• Journal of Institute of Control, Robotics and Systems
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• v.18 no.9
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• pp.806-811
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• 2012

In this paper Hartley functions are used to approximate the solutions of continuous time linear dynamical system. The Hartley function and its integral operational matrix are first presented, an efficient algorithm to solve the Stein equation is proposed. The algorithm is based on the compound matrix and the inverse of sum of matrices. Using the structure of the Hartley's integral operational matrix, the full order Stein equation should be solved in terms of the solutions of pure algebraic matrix equations, which reduces the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity of the proposed algorithm.

• Structural Engineering and Mechanics
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• v.67 no.4
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• pp.417-425
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• 2018

The main aim of this paper is to investigate the bending of Euler-Bernouilli nano-beams made of bi-directional functionally graded materials (BDFGMs) using Eringen's non-local elasticity theory in the integral form with compare the differential form. To the best of the researchers' knowledge, in the literature, there is no study carried out into integral form of Eringen's non-local elasticity theory for bending analysis of BDFGM Euler-Bernoulli nano-beams with arbitrary functions. Material properties of nano-beam are assumed to change along the thickness and length directions according to arbitrary function. The approximate analytical solutions to the bending analysis of the BDFG nano-beam are derived by using the Rayleigh-Ritz method. The differential form of Eringen's non-local elasticity theory reveals with increasing size effect parameter, the flexibility of the nano-beam decreases, that this is unreasonable. This problem has been resolved in the integral form of the Eringen's model. For all boundary conditions, it is clearly seen that the integral form of Eringen's model predicts the softening effect of the non-local parameter as expected. Finally, the effects of changes of some important parameters such as material length scale, BDFG index on the values of deflection of nano-beam are studied.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.5
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• pp.787-797
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• 1986

An implicit approach is employed to obtain a general boundary integral formulation of axisymmetric elastic problems in terms of a pair of singular integral equations. The corresponding kernel functions from the solutions of Navier's equation are derived by applying a three dimensional integral and a direct axisymmetrical approach. A numerical discretization schem including the evaluation of Cauchy principal values of the singular integral is described. Finally the typical axisymmetric elastic models are analyzed, i.e. the hollow sphere, the constant thickness and the V-notched round bar.

• International Journal of Naval Architecture and Ocean Engineering
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• v.12 no.1
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• pp.354-366
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• 2020

This work mainly focuses on determination of the fully plastic J-integral solutions for welded center cracked plates subjected to remote tension loading. Detailed three-dimensional elasticeplastic Finite Element Analyses (FEA) were implemented to compute the fully plastic J-integral along the crack front for a wide range of crack geometries, material properties and weld strength mismatch ratios for 900 cases. According to the database generated from FEA, Back-propagation Neural Network (BPNN) model was proposed to predict the values and distributions of fully plastic J-integral along crack front based on the variables used in FEA. The determination coefficient R2 is greater than 0.99, indicating the robustness and goodness of fit of the developed BPNN model. The network model can accurately and efficiently predict the elastic-plastic J-integral for weld centerline crack, which can be used to perform fracture analyses and safety assessment for welded center cracked plates with varying strength mismatch conditions under uniaxial loading.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.495-506
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• 2004

Some oscillation criteria are given for second order nonlinear differential equations by means of integral averaging technique.

• Kyungpook Mathematical Journal
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• v.33 no.2
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• pp.133-140
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• 1993

• The Pure and Applied Mathematics
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• v.24 no.3
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• pp.155-169
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• 2017

In this paper we obtain some integral inequalities involving impulses and apply our results to a certain integro-differential equation with impulses. First, we obtain a bound of the equation, and we use the bound to study some qualitative properties of the equation.

• Proceedings of the KIEE Conference
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• 2003.10a
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• pp.82-85
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• 2003

In this paper, we present the analysis of electromagnetic scattering from arbitrarily shaped three-dimensional conducting objects coated with a dielectric material. The integral equation treated here is the combined field integral equation. Numerical results of radar cross section for coated conducting structure are presented and compared with other available solutions.

• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.281-290
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• 2009

The famous Guo-Krasnosel'skii fixed point theorems concerning cone expansion and compression of norm type and order type are extended, respectively. As an application, the existence of multiple positive solutions for systems of Hammerstein type integral equations is considered.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.879-890
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• 2020

In this paper we study the stability properties of solutions of nonlinear impulsive integro-differential systems by using an integral inequality under the stability of the corresponding variational impulsive integro-differential systems. Also, we give examples to illustrate our results.