• Steel and Composite Structures
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• 제35권6호
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• pp.717-727
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• 2020

The homotopy perturbation method (HPM) to predict the pre- and post-buckling behaviour of simply supported steel beams with rectangular hollow section (RHS) is presented in this paper. The non-linear differential equations solved by HPM derive from a kinematics where large twist and cross-sections distortions are considered. The results (linear and non-linear paths) given by the present HPM are compared to those provided by the Newton-Raphson algorithm with arc length and by the commercial FEM code Abaqus. To investigate the effect of cross-sectional distortion of beams, some numerical examples are presented.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권2호
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• pp.125-136
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• 2018

In this article, a homotopy perturbation transform method (HPTM) and the Laplace transform combined with Taylor expansion method are presented for solving Volterra integral equations with a convolution kernel. The (HPTM) is innovative in Laplace transform algorithm and makes the calculation much simpler while in the Laplace transform and Taylor expansion method we first convert the integral equation to an algebraic equation using Laplace transform then we find its numerical inversion by power series. The numerical solution obtained by the proposed methods indicate that the approaches are easy computationally and its implementation very attractive. The methods are described and numerical examples are given to illustrate its accuracy and stability.

• 충청수학회지
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• 제21권4호
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• pp.533-541
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• 2008

Let X be a finite polyhedron that is of the homotopy type of the wedge of the torus and the surface with boundary. Let $f:X{\rightarrow}X$ be a self-map of X. In this paper, we prove that if the induced endomorphism of ${\pi}_1(X)$ is K-reduced, then there is an algorithm for computing the Nielsen number N(f).

• Structural Engineering and Mechanics
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• 제88권3호
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• pp.239-249
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• 2023

The Radial Point Interpolation Method (RPIM) has been proposed to overcome the difficulties associated with the use of the Radial Basis Functions (RBFs). The RPIM has the following properties: Simple implementation in terms of boundary conditions as in the Finite Element Method (FEM). A less expensive CPU time compared to other collocation meshless methods such as the Moving Least Square (MLS) collocation method. In this work, we propose an adaptive high-order numerical algorithm based on RPIM to simulate the thermoviscoplastic behavior of a material mixing observed in the Friction Stir Welding (FSW) process. The proposed adaptive meshfree RPIM algorithm adapts well to the geometric and physical data by choosing a good shape parameter with a good precision. Our numerical approach combines the RPIM and the Asymptotic Numerical Method (ANM). A numerical procedure is also proposed in this work to automatically determine an improved shape parameter for the RBFs. The efficiency of the proposed algorithm is analyzed in comparison with an iterative algorithm.

• Journal of Power Electronics
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• 제8권2호
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• pp.171-180
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• 2008

One of the major problems in electric power quality is the harmonic contents. There are several methods of indicating the quantity of harmonic contents. The most widely used measure is the total harmonic distortion (THD). Various switching techniques have been used in static converters to reduce the output harmonic content. This paper presents and compares the two harmonic optimization techniques, known as optimal minimization of the total harmonic distortion (OMTHD) technique and optimized harmonic stepped-waveform (OHSW) technique used in multi-level inverters with unequal dc sources. Both techniques are very effective and efficient for improving the quality of the inverter output voltage. First, we describe briefly the cascaded H-bridge multi-level inverter structure. Then, we present the switching algorithm for the inverter based on OHSW and OMTHD techniques. Finally, the results obtained for the two techniques are analyzed and compared. The results verify the effectiveness of the both techniques in multi-level voltage-source inverter with non-equal dc sources, clarifying the advantages of each technique.