• Steel and Composite Structures
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• v.49 no.3
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• pp.349-359
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• 2023

Dynamic response and economic of a laminated porous concrete beam reinforced by nanoparticles subjected to harmonic transverse dynamic load is investigated considering structural damping. The effective nanocomposite properties are evaluated on the basis of Mori-Tanaka model. The concrete beam is modeled by the sinusoidal shear deformation theory (SSDT). Utilizing nonlinear strains-deflection, energy relations and Hamilton's principal, the governing final equations of the concrete laminated beam are calculated. Utilizing differential quadrature method (DQM) as well as Newmark method, the dynamic displacement of the concrete laminated beam is discussed. The influences of porosity parameter, nanoparticles volume percent, agglomeration of nanoparticles, boundary condition, geometrical parameters of the concrete beam and harmonic transverse dynamic load are studied on the dynamic displacement of the laminated structure. Results indicated that enhancing the nanoparticles volume percent leads to decrease in the dynamic displacement about 63%. In addition, with considering porosity of the concrete, the dynamic displacement enhances about 2.8 time.

• Geomechanics and Engineering
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• v.35 no.2
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• pp.181-194
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• 2023

The primary objective of this study is to examine the influence of geometry on the stability characteristics of cylindrical microstructures. This investigation entails a stability analysis of a bi-directional functionally graded (BD-FG) cylindrical imperfect concrete beam, focusing on the impact of geometry. Both the first-order shear deformation beam theory and the modified coupled stress theory are employed to explore the buckling and dynamic behaviors of the structure. The cylinder-shaped imperfect beam is constructed using a porosity-dependent functionally graded (FG) concrete material, wherein diverse porosity voids and material distributions are incorporated along the radial axis of the beam. The radius functions are considered in both uniform and nonuniform variations, reflecting their alterations along the length of the beam. The combination of these characteristics leads to the creation of BD-FG configurations. In order to enable the assessment of stability using energy principles, a numerical technique is utilized to formulate the equations for partial derivatives (PDEs).

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.17 no.9
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• pp.2348-2360
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• 2023

As science and technology evolve, object detection of moving objects has been widely used in the context of machine learning and artificial intelligence. Traditional moving object detection algorithms, however, are characterized by relatively poor real-time performance and low accuracy in detecting moving objects. To tackle this issue, this manuscript proposes a modified Kalman filter algorithm, which aims to expand the equations of the system with the Taylor series first, ignoring the higher order terms of the second order and above, when the nonlinear system is close to the linear form, then it uses standard Kalman filter algorithms to measure the situation of the system. which can not only detect moving objects accurately but also has better real-time performance and can be employed to predict the trajectory of moving objects. Meanwhile, the accuracy and real-time performance of the algorithm were experimentally verified.

• Geomechanics and Engineering
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• v.36 no.4
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• pp.407-416
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• 2024

Dynamic response of a rock tunnels by laminated porous concrete beam reinforced by nanoparticles subjected to harmonic transverse dynamic load is investigated considering structural damping. The effective nanocomposite properties are evaluated on the basis of Mori-Tanaka model. The concrete beam is modeled by the exponential shear deformation theory (ESDT). Utilizing nonlinear strains-deflection, energy relations and Hamilton's principal, the governing final equations of the concrete laminated beam are calculated. Utilizing differential quadrature method (DQM) as well as Newmark method, the dynamic displacement of the concrete laminated beam is discussed. The influences of porosity parameter, nanoparticles volume percent, agglomeration of nanoparticles, boundary condition, geometrical parameters of the concrete beam and harmonic transverse dynamic load are studied on the dynamic displacement of the laminated structure. Results indicated that enhancing the nanoparticles volume percent leads to decrease in the dynamic displacement about 63%. In addition, with considering porosity of the concrete, the dynamic displacement enhances about 2.8 time.

