• Structural Engineering and Mechanics
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• 제58권3호
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• pp.423-442
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• 2016

This study considers a functionally graded (FG) elastic layer resting on homogeneous elastic substrate under axisymmetric static loading. The shear modulus of the FG layer is assumed to vary in an exponential form through the thickness. In solution, the FG layer is approximated into a multilayered medium consisting of thin homogeneous sublayers. Stiffness matrices for a typical homogeneous isotropic elastic layer and a half-space are first obtained by solving the axisymmetric elasticity equations with the aid of Hankel's transform. Global stiffness matrix is, then, assembled by considering the continuity conditions at the interfaces. Numerical results for the displacements and the stresses are obtained and compared with those of the classical elasticity and the finite element solutions. According to the results of the study, the approach employed here is accurate and efficient for elasto-static problems of FGMs.

• Structural Engineering and Mechanics
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• 제52권1호
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• pp.1-17
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• 2014

An interfacial penny-shaped crack between piezoelectric layer and elastic half-space subjected to mechanical and electric loads is investigated. Using Hankel transform technique, the mixed boundary value problem is reduced to a system of singular integral equations. The integral equations are further reduced to a system of algebraic equations with the aid of Jacobi polynomials. The stress intensity factor and energy release rate are determined. Numerical results reveal the effects of electric loadings and material parameters of composite on crack propagation and growth. The results seem useful for design of the piezoelectric composite structures and devices of high performance.

• Steel and Composite Structures
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• 제35권3호
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• pp.343-351
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• 2020

The present research deals with the multi-dual-phase-lags thermoelasticity theory for thermoelastic behavior of transversely isotropic thermoelastic thin circular plate The Laplace and Hankel transform techniques have been used to find the solution of the problem. The displacement components, stress components, and conductive temperature distribution are computed in the transformed domain with the radial distance and further determined in the physical domain using numerical inversion techniques. The effect of rotation and two temperature are depicted graphically on the resulting quantities.

• 한국구조물진단유지관리공학회 논문집
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• 제20권4호
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• pp.27-34
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• 2016

시설물의 거동 파악을 위한 대표적인 방법으로는 가속도센서에서 측정되는 동적응답을 이용하여 역해석을 통해 구조변수를 추정하는 방법이 있다. 정확한 구조변수의 추정을 위해서는 최적화된 센서의 위치가 필요한데, 본 논문에서는 다양한 최적 센서위치를 추정하는 방법을 정리하였으며, 기존 시간영역에서만 사용되었던 Hankel matrix법을 주파수영역으로 확대 개발하여 기존 최적 센서위치 추정 방법들과 결과를 비교 분석하였다. 결과 비교 및 검증을 위해 지진동에 의한 동적 해석을 수행하여 기존 및 새로운 방법으로 선택된 최적 센서위치 에서의 가속도데이터를 활용하여 FFT(Fast Fourier Transform)를 통해 진동 형상의 크기를 구하고, spline function으로 전체 자유도에 대한 진동 형상을 추정하였으며, 추정된 진동 형상과 해석적으로 구해진 진동 형상과의 MAC 지수를 통하여 다양한 방법들의 모드 추정의 정확도를 비교하였다.

• Coupled systems mechanics
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• 제8권6호
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• pp.501-522
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• 2019

The present study is concerned with the thermoelastic interactions in a two dimensional axisymmetric problem in transversely isotropic thermoelastic solid using new modified couple stress theory without energy dissipation and with two temperatures. The Laplace and Hankel transforms have been employed to find the general solution to the field equations. Concentrated normal force, normal force over the circular region, concentrated thermal source and thermal source over the circular region have been taken to illustrate the application of the approach. The components of displacements, stress, couple stress and conductive temperature distribution are obtained in the transformed domain. The resulting quantities are obtained in the physical domain by using numerical inversion technique. The effect of two temperature varying by taking different values for the two temperature on the components of normal stress, tangential stress, conductive temperature and couple stress are depicted graphically.

• 충청수학회지
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• 제31권1호
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• pp.137-149
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• 2018

In this paper, under the assumption of the symmetry point spread function, antireflective boundary conditions(AR-BCs) are considered in connection with the fast truncated Lagrange(FTL) method. The FTL method is proposed as an image restoration method for large-scale ill-conditioned BTTB(block Toeplitz with Toeplitz block) and BTHHTB(block Toeplitz-plus-Hankel matrix with Toeplitz-plus-Hankel blocks) linear systems([13, 17]). The implementation and efficiency of the FTL method in the AR-BCs are further illustrated. Especially, by employing the AR-BCs, both the continuity of the image and the continuity of its normal derivative are preserved at the boundary. A reconstructed image with less artifacts at the boundary is obtained as a result.

• Structural Engineering and Mechanics
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• 제57권2호
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• pp.327-355
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• 2016

A new analytical derivation of the elastodynamic point load solutions for an isotropic multi-layered half-space is presented by means of the precise integration method (PIM) and the approach of dual vector. The time-harmonic external load is prescribed either on the external boundary or in the interior of the solid medium. Starting with the axisymmetric governing motion equations in a cylindrical coordinate system, a second order ordinary differential matrix equation can be gained by making use of the Hankel integral transform. Employing the technique of dual vector, the second order ordinary differential matrix equation can be simplified into a first-order one. The approach of PIM is implemented to obtain the solutions of the ordinary differential matrix equation in the Hankel integral transform domain. The PIM is a highly accurate algorithm to solve sets of first-order ordinary differential equations and any desired accuracy of the dynamic point load solutions can be achieved. The numerical simulation is based on algebraic matrix operation. As a result, the computational effort is reduced to a great extent and the computation is unconditionally stable. Selected numerical trials are given to validate the accuracy and applicability of the proposed approach. More examples are discussed to portray the dependence of the load-displacement response on the isotropic parameters of the multi-layered media, the depth of external load and the frequency of excitation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제6권1호
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• pp.17-31
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• 2002

Using some techniques developed by Dragomir and Wang in the recent paper [2] in connection to Ostrowski integral inequality, we point out some approximation results for the Henkel's transform of absolutely continuous mapping.

• Journal of electromagnetic engineering and science
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• 제14권3호
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• pp.273-277
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• 2014

In this research, integral transform technique for electromagnetic scattering formulation is reviewed. Electromagnetic boundary-value problems are presented to demonstrate how the integral transforms are utilized in electromagnetic propagation, antennas, and electromagnetic interference/compatibility. Various canonical structures of slotted conductors are used for illustration; moreover, Fourier transform, Hankel transform, Mellin transform, Kontorovich-Lebedev transform, and Weber transform are presented. Starting from each integral transform definition, the general procedures for solving Helmholtz's equation or Laplace's equation for the potentials in the unbounded region are reviewed. The boundary conditions of field continuity are incorporated into particular formulations. Salient features of each integral transform technique are discussed.

• International Journal of Ocean System Engineering
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• 제1권1호
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• pp.28-31
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• 2011

An attempt was made to compute the free surface deformation due to the impact of a water droplet. The Cauchy Poisson, i.e. the initial value problem, was solved with the kinematic and dynamic free surface boundary conditions linearized. The zero order Hankel transformation and Laplace transform were applied to the related equations. The initial condition for the free surface profile was derived from a captured video image. The effect of the surface tension was not significant with the water mass used in this investigation. The computed and observed free surface deformations were compared.