Search

In this short paper we present a necessary and sufficient condition for that the one‐dimensional mass transport equation has one unique L1 weak solution.

In this paper, we study numerical methods for solving the Navier-Stokes equations in doubly connected domains. Two methods for solving the problem are considered. The first method is based on constructing a difference problem in variables of the stream function and the vortex of velocity using the uniqueness condition for pressure. The numerical solution of the elliptic equation for stream functions is found as the sum of the solutions of two simple problems of an elliptic type. One problem is with homogeneous boundary conditions, and the other is with a homogeneous equation. An alternative approach to solving the problem is the fictitious domain method with the continuation of the least coefficient. This method does not require satisfying the pressure uniqueness condition, and is simple to implement. An important direction in the development of numerical simulation methods is the study of approximate methods for solving problems of mathematical physics in complex multidimensional areas. To solve many applied problems in irregular areas, the fictitious domain method is widely used, which is characterized by a high degree of automation of programming. The main idea of the fictitious domain method is that the problem is solved not in the original complex domain, but in some other, simpler domain. This allows to create software immediately for a fairly wide class of problems with arbitrary computational domains. The possibilities of applying the fictitious domain method to the problems of hydrodynamics in the variables “stream function, vortex of velocity” are considered in many works. In this paper, we study a numerical method for solving the Navier-Stokes equations in doubly connected domains. A computational finite difference algorithm for solving an auxiliary problem of the fictitious domain method has been developed. The results of numerical modeling of the two-dimensional Navier-Stokes equations by the fictitious domain method with continuation by the lowest coefficient are presented. For this problem, a parallel algorithm was developed using the CUDA architecture, which was tested on various grid dimensions.

The general formula proposed by Landes and Begeley [1], which has been modified for years, among which more or less complicated approaches can be distinguished for determining the J-integral in laboratory conditions. One of them is the ASTM standard [2], according to which the energy required to calculate the J-integral should be decomposed into elastic and plastic parts, and thus the factor η depending on the shape of the specimen used in laboratory tests. Some approaches, e.g. the Polish standard [3], indicate that the J-integral should be calculated without decomposing into elastic and plastic parts. The normative documents mentioned do not usually mention the dependence of the η factor on the geometrical dimensions of the specimen (except for the shape of the specimen) or the dependence on the material characteristics. As shown in [4-7], the value of the coefficient η depends on the crack length and the material characteristics, however, the influence of material constants is usually discussed in a strictly defined range. It should be noted that papers [4-7] are based on the decomposition of the coefficient η value into elastic and plastic parts. The hybrid method presented in [8] for assessing selected parameters of fracture mechanics, referring to EPRI procedures [9], allows to evaluate them without the need for tedious numerical calculations, however, unlike EPRI procedures, it does not introduce the need to decompose these parameters into elastic and plastic components. In view of this fact, in this study it was decided to assess on the basis of numerical calculations carried out for the dominance of plane strain, the effect of crack length and material constants (expressed in yield strength and strain hardening exponent in R-O law) on the value of the coefficient η which is required to estimate the value of the J-integral in accordance with by Landes and Begeley [1]. The discussion presented in [10] was the inspiration to undertake this topic. In this paper, based on a comprehensive numerical analysis of SEN(B) specimens dominated by a plane strain state, for four different crack lengths and sixteen hypothetical elastic-plastic materials (characterized by different yield strength and different level of stain hardening exponent), the values of the J-integral were estimated, the impact of the crack length and material constants on the value of J-integral was assessed, an analysis of the P=f(u) curves and discussion on the effect of crack length and material constants on the value of the factor η were presented. Using the approach given in [4-7], simplification was made in the analysis and the value of the coefficient η was determined for each analysed specimen. The analysis showed a strong dependence of the coefficient η on the crack length and the strain hardening exponent n. It turned out that the coefficient η does not depend on the yield strength of the specimen material. The results were summarized in tabular form and approximated using the Table Curve 3D program. The measurable effect of the paper is a summary of numerical results – values of the coefficient η for 64 SEN(B) specimens and a new form of the function η=f(a/W, n) which was proposed, and which allowing to take into account in the process of determining the J-integral by the factor η the geometry of the specimen (relative crack length a/W) and material characteristics (n – strain hardening exponent in R-O law).

This paper concentrates on selected aspects of numerical modeling of a short span thin-walled beams. The performed numerical simulations cover different types of finite elements (shell or solid finite elements) and different mesh sizes. Moreover the shape and magnitude of an initial geometrical imperfection is also investigated. The numerical analysis were made with the Newton-Raphson procedure with geometrical and material nonlinearity. The numerical results were compared with the laboratory four point bending test of a thin-walled beam. Furthermore, some guidelines for numerical simulations of a short span thin-walled beams in bending were proposed by authors.This paper concentrates on selected aspects of numerical modeling of a short span thin-walled beams. The performed numerical simulations cover different types of finite elements (shell or solid finite elements) and different mesh sizes. Moreover the shape and magnitude of an initial geometrical imperfection is also investigated. The numerical analysis were made with the Newton-Raphson procedure with geometrical and material nonlinearity. The numerical results were compared with the laboratory four point bending test of a thin-walled beam. Furthermore, some guidelines for numerical simulations of a short span thin-walled beams in bending were proposed by authors.

