A new numerical technique for solving Caputo time-fractional biological population equation

ABSTRACT A new computational technique for the thermomechanical analysis of tires in stationary rolling contact is suggested. Different from the existing approaches, the proposed method uses the constitutive description of tire rubber components, such as large deformations, viscous hysteresis, dynamic stiffening, internal heating, and temperature dependency. A thermoviscoelastic constitutive model, which incorporates all the mentioned effects and their numerical aspects, is presented. An isentropic operator-split algorithm, which ensures numerical stability, was chosen for solving the coupled mechanical and energy balance equations. For the stationary rolling-contact analysis, the constitutive model presented and the operator-split algorithm are embedded into the Arbitrary Lagrangian Eulerian (ALE)–relative kinematic framework. The flow of material particles and their inelastic history within the spatially fixed mesh is described by using the recently developed numerical technique based on the Time Discontinuous Galerkin (TDG) method. For the efficient numerical solutions, a three-phase, staggered scheme is introduced. First, the nonlinear, mechanical subproblem is solved using inelastic constitutive equations. Next, deformations are transferred to the subsequent thermal phase for the solution of the heat equations concerning the internal dissipation as a source term. In the third step, the history of each material particle, i.e., each internal variable, is transported through the fixed mesh corresponding to the convective velocities. Finally, some numerical tests with an inelastic rubber wheel and a car tire model are presented.

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A Forward-Solving Numerical Technique for Dynamic Consumption and Portfolio Allocation Problems

SSRN Electronic Journal ◽

10.2139/ssrn.687622 ◽

2005 ◽

Author(s):

George Chacko ◽

Maxim Golts ◽

Mihir A. Desai ◽

Vladimir Novakovsky

Keyword(s):

Numerical Technique ◽

Portfolio Allocation ◽

Allocation Problems

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The study of acoustic scattering from a single sound-permeable sphere

Multiphase Systems ◽

10.21662/mfs2018.4.012 ◽

2018 ◽

Vol 13 (4) ◽

pp. 79-91 ◽

Cited By ~ 1

Author(s):

E.Sh. Nasibullaeva

Keyword(s):

Speed Of Sound ◽

Numerical Technique ◽

Acoustic Scattering ◽

Computer Time ◽

Physical Parameters ◽

Fast Method ◽

Scattering Field ◽

Permeable Sphere ◽

Test Verification ◽

Good Agreement

The paper presents a generalized mathematical model and numerical investigation of the problem of acoustic scattering from a single sound-permeable sphere during the passage of two types of waves - spherical from a monopole radiation source and a plane one. In solving the Helmholtz equation, a numerical technique based on the fast method of multipoles is used, which allows achieving high accuracy of the results obtained at the lowest cost of computer time. The calculations are compared with known experimental data and a good agreement is obtained. The formulas for calculating the main characteristic of the scattering field (the total scattering cross section) for a sound-permeable sphere are generalized. The effect on this characteristic of the physical parameters of media outside and inside the sphere, such as the density and speed of sound, is shown. A numerical parametric analysis of the pressure distribution around a single sound-permeable sphere for different values of the wave radius, density, and speed of sound of the outer and inner medium of the sphere is carried out. The obtained results will later be used for test verification calculations for the numerical solution of the generalized problem of acoustic scattering of a set of sound-permeable spheres (coaxial or arbitrarily located in space).

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A numerical technique for a general form of nonlinear fractional-order differential equations with the linear functional argument

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2019-0281 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Khalid K. Ali ◽

Mohamed A. Abd El salam ◽

Emad M. H. Mohamed

Keyword(s):

Differential Equations ◽

Collocation Method ◽

Fractional Order ◽

Linear Functional ◽

Numerical Technique ◽

Operational Matrix ◽

Fractional Order Differential Equations ◽

The Given ◽

Functional Argument ◽

Special Case

AbstractIn this paper, a numerical technique for a general form of nonlinear fractional-order differential equations with a linear functional argument using Chebyshev series is presented. The proposed equation with its linear functional argument represents a general form of delay and advanced nonlinear fractional-order differential equations. The spectral collocation method is extended to study this problem as a discretization scheme, where the fractional derivatives are defined in the Caputo sense. The collocation method transforms the given equation and conditions to algebraic nonlinear systems of equations with unknown Chebyshev coefficients. Additionally, we present a general form of the operational matrix for derivatives. A general form of the operational matrix to derivatives includes the fractional-order derivatives and the operational matrix of an ordinary derivative as a special case. To the best of our knowledge, there is no other work discussed this point. Numerical examples are given, and the obtained results show that the proposed method is very effective and convenient.

