• Advances in aircraft and spacecraft science
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• 제5권6호
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• pp.671-689
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• 2018

Bending, buckling and free vibration responses of functionally graded (FG) higher-order beams resting on two parameter (Winkler-Pasternak) elastic foundation are studied using a new inverse hyperbolic beam theory. The material properties of the beam are graded along the thickness direction according to the power-law distribution. In the present theory, the axial displacement accounts for an inverse hyperbolic distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the top and bottom surfaces of the beams. Hamilton's principle is employed to derive the governing equations of motion. Navier type analytical solutions are obtained for the bending, bucking and vibration problems. Numerical results are obtained to investigate the effects of power-law index, length-to-thickness ratio and foundation parameter on the displacements, stresses, critical buckling loads and frequencies. Numerical results by using parabolic beam theory of Reddy and first-order beam theory of Timoshenko are specially generated for comparison of present results and found in excellent agreement with each other.

• 한국재난정보학회 논문집
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• 제4권2호
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• pp.52-66
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• 2008

It has been a growing concern about reusing Sudokwon landfill 2nd site and other sanitary landfills located around the metropolitan areas. In this paper, settlement characteristics of Sudokwon landfill 2nd site were studied by analyzing the data collected over the period of six years. Three equations are combined in order to modeling the long-term settlement behavior of refuse landfill caused by mechanical secondary composition and secondary composition caused by the decomposition of biodegradable refuse. It is suggested that mechanical secondary composition is linear with respect to the logarithm of time. The models proposed by hyperbolic method and Gibson & Lo model, power creep law are considered to be suitable for the long-term prediction value of Sudokwon landfill 2nd site. The fifteen-year-period prediction value of hyperbolic method and Gibson & Lo model is considerably different from that of power creep law model. The average settlement for Block I in Sudokwon 2nd site is approximately 3.9m with 4 steps of final landfill stages.

• 동력기계공학회지
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• 제3권3호
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• pp.14-21
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• 1999

The wave nature of heat conduction has been developed in situations involving extreme thermal gradients, very short times, or temperatures near absolute zero. Under the excitation of a periodic surface heating in a finite medium, the hyperbolic and parabolic heat conduction equations and the damped wave equations in heat flux are presented for comparative analysis by using the Green's function with the integral transform technique. The Kummer transformation is also utilized to accelerate the rate of convergence of these solutions. On the other hand, the temperature distributions are obtained through integration of the energy conservation law with respect to time. For hyperbolic heat conduction, the heat flux distribution does not exist throughout all the region in a finite medium within the range of very short times(${\xi}<{\eta}_l$). It is shown that due to the thermal relaxation time, the hyperbolic heat conduction equation has thermal wave characteristics as the damped wave equation has wave nature.

• 대한수학회보
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• 제50권1호
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• pp.201-216
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• 2013

In this note, we consider the Riemann problem for a two-dimensional nonstrictly hyperbolic system of conservation laws. Without the restriction that each jump of the initial data projects one planar elementary wave, six topologically distinct solutions are constructed by applying the generalized characteristic analysis method, in which the delta shock waves and the vacuum states appear. Moreover we demonstrate that the nature of our solutions is identical with that of solutions to the corresponding one-dimensional Cauchy problem, which provides a verification that our construction produces the correct global solutions.

• Advances in materials Research
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• 제6권1호
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• pp.13-26
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• 2017

In this work we introduce a higher-order hyperbolic shear deformation model for bending and frees vibration analysis of functionally graded beams. In this theory and by making a further supposition, the axial displacement accounts for a refined hyperbolic distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the beam boundary surfaces, so no need of any shear correction factors (SCFs). The material properties are continuously varied through the beam thickness by the power-law distribution of the volume fraction of the constituents. Based on the present refined hyperbolic shear deformation beam model, the governing equations of motion are obtained from the Hamilton's principle. Analytical solutions for simply-supported beams are developed to solve the problem. To verify the precision and validity of the present theory some numerical results are compared with the existing ones in the literature and a good agreement is showed.