In this paper, we solve the fractional Bagley-Torvik equation by using discrete cubic spline and a fourth order approxi-mation based on weighted shifted Grunwald-Letnikov difference operator. By matrix analysis, the numerical scheme is proved to be uniquely solvable and third order accurate. An example is presented to verify the efficiency of the numerical scheme and to compare with other methods in the literature.In this paper, we solve the fractional Bagley-Torvik equation by using discrete cubic spline and a fourth order approxi-mation based on weighted shifted Grunwald-Letnikov difference operator. By matrix analysis, the numerical scheme is proved to be uniquely solvable and third order accurate. An example is presented to verify the efficiency of the numerical scheme and to compare with other methods in the literature.

A marine propeller generates adequate thrust to propel a vessel at some design speed. so, propeller is the core to optimum performance on a ship. Considerations are made to match the engine ’s power and shaft speed, as well as the size of the vessel and the ship’s operating speed, with an appropriately designed propeller. As marine propeller has complicated geometries, the flow around the propeller is complicated. In generally, the performance characteristics of a propeller is determined and analyze by experiments like open water and self-propulsion model test which are costly at the initial stage of the design. Numerical analysis using Computational Fluid Dynamics simulations could be an important alternative on this case. This study presents the investigation of marine propeller hydrodynamic performance and parameters through Computational Fluid Dynamic analysis. In this paper, a B-series propeller model is developed with respect to some design constraints such as ship speed, vessel draft etc. and analyzed the performance using CFD tools. In this analysis, we consider Realizable k-ω Turbulence Model & Multiple Reference Frame Model. Results found that all thrust coefficient (KT) and torque coefficient 10 (KQ) decreases with the increasing advance coefficient (J). The efficiency of propeller performance had also consistently showed characteristic trend of nonlinear increases to a peak an optimum value before decreasing drastically with increasing J value. The numerical results obtained from CFD Tool are compared with theoretical available publish data.A marine propeller generates adequate thrust to propel a vessel at some design speed. so, propeller is the core to optimum performance on a ship. Considerations are made to match the engine ’s power and shaft speed, as well as the size of the vessel and the ship’s operating speed, with an appropriately designed propeller. As marine propeller has complicated geometries, the flow around the propeller is complicated. In generally, the performance characteristics of a propeller is determined and analyze by experiments like open water and self-propulsion model test which are costly at the initial stage of the design. Numerical analysis using Computational Fluid Dynamics simulations could be an important alternative on this case. This study presents the investigation of marine propeller hydrodynamic performance and parameters through Computational Fluid Dynamic analysis. In this paper, a B-series propeller model is developed with respect to some design constraints such as ship speed, vessel draft etc. and analy...

The paper presents the results of computer modelling using FEA and experimental researches of the influence of technological parameters of burnishing rolling process on resistance to fatigue wear of shafts. For solution of elaborate equation of motion the explicit method was used. This allows to carries out the time analysis of the displacements, strains and stresses state’s in workpieces. In addition, the numerical analyses for the fatigue wear component after burnishing for low frequency loads were carried out. The results of the numerical analysis were experimentally verified by researching the surface layer after burnishing. In addition the shafts on fatigue wear were tested.The paper presents the results of computer modelling using FEA and experimental researches of the influence of technological parameters of burnishing rolling process on resistance to fatigue wear of shafts. For solution of elaborate equation of motion the explicit method was used. This allows to carries out the time analysis of the displacements, strains and stresses state’s in workpieces. In addition, the numerical analyses for the fatigue wear component after burnishing for low frequency loads were carried out. The results of the numerical analysis were experimentally verified by researching the surface layer after burnishing. In addition the shafts on fatigue wear were tested.

Induction heating is a process of heat generation which uses metal conductors and the Joule effect. The induction heating process has many applications in industry, such as metal melting, preheating for forging operations, hardening, and welding. A model of induction heating is given by a coupled system of partial differential equations relating temperature field and magnetic potential. Precisely, a coupled system of Maxwell and heat equations is given in the workpiece, while in the exterior domain the Laplace equation for the magnetic potential is formulated. Finally, nonlinear boundary condition for the heat equation, transmission conditions and asymptotic condition for the magnetic potential are given. Solution of such coupled multifield problems requires advanced coupled numerical methods. Therefore, in this paper we present a coupled numerical approach connecting Finite Difference Method and discrete potential theory. The use of discrete potential theory is motivated by the fact that asymptotic conditions are satisfied exactly on the discrete level. Thus, a general scheme for the coupled numerical method is presented in this paper.Induction heating is a process of heat generation which uses metal conductors and the Joule effect. The induction heating process has many applications in industry, such as metal melting, preheating for forging operations, hardening, and welding. A model of induction heating is given by a coupled system of partial differential equations relating temperature field and magnetic potential. Precisely, a coupled system of Maxwell and heat equations is given in the workpiece, while in the exterior domain the Laplace equation for the magnetic potential is formulated. Finally, nonlinear boundary condition for the heat equation, transmission conditions and asymptotic condition for the magnetic potential are given. Solution of such coupled multifield problems requires advanced coupled numerical methods. Therefore, in this paper we present a coupled numerical approach connecting Finite Difference Method and discrete potential theory. The use of discrete potential theory is motivated by the fact that asymptotic condi...

