surface. An infinite one dimensional FGM plate is considered. The temperature distribution in the FGM is obtained by approximate Green's function solution. To expedite the convergence of the solutions, alternative Green's function solution is derived and shows good agreement with results from finite difference method. Thermal stresses are calculated using temperature distribution of the plate.

• Nuclear Engineering and Technology
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• v.29 no.1
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• pp.7-14
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• 1997

Grain boundary diffusion plays a significant role in fission gas release, which is one of the crucial processes dominating nuclear fuel performance. Gaseous fission produce such as Xe and Kr generated during nuclear fission have to diffuse in the grain lattice and the boundary inside fuel pellets before they reach the open spaces in a fuel rod. These processes can be studied by 'tracer diffusion' techniques, by which grain boundary diffusivity can be estimated and directly used for low burn-up fission gas release analysis. However, only a few models accounting for the both processes are available and mostly handle them numerically due to mathematical complexity. Also the numerical solution has limitations in a practical use. In this paper, an approximate analytical solution in case of stationary grain boundary in a polycrystalline solid is developed for the tracer diffusion techniques. This closed-form solution is compared to available exact and numerical solutions and it turns out that it makes computation not only greatly easier but also more accurate than previous models. It can be applied to theoretical modelings for low bum-up fission gas release phenomena and experimental analyses as well, especially for PIE (post irradiation examination).

• Structural Engineering and Mechanics
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• v.51 no.3
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• pp.519-530
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• 2014

This paper attempts to investigate the nonlinear dynamic analysis of strong nonlinear problems by proposing a new analytical method called Hamiltonian Approach (HA). Two different cases are studied to show the accuracy and efficiency of the method. This approach prepares us to obtain the nonlinear frequency of the nonlinear systems with the first order of the solution with a high accuracy. Finally, to verify the results we present some comparisons between the results of Hamiltonian approach and numerical solutions using Runge-Kutta's [RK] algorithm. This approach has a powerful concept and the high accuracy, so it can be apply to any conservative nonlinear problems without any limitations.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2009.04a
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• pp.97-102
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• 2009

In hot strip rolling, sound prediction of the temperature of the strip is vital for achieving the desired finishing mill draft temperature (FDT). In this paper, a precision on-line model for the prediction of temperature distributions along the thickness of the strip in the finishing mill is presented. The model consists of an analytic model for the prediction of temperature distributions in the inter-stand zone, and a semi-analytic model for the prediction of temperature distributions in the bite zone in which thermal boundary conditions as well as heat generation due to deformation are predicted by finite element-based, approximate models. The prediction accuracy of the proposed model is examined through comparison with predictions from a finite element process model.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.10a
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• pp.87-94
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• 1997

The circular plate resting on Boussinesq's half-space model under axisymmetric loading is studied by a finite element procedure to evaluate the distribution of contact pressure between plate and elastic half-space. The displacement of half-space due to axisymmetric surface loading can be evaluated by double integration of Boussinesq's solution. On that case the analytical integration can be executed for the radial direction but the analytical integration for the circumferential direction is impossible and the numerical integration should be considered. With the radial integration we can get non-dimensional function. Then the numerical integration for the formula is executed for the circumferential direction and the results are approximated 5th order Polynomials by using the least square method. With these 5th order approximate formula, the flexibility matrix of half-space is constructed as the coefficient matrix of nodal contact pressure by the finite element procedures. Iteration procedures are attempted by using this method to determine the separated region.