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Calibration Strategy to Determine the Interaction Properties of Fertilizer Particles Using Two Laboratory Tests and DEM

Agriculture ◽

10.3390/agriculture11070592 ◽

2021 ◽

Vol 11 (7) ◽

pp. 592

Author(s):

Sugirbay Adilet ◽

Jian Zhao ◽

Nukeshev Sayakhat ◽

Jun Chen ◽

Zagainov Nikolay ◽

...

Keyword(s):

Discrete Element Method ◽

Laboratory Tests ◽

Agricultural Research ◽

Numerical Technique ◽

Interaction Parameters ◽

Nonlinear Relationship ◽

Granular Assemblies ◽

Real Behavior ◽

Transient Forces ◽

Central Composite

Investigating the interactions of granular fertilizers with various types of equipment is an essential part of agricultural research. A numerical technique simulating the mechanical behavior of granular assemblies has the advantage of data trackings, such as the trajectories, velocities, and transient forces of the particles at any stage of the test. The interaction parameters were calibrated to simulate responses of granular fertilizers in EDEM, a discrete element method (DEM) software. Without a proper calibration of the interaction parameters between the granular fertilizers and various materials, the simulations may not represent the real behavior of the granular fertilizers. Therefore, in this study, a strategy is presented to identify and select a set of DEM input parameters of granular fertilizers using the central composite design (CCD) to establish the nonlinear relationship between the dynamic macroscopic granular fertilizer properties and the DEM parameters. The determined interaction properties can be used to simulate granular fertilizers in EDEM.

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A Comprehensive Review of Isogeometric Topology Optimization: Methods, Applications and Prospects

Chinese Journal of Mechanical Engineering ◽

10.1186/s10033-020-00503-w ◽

2020 ◽

Vol 33 (1) ◽

Author(s):

Jie Gao ◽

Mi Xiao ◽

Yan Zhang ◽

Liang Gao

Keyword(s):

Topology Optimization ◽

Computer Aided Design ◽

Numerical Technique ◽

Optimization Methods ◽

Negative Influence ◽

Comprehensive Overview ◽

Promising Alternative ◽

Computer Aided ◽

Optimal Material ◽

Material Layout

AbstractTopology Optimization (TO) is a powerful numerical technique to determine the optimal material layout in a design domain, which has accepted considerable developments in recent years. The classic Finite Element Method (FEM) is applied to compute the unknown structural responses in TO. However, several numerical deficiencies of the FEM significantly influence the effectiveness and efficiency of TO. In order to eliminate the negative influence of the FEM on TO, IsoGeometric Analysis (IGA) has become a promising alternative due to its unique feature that the Computer-Aided Design (CAD) model and Computer-Aided Engineering (CAE) model can be unified into a same mathematical model. In the paper, the main intention is to provide a comprehensive overview for the developments of Isogeometric Topology Optimization (ITO) in methods and applications. Finally, some prospects for the developments of ITO in the future are also presented.

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An Approach to Determine Optimal Bow Configuration of Polar Ships under Combined Ice and Calm-Water Conditions

Journal of Marine Science and Engineering ◽

10.3390/jmse9060680 ◽

2021 ◽

Vol 9 (6) ◽

pp. 680

Author(s):

Hui Li ◽

Yan Feng ◽

Muk Chen Ong ◽

Xin Zhao ◽

Li Zhou

Keyword(s):

Numerical Simulation ◽

Water Resistance ◽

Numerical Technique ◽

Experimental Studies ◽

Resistance Index ◽

Simulation Method ◽

Present Approach ◽

Calm Water ◽

Level Ice ◽

Ice Resistance

Selecting an optimal bow configuration is critical to the preliminary design of polar ships. This paper proposes an approach to determine the optimal bow of polar ships based on present numerical simulation and available published experimental studies. Unlike conventional methods, the present approach integrates both ice resistance and calm-water resistance with the navigating time. A numerical simulation method of an icebreaking vessel going straight ahead in level ice is developed using SPH (smoothed particle hydrodynamics) numerical technique of LS-DYNA. The present numerical results for the ice resistance in level ice are in satisfactory agreement with the available published experimental data. The bow configurations with superior icebreaking capability are obtained by analyzing the sensitivities due to the buttock angle γ, the frame angle β and the waterline angle α. The calm-water resistance is calculated using FVM (finite volume method). Finally, an overall resistance index devised from the ship resistance in ice/water weighted by their corresponding weighted navigation time is proposed. The present approach can be used for evaluating the integrated resistance performance of the polar ships operating in both a water route and ice route.

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