The Numerical analysis of heat treatments of TiCN coated AA7075 aluminium alloys is presented in this paper. The Convection-Diffusion-Reaction (CDR) equation with solutions in the Streamlined-Upward Petrov-Galerkin (SUPG) method for different parameters is provided for the understanding of the process. An experimental process to improve the surface properties of AA-7075 aluminium alloy was attempted through the coatings of TiCN and subsequent heat treatments. From the experimental process, optimized temperature and time was obtained which gave the maximum surface hardness and corrosion resistance. The paper gives an understanding and use of the CDR equation for application of the process. Expression to determine convection, diffusion and reaction parameters are provided which is used to obtain the overall expression of the heat treatment process. With the substitution of the optimized temperature and time, the governing equation may be obtained. Additionally, the total energy consumed during the heat treatment process is also developed to give a mathematical formulation of the energy consumed.

This paper mainly deals with the mathematical modeling, numerical analysis and Comparison of the thermal performance characteristics of a two-dimensional model of a nuclear fuel element cooled in a surrounding medium with those of one-dimensional model for different cladding materials and cladding thickness. Accordingly, the steady state equations governing the temperature field both for one and two-dimensional models with appropriate boundary conditions are solved numerically using second order central finite difference scheme. Line-by-Line method of solution procedure is then employed to get the algebraic equations which are solved using the famous Thomas Algorithm. Numerically simulated results for a wide range of Biot number, Bi, Conductivity ratio Cr, thickness ratio Th and heat generation parameter, Qt are presented and discussed. It is observed that the one dimensional model prediction is satisfactory only for lower values of parameters considered, for higher values of parameters it over predicts the two dimensional model. It is also observed that for fixed values of Ar, Qt and Bi, there exists a critical value of Th beyond which maximum temperature in the fuel element exceeds its allowable limit.This paper mainly deals with the mathematical modeling, numerical analysis and Comparison of the thermal performance characteristics of a two-dimensional model of a nuclear fuel element cooled in a surrounding medium with those of one-dimensional model for different cladding materials and cladding thickness. Accordingly, the steady state equations governing the temperature field both for one and two-dimensional models with appropriate boundary conditions are solved numerically using second order central finite difference scheme. Line-by-Line method of solution procedure is then employed to get the algebraic equations which are solved using the famous Thomas Algorithm. Numerically simulated results for a wide range of Biot number, Bi, Conductivity ratio Cr, thickness ratio Th and heat generation parameter, Qt are presented and discussed. It is observed that the one dimensional model prediction is satisfactory only for lower values of parameters considered, for higher values of parameters it over predicts t...

In this paper, the authors pointed out a study on the profitable combination of forming techniques. More in detail, the attention has been put on the combination of the single point incremental forming (SPIF) and, generally, speaking, of an additional process that can lead to a material thickening on the initial blank considering the local thinning which the sheets undergo at. Focalizing the attention of the research on the excessive thinning of parts made by SPIF, a hybrid approach can be thought as a viable solution to reduce the not homogeneous thickness distribution of the sheet. In fact, the basic idea is to work on a blank previously modified by a deformation step performed, for instance, by forming, additive or subtractive processes. To evaluate the effectiveness of this hybrid solution, a FE numerical model has been defined to analyze the thickness variation on tailored sheets incrementally formed optimizing the material distribution according to the shape to be manufactured. Simulations based on the explicit formulation have been set up for the model implementation. The mechanical properties of the sheet material have been taken in literature and a frustum of cone as benchmark profile has been considered for the performed analysis. The outcomes of numerical model have been evaluated in terms of both maximum thinning and final thickness distribution. The feasibility of the proposed approach will be deeply detailed in the paper.

The paper considers the influence of the assumed error indicator on the final adapted mesh. Provided that threshold values of an error are increased by applying the adaptive procedure, it turns out that final mesh depends on the assumed error indicator. In the paper, there were used the standard error estimates and the error indicator proposed by the author. The proposed error indicator is based on applying hierarchically generalized finite difference method (FDM). In the case of the proposed error indicator, the final adapted mesh is the most optimal for the exact solution.

