• Structural Engineering and Mechanics
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• 제19권3호
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• pp.281-295
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• 2005

An analytical method is presented to solve the elastodynamic problem of finitely long hollow cylinder subjected to torsional impact often occurs in engineering mechanics. The analytical solution is composed of a solution of quasi-static equation satisfied with the non-homogeneous boundary condition and a solution of dynamic equation satisfied with homogeneous boundary condition. The quasi-static solution is obtained directly by solving the quasi-static equation satisfied with the non-homogeneous boundary condition. The solution of the non-homogeneous dynamic equation is obtained by means of finite Hankel transform on the radial variable, r, Laplace transform on time variable, t, and finite Fourier transform on axial variable, z. Thus, the solution for finitely long, hollow cylinder subjected to torsion impact is obtained. In the calculating examples, the response histories and distributions of shear stress in the finitely long hollow cylinder subjected to an exponential decay torsion load are obtained, and the results have been analyzed and discussed. Finally, a dynamic finite element for the same problem is carried out by using ABAQUS finite element analysis. Comparing the analytical solution with the finite element solution, it can be found that two kinds of results obtained by means of two different methods agree well. Therefore, it is further concluded that the analytical method and computing process presented in the paper are effective and accurate.

• Structural Engineering and Mechanics
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• 제82권6호
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• pp.725-734
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• 2022

This work presents a simple exponential shear deformation theory for the flexural and free vibration responses of thick bridge deck. Contrary to the existing higher order shear deformation theories (HSDT) and the first shear deformation theory (FSDT), the proposed model uses a new displacement field which incorporates undetermined integral terms and involves only two variables. Governing equations and boundary conditions of the theory are derived by the principle of virtual work. The simply supported thick isotropic square and rectangular plates are considered for the detailed numerical studies. Results of displacements, stresses and frequencies are compared with those of other refined theories and exact theory to show the efficiency of the proposed theory. Good agreement is achieved of the present results with those of higher order shear deformation theory (HSDT) and elasticity theory. Moreover, results demonstrate that the developed two variable refined plate theory is simple for solving the flexural and free vibration responses of thick bridge deck and can achieve the same accuracy of the existing HSDTs which have more number of variables.

• 해양환경안전학회지
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• 제22권1호
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• pp.129-137
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• 2016

본 연구의 목적은 가까운 미래의 선박운동정보를 이용하는 피드포워드 제어알고리즘과 FPSO 운동 수치 시뮬레이션 모델을 개발하고 시뮬레이션을 통하여 제어알고리즘의 성능을 검증하는 것이다. 본 논문에서는 조류, 바람, 파력 등의 환경하중에 의하여 발생한 선체운동의 미래 예측치를 활용한 피드포워드 제어력을 추가적으로 가지는 Dynamic Positioning System에 대하여 연구한다. 먼저, 조류력, 풍력 및 파력에 대한 수학모델을 선정하여 환경하중에서의 선체운동을 계산하고, 현재의 선체운동 값과 Brown 지수평활 예측모형을 활용하여 미래 선체운동 값을 예측하였다. 또한 위치 유지와 Heading angle 제어를 위한 제어력을 PID(Proportional-Integral-Derivative)이론을 이용하여 결정한 피드백 제어기와 미래 선체운동 값을 이용하여 결정한 피드포워드 제어기로 구성하였다. 그리고 각 Thruster에 요구되는 추력은 라그랑지승수법을 활용하여 분배하였다. 마지막으로 FPSO(Floating Production Storage and Offloading)의 운동과 Dynamic Positioning System에 대한 시뮬레이션 모델을 구축하여 선박의 위치 및 Heading angle 제어에 관한 시뮬레이션을 수행하여 제안하는 피드백 제어기와 피드포워드 제어기를 동시에 가지는 제어시스템의 성능을 평가하였다. 본 연구의 결과, 피드백 및 피드 포워드 제어기가 적용된 DPS 제어시스템이 기존의 피드백 제어기보다 위치유지 및 헤딩각 유지 능력에서 개선되었고 각 Thruster에 요구되는 평균 제어력 및 최대 제어력의 크기도 감소함을 보였다. 이에 따라 DPS에 요구되는 동력 감축과 Azimuth Thruster 용량의 감소로 인하여 비용 절감의 효과를 기대할 수 있다.