• 소성∙가공
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• 제4권2호
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• pp.159-168
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• 1995

The torsion tests in the range of $550~800^{\circ}C$, $5.0{\times}10^{-3}~5.0{\times}10^0/sec$ were performed to study the effects of strain rate$(\.{\varepsilon})$ and temperature(T) on the hot strength of Cu-Zn alloy. High temperature flow stresses of this alloy increased with increasing $\.{\varepsilon}$ and/or decreasing T, and than the more grain refinement could be obtained. The flow curves exhibited a peak followed by a steady steady state regime as a result of dynamic recrystallization. The hot strength dependence of $\.{\varepsilon}$ and T was described by a hyperbolic sine law, $\.{\varepsilon}=A(sinh0.017{\sigma})^4.81$exp(-216KJ/mol). Hot strength could be reduced at the arbitary condition, $\.{\varepsilon}$ and T, by constitutive parameter Z(Zenner-Hollomon parameter), $Z=A(sinh{\alpha}{\sigma})^n=\.{\varepsilon}$exp(Q/RT).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권4호
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• pp.279-294
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• 2013

We are interested in an adaptive grid method for hyperbolic equations. A multiresolution analysis, based on a biorthogonal family of interpolating scaling functions and lifted interpolating wavelets, is used to dynamically adapt grid points according to the physical field profile in each time step. Traditional finite-difference schemes with fixed stencils produce high oscillations around sharp discontinuities. In this paper, we hybridize high-resolution schemes, which are suitable for capturing singularities, and apply a finite-difference approach to the scaling functions at non-singular points. We use a total variation diminishing Runge-Kutta method for the time integration. The computational cost is proportional to the number of points present after compression. We provide several numerical examples to verify our approach.

• Earthquakes and Structures
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• 제16권2호
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• pp.177-183
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• 2019

In this paper, a new refined hyperbolic shear deformation beam theory for the bending analysis of functionally graded beam is presented. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the functionally graded beam without using shear correction factors. In addition, the effect of different micromechanical models on the bending response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams whose properties vary continuously across the thickness according to a simple power law. Based on the present theory, the equilibrium equations are derived from the principle of virtual work. Navier type solution method was used to obtain displacement and stresses, and the numerical results are compared with those available in the literature. A detailed parametric study is presented to show the effect of different micromechanical models on the flexural response of a simply supported FG beams.

• Geomechanics and Engineering
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• 제8권3호
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• pp.305-321
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• 2015

In this paper, a new hyperbolic shear deformation plate theory based on neutral surface position is developed for the static analysis of functionally graded plates (FGPs). The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The neutral surface position for a functionally graded plate which its material properties vary in the thickness direction is determined. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Based on the present new hyperbolic shear deformation plate theory and the neutral surface concept, the governing equations of equilibrium are derived from the principle of virtual displacements. Numerical illustrations concern flexural behavior of FG plates with Metal-Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, volume fraction profiles, aspect ratios and length to thickness ratios. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Steel and Composite Structures
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• 제20권4호
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• pp.889-911
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• 2016

Using the hyperbolic shear deformation plate model and including plate-foundation interaction (Winkler and Pasternak model), an analytical method in order to determine the deflection and stress distributions in simply supported rectangular functionally graded plates (FGP) subjected to a sinusoidal load, a temperature and moisture fields. The present theory exactly satisfies stress boundary conditions on the top and the bottom of the plate. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain is given. Materials properties of the plate (elastic, thermal and moisture expansion coefficients) are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. Numerical examples are presented and discussed for verifying the accuracy of the present theory in predicting the bending response of FGM plates under sinusoidal load and a temperature field as well as moisture concentration. The effects of material properties, temperature, moisture, plate aspect ratio, side-to-thickness ratio, ratio of elastic coefficients (ceramic-metal) and three distributions for both temperature and moisture on deflections and stresses are investigated.