This paper is devoted to a numerical approach of the biomechanics behavior modeling of a dental implant supported prothesis made up of three elements, and the surrounding bone under the masticatory forces loading. A clinical situation involving both biological (the bone tissue) and non-biological (the three elements of implant prosthesis) materials is simulated. This problem involves fine technical structure details – the threads, tapers, etc with a great impact in masticatory force transmission. Modeling the contact between the implant and the bone tissue is important to a proper bone-implant interface model and implant design. A three-dimensional numerical model is proposed in order to calculate the state of stress and displacement of this complex structure in order to evaluate its stability by determining the risk zones of stress concentration. The results of numerical modeling are in good agreement with other numerical results and clinical casesA comparison between this numerical analysis and clinical cases is performed and a good agreement is obtained.This paper is devoted to a numerical approach of the biomechanics behavior modeling of a dental implant supported prothesis made up of three elements, and the surrounding bone under the masticatory forces loading. A clinical situation involving both biological (the bone tissue) and non-biological (the three elements of implant prosthesis) materials is simulated. This problem involves fine technical structure details – the threads, tapers, etc with a great impact in masticatory force transmission. Modeling the contact between the implant and the bone tissue is important to a proper bone-implant interface model and implant design. A three-dimensional numerical model is proposed in order to calculate the state of stress and displacement of this complex structure in order to evaluate its stability by determining the risk zones of stress concentration. The results of numerical modeling are in good agreement with other numerical results and clinical casesA comparison between this numerical analysis and clinical...

This paper presents the calculation of the gas flow through the piston ring pack of the combustion engine. The paper compares the solution of ordinary differential equations using the standard numerical methods (ode solvers present in MATLAB) with a new method based on the Taylor series – Modern Taylor Series Method.This paper presents the calculation of the gas flow through the piston ring pack of the combustion engine. The paper compares the solution of ordinary differential equations using the standard numerical methods (ode solvers present in MATLAB) with a new method based on the Taylor series – Modern Taylor Series Method.

In the paper a kind of meshless discretization technique, called the Kansa method, is investigated in the context of problems with multiple boundary conditions. This numerical method uses interpolant composed of radial basis functions as well as collocation technique to discretize differential equations. To overcome the problem that appears for equations with multiple boundary conditions, where more equations should be associated with a boundary node than degrees of freedom that exist at this node, an extension of the method is proposed. The key idea lies in the modification of the interpolant with the use of Hermite formulation. The details of the approach are shown in the paper. Moreover, the special attention is paid to estimate respective value of the shape parameter included in radial functions to ensure stability of the solution process and high accuracy. To illustrate usefulness, accuracy and convergence of the method, it is employed to solve a test problem of the bending Kirchhoff plate.

The shearing process such as the blanking of sheet metals has been used often to prepare workpieces for subsequent forming operations. The use of FEM simulation is increasing for investigation and optimizing the blanking process. In the current literature a blanking FEM simulations for the limited capability and large computational cost of the three dimensional (3D) analysis has been largely limited to two dimensional (2D) plane axis-symmetry problems. However, a significant progress in modelling which takes into account the influence of real material (e.g. microstructure of the material), physical and technological conditions can be obtained by using 3D numerical analysis methods in this area. The objective of this paper is to present 3D finite element analysis of the ductile fracture, strain distribution and stress in blanking process with the assumption geometrical and physical nonlinearities. The physical, mathematical and computer model of the process are elaborated. Dynamic effects, mechanical coupling, constitutive damage law and contact friction are taken into account. The application in ANSYS/LS-DYNA program is elaborated. The effect of the main process parameter a blanking clearance on the deformation of 1018 steel and quality of the blank’s sheared edge is analyzed. The results of computer simulations can be used to forecasting quality of the final parts optimization.The shearing process such as the blanking of sheet metals has been used often to prepare workpieces for subsequent forming operations. The use of FEM simulation is increasing for investigation and optimizing the blanking process. In the current literature a blanking FEM simulations for the limited capability and large computational cost of the three dimensional (3D) analysis has been largely limited to two dimensional (2D) plane axis-symmetry problems. However, a significant progress in modelling which takes into account the influence of real material (e.g. microstructure of the material), physical and technological conditions can be obtained by using 3D numerical analysis methods in this area. The objective of this paper is to present 3D finite element analysis of the ductile fracture, strain distribution and stress in blanking process with the assumption geometrical and physical nonlinearities. The physical, mathematical and computer model of the process are elaborated. Dynamic effects, mechanical coupl...

The paper presents numerical tests results of the steel beam with sinusoidally corrugated web, which were performed in the Autodesk Algor Simulation Professional 2010. The analysis was preceded by laboratory tests including the beam’s work under the influence of the four point bending as well as the study of material characteristics. Significant web’s thickness and use of tools available in the software allowed to analyze the behavior of the plate girder as beam, and also to observe the occurrence of stresses in the characteristic element - the corrugated web. The stress distribution observed on the both web’s surfaces was analyzed.The paper presents numerical tests results of the steel beam with sinusoidally corrugated web, which were performed in the Autodesk Algor Simulation Professional 2010. The analysis was preceded by laboratory tests including the beam’s work under the influence of the four point bending as well as the study of material characteristics. Significant web’s thickness and use of tools available in the software allowed to analyze the behavior of the plate girder as beam, and also to observe the occurrence of stresses in the characteristic element - the corrugated web. The stress distribution observed on the both web’s surfaces was analyzed.

This paper presents the new numerical method based on the Taylor series. This method is used to solve a control problem with a simple system. The paper also presents the control problem and the numerical methods used to solve it. It also compares the results obtained by state of the art solvers and the proposed numerical method.This paper presents the new numerical method based on the Taylor series. This method is used to solve a control problem with a simple system. The paper also presents the control problem and the numerical methods used to solve it. It also compares the results obtained by state of the art solvers and the proposed numerical method.