• Journal of the Korean Mathematical Society
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• v.61 no.4
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• pp.621-657
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• 2024

In this study, the numerical solution of a space-fractional Burgers' equation with initial and boundary conditions is considered. This equation is the simplest nonlinear model for diffusive waves in fluid dynamics. It occurs in a variety of physical phenomena, including viscous sound waves, waves in fluid-filled viscous elastic pipes, magneto-hydrodynamic waves in a medium with finite electrical conductivity, and one-dimensional turbulence. The proposed QBS/CNG technique consists of the Galerkin method with a function basis of quadratic B-splines for the spatial discretization of the space-fractional Burgers' equation. This is then followed by the Crank-Nicolson approach for time-stepping. A linearized scheme is fully constructed to reduce computational costs. Stability analysis, error estimates, and convergence rates are studied. Finally, some test problems are used to confirm the theoretical results and the proposed method's effectiveness, with the results displayed in tables, 2D, and 3D graphs.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.321-331
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• 2024

We consider the numerical treatment of blow-up problems having non-monotonic singular solutions that tend to infinity at some point in the domain. The use of standard numerical methods for solving problems with blow-up solutions can lead to significant errors. The reason being that solutions of such problems have singularities whose positions are unknown in advance. To be able to integrate such non-monotonic blow-up problems, we describe and use a method of non-local transformations. To show the efficiency of the method, we present a comparison of exact and numerical solutions in addition to some comparison with the work of other authors.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.1017-1034
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• 2023

In this paper, we work two different problems. First, we investigate a new class of fractional differential equations involving Caputo sequential derivative with some (e₁, e₂, θ)-periodic conditions. The existence and uniqueness of solutions are proven. The stability of solutions is also discussed. The second part includes studying traveling wave solutions of a conformable fractional Korteweg-de Vries-Burger (KdV Burger) equation through the Tanh method. Graphs of some of the waves are plotted and discussed, and a conclusion follows.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.435-450
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• 2024

This study depends on the modified conformable fractional derivative definition to generalize and proves some theorems of the classical power series into the fractional power series. Furthermore, a comprehensive formulation of the generalized Taylor's series is derived within this context. As a result, a new technique is introduced for the fractional power series. The efficacy of this new technique has been substantiated in solving some fractional differential equations.

• Ocean Systems Engineering
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• v.14 no.3
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• pp.237-259
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• 2024

Although the investigation on the effect of loaded out-of-plane braces on the values of the stress concentration factor (SCF) in offshore tubular joints has been the objective of numerous research works, a number of quite important cases still exist that have not been studied thoroughly due to the diversity of joint types and loading conditions. One of these cases is the multi-planar tubular KK-joint subjected to axial loading. Tubular KK-joints are among the most common joint types in jacket substructure of offshore wind turbines (OWTs). In the present research, data extracted from the stress analysis of 243 finite element (FE) models, verified against available experimental data, was used to study the effects of geometrical parameters on the chord-side SCFs in multi-planar tubular KK-joints subjected to axial loading. Parametric FE study was followed by a set of nonlinear regression analyses to develop three new SCF parametric equations for the fatigue analysis and design of axially loaded multi-planar KK-joints.

• Structural Engineering and Mechanics
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• v.92 no.1
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• pp.53-64
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• 2024

This paper presents an innovative theoretical and numerical model to predict the lateral-torsional buckling (LTB) of simply supported steel I-beams with external prestressed tendons. The model incorporates an updated prestressing force, accounting for thermal effects and various external loadings. Critical multipliers are determined by solving an eigenvalue problem derived from applying Galërkin's approach to a set of nonlinear equilibrium equations. Validation is carried out through Finite Element Method (FEM) simulations, incorporating a new expression for an equivalent thermal expansion coefficient for the beam-tendon system, addressing both mechanical and thermal deformations. The primary aim is to estimate critical conditions considering material property degradation due to fire. The present results are generally in good agreement with those provided by the literature.