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# Math. Comput. Appl., Volume 21, Issue 1 (March 2016) – 5 articles

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1546 KiB
Article
Math. Comput. Appl. 2016, 21(1), 5; https://doi.org/10.3390/mca21010005 - 09 Mar 2016
Viewed by 3187
Abstract
In this study, an elasto-plastic stress analysis is proposed in an aluminum adherend and a ductile adhesive. Elasto-plastic analysis was carried out for the aluminum adherend and DP460 ductile adhesive in a double-lap joint. The analytical solution was compared with the finite element [...] Read more.
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1393 KiB
Article
Variant of Constants in Subgradient Optimization Method over Planar 3-Index Assignment Problems
Math. Comput. Appl. 2016, 21(1), 4; https://doi.org/10.3390/mca21010004 - 08 Mar 2016
Cited by 1 | Viewed by 2675
Abstract
A planar 3-index assignment problem (P3AP) of size n is an NP-complete problem. Its global optimal solution can be determined by a branch and bound algorithm. The efficiency of the algorithm depends on the best lower and upper bound of the problem. The [...] Read more.
A planar 3-index assignment problem (P3AP) of size n is an NP-complete problem. Its global optimal solution can be determined by a branch and bound algorithm. The efficiency of the algorithm depends on the best lower and upper bound of the problem. The subgradient optimization method, an iterative method, can provide a good lower bound of the problem. This method can be applied to the root node or a leaf of the branch and bound tree. Some conditions used in this method may result in one of those becoming optimal. The formulas used in this method contain some constants that can be evaluated by computational experiments. In this paper, we show a variety of initial step length constants whose values have an effect on the lower bound of the problem. The results show that, for small problem sizes, when n < 20, the most suitable constants are best chosen in the interval [0.1, 1]. Meanwhile, the interval [0.05, 0.1] is the best interval chosen for the larger problem sizes, when n ≥ 20. Full article
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2313 KiB
Article
Nonlinear Vibration of a Nanobeam on a Pasternak Elastic Foundation Based on Non-Local Euler-Bernoulli Beam Theory
Math. Comput. Appl. 2016, 21(1), 3; https://doi.org/10.3390/mca21010003 - 07 Mar 2016
Cited by 42 | Viewed by 6780
Abstract
In this study, the non-local Euler-Bernoulli beam theory was employed in the nonlinear free and forced vibration analysis of a nanobeam resting on an elastic foundation of the Pasternak type. The analysis considered the effects of the small-scale of the nanobeam on the [...] Read more.
In this study, the non-local Euler-Bernoulli beam theory was employed in the nonlinear free and forced vibration analysis of a nanobeam resting on an elastic foundation of the Pasternak type. The analysis considered the effects of the small-scale of the nanobeam on the frequency. By utilizing Hamilton’s principle, the nonlinear equations of motion, including stretching of the neutral axis, are derived. Forcing and damping effects are considered in the analysis. The linear part of the problem is solved by using the first equation of the perturbation series to obtain the natural frequencies. The multiple scale method, a perturbation technique, is applied in order to obtain the approximate closed solution of the nonlinear governing equation. The effects of the various non-local parameters, Winkler and Pasternak parameters, as well as effects of the simple-simple and clamped-clamped boundary conditions on the vibrations, are determined and presented numerically and graphically. The non-local parameter alters the frequency of the nanobeam. Frequency-response curves are drawn. Full article
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2517 KiB
Article
Numerical Simulation Study on the Flow Field Out of a Submerged Abrasive Water Jet Nozzle
Math. Comput. Appl. 2016, 21(1), 2; https://doi.org/10.3390/mca21010002 - 04 Mar 2016
Cited by 2 | Viewed by 4292
Abstract
In order to optimize the parameters of pre-mixed abrasive water jet cutting technology, make it more efficient in the coal mine gas environment and solve the problem of hard coal and the difficulty of rock drilling, FLUENT software was used to get the [...] Read more.
In order to optimize the parameters of pre-mixed abrasive water jet cutting technology, make it more efficient in the coal mine gas environment and solve the problem of hard coal and the difficulty of rock drilling, FLUENT software was used to get the isothermal, incompressible, steady flow field out of a submerged abrasive water jet nozzle through numerical simulation, with different particle sizes and different confining pressures under submerged conditions. The results show that, under submerged conditions, the maximum velocity of the abrasive particle outside the pre-mixed abrasive water jet nozzle is about 6 mm far away from the nozzle; the abrasive particle diameter has little influence on the velocity outside the nozzle. The external confining pressure of the nozzle has an important influence on the velocity, which is that the jet velocity of the same position decreases with the increase of confining pressure and the relationship between the confining pressure of different distance from the nozzle exit and the abrasive velocity is exponential function. The results of the simulation laid the foundation for optimizing the nozzle structure, improving efficiency and developing the abrasive water jet nozzle. Full article
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194 KiB
Article
A New Perturbation Approach to Optimal Polynomial Regression
Math. Comput. Appl. 2016, 21(1), 1; https://doi.org/10.3390/mca21010001 - 04 Mar 2016
Cited by 3 | Viewed by 2740
Abstract
A new approach to polynomial regression is presented using the concepts of orders of magnitudes of perturbations. The data set is normalized with the maximum values of the data first. The polynomial regression of arbitrary order is then applied to the normalized data. [...] Read more.
A new approach to polynomial regression is presented using the concepts of orders of magnitudes of perturbations. The data set is normalized with the maximum values of the data first. The polynomial regression of arbitrary order is then applied to the normalized data. Theorems for special properties of the regression coefficients as well as some criteria for determining the optimum degrees of the regression polynomials are posed and proven. The new approach is numerically tested, and the criteria for determining the best degree of the polynomial for regression are discussed. Full article
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