• Geomechanics and Engineering
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• 제14권6호
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• pp.519-532
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• 2018

In this work, two dimensional (2D) and quasi three-dimensional (quasi-3D) HSDTs are proposed for bending and free vibration investigation of functionally graded (FG) plates using hyperbolic shape function. Unlike the existing HSDT, the proposed theories have a novel displacement field which include undetermined integral terms and contains fewer unknowns. The material properties of the plate is inhomogeneous and are considered to vary continuously in the thickness direction by three different distributions; power-law, exponential and Mori-Tanaka model, in terms of the volume fractions of the constituents. The governing equations which consider the effects of both transverse shear and thickness stretching are determined through the Hamilton's principle. The closed form solutions are deduced by employing Navier method and then fundamental frequencies are obtained by solving the results of eigenvalue problems. In-plane stress components have been determined by the constitutive equations of composite plates. The transverse stress components have been determined by integrating the 3D stress equilibrium equations in the thickness direction of the FG plate. The accuracy of the present formulation is demonstrated by comparisons with the different 2D, 3D and quasi-3D solutions available in the literature.

• Advances in Computational Design
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• 제5권4호
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• pp.417-443
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• 2020

Tunnels have been an integral part of human civilization. Due to complexity in its design and structure, the stability of underground structures under extreme loading conditions has utmost importance. Increased terrorism and geo-political conflicts have forced the engineers and researchers to study the response of underground structures, especially tunnels under blast loading. The present study has been carried out to seek the response of tunnel structures under blast load using the finite element technique. The tunnel has been considered in quartzite rock of northern India. The Mohr-Coulomb constitutive model has been adopted for the elastoplastic behaviour of rock. The rock model surrounding the tunnel has dimensions of 30 m x 30 m x 35 m. Both unlined and lined (concrete) tunnel has been studied. Concrete Damage Plasticity model has been considered for the concrete lining. Four different parameters (i.e., tunnel diameter, liners thickness, overburden depth and mass of explosive) have been varied to observe the behaviour under different condition. To carry out blast analysis, Coupled-Eulerian-Lagrangian (CEL) modelling has been adopted for modelling of TNT (Trinitrotoluene) and enclosed air. JWL (Jones-Wilkins-Lee) model has been considered for TNT explosive modelling. The paper concludes that deformations in lined tunnels follow a logarithmic pattern while in unlined tunnels an exponential pattern has been observed. The stability of the tunnel has increased with an increase in overburden depth in both lined and unlined tunnels. Furthermore, the tunnel lining thickness also has a significant effect on the stability of the tunnel, but in smaller diameter tunnel, the increase in tunnel lining thickness has not much significance. The deformations in the rock tunnel have been decreased with an increase in the diameter of the tunnel.

• Environmental Analysis Health and Toxicology
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• 제11권1_2호
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• pp.1-10
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• 1996

A decrease in stratospheric ozone probably caused by chloroflurocarbons (CFCs) emissions, has been observed large parts of-the globe. It is generally accepted that if ozone levels in the stratosphere are depleted, greater amounts of shortwave ultraviolet radiationB (UVB) will reach the earth's surface, resulting in increased incidence of nonmelanoma skin cancer. In this study, we evaluated several mathematical models, such as a power and an exponential model, and a geometric model considering the surface area of a human body part and ages for the prediction of Skin cancer incidence caused by exposure to the UVB radiation. These models basically estimated the risk of skin cancer based on those measurements of the local ozone in stratosphere and UVB. Both were measured at a part of Seoul with a Dobson ozone spectrometer and Robertson-Berger UV Biometer for 1995. As a result, we calculated the point estimation applying a biological amplification factor (BAF), UVB radiation and other factors. We used a Monte-Carlo simulation technique with assumption on the distribution of each considered factor. The sensitivity analysis of model by there components conducted using Gaussian sensitivity method. The annual integral of UVB radiation was 2275 MED (minimal erythema dose)/yr. Also, an estimate of the annual amount of UVB reaching the earth's surface at a korea's latitude and altitude was 3328 MED/yr. The values of the radiation amplification factor (RAF) were ranged from 0.9 to 1.5 in Seoul. To give the effective factors required to model the prediction of skin cancer incidence caused by exposure to the UVB radiation in Korea, we studied the pros and cons of above mentioned models with the application of those parameters measured in Seoul, Korea.

• Coupled systems mechanics
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• 제9권3호
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• pp.237-264
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• 2020

This article investigates the static behaviour of functionally graded (FG) plates sometimes declared as advanced composite plates by using a simple and accurate quasi-3D and 2D hyperbolic higher-order shear deformation theories. The properties of functionally graded materials (FGMs) are assumed to vary continuously through the thickness direction according to exponential law distribution (E-FGM). The kinematics of the present theories is modeled with an undetermined integral component and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate; therefore, it does not require the shear correction factor. The fundamental governing differential equations and boundary conditions of exponentially graded plates are derived by employing the static version of principle of virtual work. Analytical solutions for bending of EG plates subjected to sinusoidal distributed load are obtained for simply supported boundary conditions using Navier'is solution procedure developed in the double Fourier trigonometric series. The results for the displacements and stresses of geometrically different EG plates are presented and compared with 3D exact solution and with other quasi-3D and 2D higher-order shear deformation theories to verify the accuracy of the present theory.