This paper presents the characteristics of the process of longitudinal rolling of shafts and the geometry of the working section of forming rollers with a secant profile. In addition, the analytical formulae defining the geometry of a roller profile were determined. The experiments were carried out on shafts made of S235JR and C45 structural steels and the MSC.Marc + Mentat program was used for the numerical analysis of the rolling process based on the finite element method. The paper analyses the effect of roller geometry on the changes in value of the widening coefficient and the diameter reduction coefficient for the first forming passage. It was found that the mechanical properties of the shaft material have a slight influence on the widening coefficient. The value of the widening coefficient of the shaft increases with increase in the initial diameter of the shaft. Increasing shaft diameter causes an increase of strain gradient on the cross-section of the shaft.

With the progress of China’s nuclear power industry, nuclear power plant valve products is in a period of rapid development, high performance, low cost, short cycle of design requirements for nuclear power valve is proposed, so there is an urgent need for advanced digital design method and integrated design platform to provide technical support. Especially in the background of the nuclear power plant leakage in Japan, it is more practical to improve the design capability and product performance of the nuclear power valve. The finite element numerical analysis is a common and effective method for the development of nuclear power valves. Nuclear power valve has high safety, complexity of valve chamber and nonlinearity of seal joint surface. Therefore, it is urgent to establish accurate prediction models for earthquake prediction and seal failure to meet engineering accuracy and calculation conditions. In this paper, a general method of finite element modeling for nuclear power valve assembly and key components is presented, aiming at revealing the characteristics and rules of finite element modeling of nuclear power valves, and putting forward aprecision control strategy for finite element models for nuclear power valve characteristics analysis.With the progress of China’s nuclear power industry, nuclear power plant valve products is in a period of rapid development, high performance, low cost, short cycle of design requirements for nuclear power valve is proposed, so there is an urgent need for advanced digital design method and integrated design platform to provide technical support. Especially in the background of the nuclear power plant leakage in Japan, it is more practical to improve the design capability and product performance of the nuclear power valve. The finite element numerical analysis is a common and effective method for the development of nuclear power valves. Nuclear power valve has high safety, complexity of valve chamber and nonlinearity of seal joint surface. Therefore, it is urgent to establish accurate prediction models for earthquake prediction and seal failure to meet engineering accuracy and calculation conditions. In this paper, a general method of finite element modeling for nuclear power valve assembly and key compone...

The paper presents the development of recently proposed kinetic model of dynamic mechanical behavior of brittle solids. The model uses the ideas of kinetic theory of strength to describe the inelastic deformation and fracture. The main feature of the modified dynamic model is the introduction of two relaxation times, which determine the patterns of inelastic deformation under dynamic loading, including the dependences of the values of the cohesion and strain hardening coefficient on the strain rate. These relaxation times have the meaning of a generation time of damage of the smallest ranks and a characteristic time of formation of a system of local damage and cracks of the greatest rank. The advantage of a developed dynamic model is the possibility of its implementation within different conventional models of inelasticity of brittle solids. In the paper we implemented the kinetic model within the classical “quasi-static” Nikolaevsky’s plasticity model (non-associated plastic flow rule with the plasticity criterion in the form of Mises–Schleicher). We verified the model and determined its parameters by the example of high-strength concrete. The developed dynamic model can be implemented within the framework of various Lagrangian numerical methods (including finite and discrete element methods) using an explicit integration scheme.

The importance of the wind tunnel facilities in the aeronautical and space industry is crucial because an experimental test campaign could provide a precise overview of the aerodynamic loads in free-stream conditions of studied vehicle. In order to provide accurate and reliable results coming from the wind tunnel, an appropriate post processing is required. Over the time, the subject of the Wind Tunnel Data Corrections has been treated by many authors. The most important corrections are related to the presence of the walls of the test section and the presence of the sting (adaptor) which connect the model with the pitching system of the wind tunnel. All these interferences (due to presence of walls test section and sting) induce different boundary conditions of the flow compared to the free-stream conditions. The general idea in most papers is to apply corrections using classical methods derived from potential flow theory (available just for subsonic flow regimes in either solid walls or open test section), or using the numerical methods, like panel or CFD techniques (valid for all flow regimes) replicating as close as possible the test configuration and condition. Nowadays, the numerical methods are preferred for all regimes due to increased accuracy given by the higher computational capabilities and development of adequate models and algorithms. The purpose of the present paper is to describe the procedure of applying of the corrections to the wind tunnel data (aerodynamic coefficients) adopting the CFD techniques using the commercial solver Fluent, for a slender body.

This paper deals with the numerical investigation of ellipticity of the boundary value problem for isothermal finite strain elasto-plasticity. Ellipticity can be lost when softening occurs. A discontinuity surface then appears in the considered material body and this is associated with the ill-posedness of the boundary value problem. In the paper the condition for ellipticity loss is derived using the deformation gradient and the first Piola-Kirchhoff stress tensor. Next, the obtained condition is implemented and numerically tested within symbolic-numerical tools AceGen and AceFEM using the benchmark of an elongated rectangular plate with imperfection in plane stress and plane strain conditions.