• 한국전자파학회논문지
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• 제12권1호
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• pp.92-98
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• 2001

Closed-form 그린함수를 사용하여 다층 평판 구조체의 산란 문제를 해석할 경우, 주된 어려운 문제점 중의 하나의 대각행렬 요소의 계산결과가 느리게 수렴하고 안정되지 않다는 점이다. 즉, 대각행렬 요소 계산시 전원 자신의 항에 해당되는 $e^{-jkr}/{\gamma}$ 형태의 특이 적분처리를 했음에도 불구하고 계산결과의 느린 수렴도 문제가 몇 개의 복소 영상항에 해당하는 적분과정에 여전히 남아있음을 알 수 있었다. 이와 같은 문제점을 해소하기 위해, 일반화된 지수함수와 2중적분을 극좌표계에서 가우스 구적법을 사용하여 계산할 수 있는 새로운 적분 기법을 제시하고자 한다. 새로운 적분기법을 알로리즘의 안정성과 수렴도에 관하여 본 논문에서 논의되면, 그 타당성을 확인하기 위해 마이크로스트립 패치 안테나의 산란 문제에 이 적분법을 적용해 보았다.

• Kyungpook Mathematical Journal
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• 제28권2호
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• pp.185-196
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• 1988

We study existence of polynomial integrating factors and solutions F(x, y)=c of first order nonlinear differential equations. We characterize the homogeneous case, and give algorithms for finding existence of and a basis for polynomial solutions of linear difference and differential equations and rational solutions or linear differential equations with polynomial coefficients. We relate singularities to nature of the solution. Solution of differential equations in closed form to some degree might be called more an art than a science: The investigator can try a number of methods and for a number of classes of equations these methods always work. In particular integrating factors are tricky to find. An analogous but simpler situation exists for integrating inclosed form, where for instance there exists a criterion for when an exponential integral can be found in closed form. In this paper we make a beginning in several directions on these problems, for 2 variable ordinary differential equations. The case of exact differentials reduces immediately to quadrature. The next step is perhaps that of a polynomial integrating factor, our main study. Here we are able to provide necessary conditions based on related homogeneous equations which probably suffice to decide existence in most cases. As part of our investigations we provide complete algorithms for existence of and finding a basis for polynomial solutions of linear differential and difference equations with polynomial coefficients, also rational solutions for such differential equations. Our goal would be a method for decidability of whether any differential equation Mdx+Mdy=0 with polynomial M, N has algebraic solutions(or an undecidability proof). We reduce the question of all solutions algebraic to singularities but have not yet found a definite procedure to find their type. We begin with general results on the set of all polynomial solutions and integrating factors. Consider a differential equation Mdx+Ndy where M, N are nonreal polynomials in x, y with no common factor. When does there exist an integrating factor u which is (i) polynomial (ii) rational? In case (i) the solution F(x, y)=c will be a polynomial. We assume all functions here are complex analytic polynomial in some open set.

• Steel and Composite Structures
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• 제51권2호
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• pp.185-202
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• 2024

In this research paper, and for the first time, wave propagations in sigmoidal imperfect functionally graded material plates are investigated using a simplified quasi-three-dimensionally higher shear deformation theory (Quasi-3D HSDTs). By employing an indeterminate integral for the transverse displacement in the shear components, the number of unknowns and governing equations in the current theory is reduced, thereby simplifying its application. Consequently, the present theories exhibit five fewer unknown variables compared to other Quasi-3D theories documented in the literature, eliminating the need for any correction coefficients as seen in the first shear deformation theory. The material properties of the functionally graded plates smoothly vary across the cross-section according to a sigmoid power law. The plates are considered imperfect, indicating a pore distribution throughout their thickness. The distribution of porosities is categorized into two types: even or uneven, with linear (L)-Type, exponential (E)-Type, logarithmic (Log)-Type, and Sinus (S)-Type distributions. The current quasi-3D shear deformation theories are applied to formulate governing equations for determining wave frequencies, and phase velocities are derived using Hamilton's principle. Dispersion relations are assumed as an analytical solution, and they are applied to obtain wave frequencies and phase velocities. A comprehensive parametric study is conducted to elucidate the influences of wavenumber, volume fraction, thickness ratio, and types of porosity distributions on wave propagation and phase velocities of the S-FGM plate. The findings of this investigation hold potential utility for studying and designing techniques for ultrasonic inspection and structural health monitoring.