Numerical computation packages are widely used both in teaching and research. These packages consist of license (proprietary) and open source software (non-proprietary). One of the reasons to use the package is a complexity of mathematics function (i.e., linear problems). Also, number of variables in a linear or non-linear function has been increased. The aim of this paper was to reflect on key aspects related to the method, didactics and creative praxis in the teaching of linear equations in higher education. If implemented, it could be contribute to a better learning in mathematics area (i.e., solving simultaneous linear equations) that essential for future engineers. The focus of this study was to introduce an additional numerical computation package of Scilab as an alternative low-cost computing programming. In this paper, Scilab software was proposed some activities that related to the mathematical models. In this experiment, four numerical methods such as Gaussian Elimination, Gauss-Jordan, Inverse ...

This paper reports a new numerical method based on Bernoulli polynomials for the solution of Helmholtz equations. The method uses matrix forms of Bernoulli polynomials and their derivatives by means of collocation points. Aim of this paper is to solve Helmholtz equations using this matrix relations. © 2017 Author(s).

The paper deals with the boiling process mechanism, the results of the boiling intensification methods analysis at subatmospheric pressure are presented. The calculation methodology for the boiling process on the surface performed in the form of capillary slotted channels is represented. Heat transfer coefficients variations calculation dependences defined by analytical and numerical methods applying are described. The heat exchange surface geometrical characteristics impact on the heat exchange capacity in vacuum conditions was investigated.The paper deals with the boiling process mechanism, the results of the boiling intensification methods analysis at subatmospheric pressure are presented. The calculation methodology for the boiling process on the surface performed in the form of capillary slotted channels is represented. Heat transfer coefficients variations calculation dependences defined by analytical and numerical methods applying are described. The heat exchange surface geometrical characteristics impact on the heat exchange capacity in vacuum conditions was investigated.

Thermo-mechanical numerical modelling and simulation of extrusion processes faces several serious challenges. Large plastic deformations in combination with a strong coupling of thermal with mechanical effects leads to a high numerical demand for the solution as well as for the handling of mesh distortions. The two numerical methods presented in this paper also reflect two different ways to deal with mesh distortions. Lagrangian Finite Element Methods (FEM) tackle distorted elements by building a new mesh (called re-meshing) whereas Arbitrary Lagrangian Eulerian (ALE) methods use an “advection” step to remap the solution from the distorted to the undistorted mesh. Another difference between conventional Lagrangian and ALE methods is the separate treatment of material and mesh in ALE, allowing the definition of individual velocity fields. In theory, an ALE formulation contains the Eulerian formulation as a subset to the Lagrangian description of the material. The investigations presented in this paper were dealing with the direct extrusion of a tube profile using EN-AW 6082 aluminum alloy and a comparison of experimental with Lagrangian and ALE results. The numerical simulations cover the billet upsetting and last until one third of the billet length is extruded. A good qualitative correlation of experimental and numerical results could be found, however, major differences between Lagrangian and ALE methods concerning thermo-mechanical coupling lead to deviations in the thermal results.

Islamic banking in Malaysia offers variety of products based on Islamic principles. One of the concepts is a diminishing musyarakah. The concept of diminishing musyarakah helps Muslims to avoid transaction which are based on riba. The diminishing musyarakah can be defined as an agreement between capital provider and entrepreneurs that enable entrepreneurs to buy equity in instalments where profits and losses are shared based on agreed ratio. The objective of this paper is to determine the internal rate of return (IRR) for a diminishing musyarakah model by applying a numerical method. There are several numerical methods in calculating the IRR such as by using an interpolation method and a trial and error method by using Microsoft Office Excel. In this paper we use a bisection method and secant method as an alternative way in calculating the IRR. It was found that the diminishing musyarakah model can be adapted in managing the performance of joint venture investments. Therefore, this paper will encourage mo...

This paper summarizes the experimental campaign and numerical analysis performed aimed to analyze the potential benefit available employing a trapping vortex cell system on a high thickness symmetric aero-foil without steady suction or injection mass flow. In this work, the behavior of a two dimensional model equipped with a span wise adjusted circular cavity has been researched. Pressure distribution on the model surface and inside and the complete flow field round the model have been measured. Experimental tests have been performed varying the wind tunnel speed and also the angle of attack. For numerical analysis the two dimensional model of the airfoil and the mesh is formed through ANSYS Meshing that is run in Fluent for numerical iterate solution. In the paper the performed test campaign, the airfoil design, the adopted experimental set-up, the numerical analysis, the data post process and the results description are reported, compared a discussed.

This paper provides an optical characterization and numerical prediction of local deformations appearing on the visible side of composite sandwich panels used for interior furniture of business airplanes. During manufacturing of furniture panels, metallic inserts are bonded inside the sandwich panel using an epoxy adhesive. Surface defects appear on the visible side of the panels due to curing of the adhesive, but also because of temperature gradients and humidity during manufacturing and in service. This paper presents an optical characterization based on deflectometry principle, that allows qualitative and quantitative analyses of the surface deformations in 3-dimensions. In addition, this paper presents a parametric model based on finite elements to predict the formation of surface defects using ABAQUS. A comparison is presented between the experimental observations and numerical predictions with good agreement between them.

This paper presents the numerical model of the measuring stand - the wind tunnel, in which is fixed the cylinder with cooling inlet oscillating stream. The aim of this work is the juxtaposition and comparison of characteristic values concerning the oscillating turbulent flow around cylinder, obtained from the experiment conducted in the wind tunnel at the Institute of Thermal Machinery, Czestochowa University of Technology with the data obtained as a result of numerical modeling of unsteady flow phenomena with heat transfer processes. Model discussed in this paper was created using a commercial program ANSYS FLUENT, that is used for mathematical modeling of flow and heat transfer processes. The expected outcome of this study is that it is possible in a way that doesn’t require large expenditures of time, numerical modeling a similar stand, which greatly facilitated by further research into the very large issue of unsteady flows.

Reliable modeling of multiphase pipe flows demand the development of fast and robust numerical techniques. The presented in this paper study proposes a multi-fluid model and its implementation using the Jacobian-Free Newton-Krylov (JFNK) method. The fully implicit formulation framework described in this paper will enable to efficiently solve governing fluid flow equations. A reduction of a multi-fluid model in zones of phase disappearance based on the phase state distribution over the cells is considered within the numerical method where the single phase cells and multiphase cells are distinguished by solving reduced set of governing equations for single phase cells. Current algorithm for slug flows simulations and further perspectives are proposed and discussed in this paper.

This paper presents the numerical method applied to predict the performance and wave wash of the river craft. In recent years fast ferries have been introduced on many ferry routes all over the world. Mainly when operating in shallow waters and near the coast, the waves generated by these crafts give escalate to clash with recreational use of beaches and coastal waters. The performance of HSC vehicle in these areas and the potential coastal erosion caused by a changed wave impact has been a subject of concern. In this paper, a finite volume method (FVM) and RANS approach was applied to investigate the wave wash, resistance, trim, and pressure acted on the craft. Actually a dynamic mesh with two degrees of freedom was used and the results were compared with a markedly proper experimental results and the competency of applied method was proved.

The aim of this paper is to develop numerical methods for solving systems of integral equations with cardinal splines. The unknown functions are expressed as a linear combination of horizontal translations of certain cardinal spline functions with small compact supports. Then a simple system of equations on the coefficients is obtained for the system of integral equations. It is relatively straight forward to solve the system of unknowns and an approximation of the original solution with high accuracy is achieved. Several cardinal splines are used in the paper to enhance the accuracy. The sufficient condition for the existence of the inverse matrix is examined and the convergence rate is investigated. Examples are given to demonstrate the benefits of the methods.

The paper describes different studies linked to extrusion problems encountered during production in the cable industry. Extrusion simulation or rheology analysis can be used to understand the origin of the problems in cable manufacturing and to set up durable industrial solutions by selecting the appropriate compounds, optimizing screw profiles, modifying the geometries of the tooling or adapting the processing conditions. Our investigations based on the COMPUPLAST® Virtual Extrusion Laboratory™ software, have brought large understanding and these investigations are cheaper and faster alternatives to real experiments (trials/errors) when analyzing and optimizing extrusion processes. Three examples are presented in the paper.

In this paper behavior of steel shear wall Composited (CSSW) with carbon fiber polymer in different angles have investigated. The present experimental and numerical studies conducted to carry out the effects of fiber polymer, angle of fiber polymer. Results showed that the CFRP enhance the behavior of CSSW. Despite the advantages of CSSW, there are some hardness which is caused the use of CSSW become restricted, as evaluating the shear stiffness and ultimate strength which those parameters will need to design and analysis. Analysis of CSSW, due to their out of plan buckling and post buckling behavior is extremely abstruse. Nonlinear analysis of CSSW is possible with finite element software, but nonlinear geometry and material is difficult and it tacks a long time. According to the problems mentioned representing valid formulas in nonlinear region is quite necessary which the formulas obtained from numerical analysis have suggest in this paper.

The paper presents a comparative analysis of biomechanical behavior of eight models of ulna bone having different number of surface patches from 3D reconstruction stage and different meshing structures from numerical analysis. The paper objective is to study the meshing influence on numerical analysis of a biomechanical structure to develop an optimized model. The 3D virtual parametrical model of the human ulna bone was obtained using a Computer Tomograph to acquire the bone images, 3D Mimics 10.01 image-processing software and Geomagic Studio 10 environment to convert the discrete 2D images into 3D volumes, and Solid Edge environment to convert into solid body. The four models having different number of surface patches were imported in ANASYS V12 environment to analyze and compare the biomechanical behavior of the ulna bone. Each model was meshed in two ways: default and imposing element size 1 mm. Numerical analysis evidenced significant differences for Equivalent Stress and Shear Stress. Regarding the ...

Flange vertical buckling is one of the collapse types of an I‐shaped steel girder under bending, and has been considered to occur only in girders with very slender web plate. However, in authors’ experimental test on the hybrid steel girders, the flange vertical buckling was observed in one of the test models. In this paper, a numerical analysis is made on flange vertical buckling in a hybrid steel girder. The aim of this paper is, as a first step on the research on flange vertical buckling of hybrid steel girders, reproducing and realizing the flange vertical buckling with the numerical analysis, and to study the basic behaviour of flange vertical buckling of the hybrid steel girders.

In this paper, non‐equilibrium kinetics and transport processes in a viscous hypersonic flow of reacting CO2/CO/O2/C/O mixture are studied on the basis of the kinetic theory methods. Vibrational excitation of CO2, CO and O2 molecules as well as non‐equilibrium dissociation, recombination and exchange reactions are taken into account and the influence of non‐equilibrium kinetics on transport properties is studied. A five‐temperature model for a non‐equilibrium flow suitable for applications is derived from the kinetic theory and used for the evaluation of transport properties of considered mixture under re‐entry conditions. The paper presents the closed set of non‐equilibrium flow equations, expressions for transport properties and results of calculations.

The paper uses three‐dimensional quasi‐steady molecular statics nanocutting model to perform simulative cutting of single‐crystal silicon. The study is different from the past literature that those papers mostly used molecular dynamics (MD) to perform simulation of nanocutting. Regarding the simulated cutting of single‐crystal silicon performed by the paper by using the nanoscale cutting model of three‐dimensional quasi‐steady nanoscale molecular statics method, it is a concept that the method of calculating the movement track of each atom is used to directly acquire the applied equilibrium force when each atom moves for a small distance. The paper uses optimized method to solve the equation of equilibrium force, find out the new movement position, and step by step calculate the cutting behavior in times of cutting. In order to prove the feasibility of the paper’s use of three‐dimensional quasi‐steady molecular statics nanoscale cutting model of single‐crystal silicon, the paper simulates a diamond cuttin...

The main focus of the paper is the analysis of the influence of residual stress on the ultimate limit state of a hot‐rolled member in compression. The member was modelled using thin‐walled elements of type SHELL 181 and meshed in the programme ANSYS. Geometrical and material non‐linear analysis was used. The influence of residual stress was studied using variance‐based sensitivity analysis. In order to obtain more general results, the non‐dimensional slenderness was selected as a study parameter. Comparison of the influence of the residual stress with the influence of other dominant imperfections is illustrated in the conclusion of the paper. All input random variables were considered according to results of experimental research.

In the paper we examine a modification of the classical Vehicle Routing Problem (VRP) in which shapes of transported cargo are accounted for. This problem, known as a three‐dimensional VRP with loading constraints (3D‐VRP), is appropriate when transported commodities are not perfectly divisible, but they have fixed and heterogeneous dimensions. In the paper restrictions on allowable cargo positionings are also considered. These restrictions are derived from business practice and they extended the baseline 3D‐VRP formulation as considered by Koloch and Kaminski (2010). In particular, we investigate how additional restrictions influence relative performance of two proposed optimization algorithms: the nested and the joint one. Performance of both methods is compared on artificial problems and on a big‐scale real life case study.

Homogenization of microstructure in composites is studied in this paper. If linesar and even nonlinear behavior of phases is considered, large backgrounds not only in numerical methods but also in mathematical theories are successively developed. A little bit different situation occurs when debonding fibers from matrix is assumed as possible phenomenon. Such problem is strongly nonlinear and requires special attention. Previously Uzawa’s algorithm was used in some publications of the first author; in this paper debonding process is described by the penalty method being derived in a natural way, which has a viewable physical meaning.

This paper presents the boundary element method (BEM) algorithm for the 2D steady‐state heat conduction problem of particulate composite in which a thermal boundary resistance exists at constituent interfaces. The numerical implementation of the boundary integral equations is based on linear elements after boundary discretization. BEM formulation which incorporates the imperfect interface effects is developed for steady 2D simulations of the temperature distributions of composites containing randomly distributed particles of different sizes. The randomly distributed particles investigated in this paper include circular particles and square particles with different orientations. The temperature distributions of steady‐state conduction inside the composite are simulated using the present BEM formulation. Numerical examples for composite with different particle geometries are presented, which illustrate the accuracy, suitability and efficiency of the present BEM algorithm for the approximations of steady‐state heat conduction under either perfect or imperfect interfacial thermal contact conditions. The main advantage of BEM compared with the conventional methods is that it significantly reduces the dimensionality of the problem, resulting in a comparatively smaller system of equations to be solved. Compared to available solutions obtained by other numerical method, it provides an efficient and powerful analytical tool for steady‐state solutions of constituents, such as particles with thermal barrier resistance across interfaces.

In this paper we revisit the known problem of the explosion suppression by a cloud of inert and solid particles. This issue has been so far investigated experimentally where the most important task has been to find the proper suppressant, estimate its quantity, as well as design the quenching device. Also some attention has been paid to numerical investigation where by use of computer simulation the same questions have been asked. In this paper we also focus on the numerical study, where the first moment of the suppressing process is analysed: the exact behaviour of the particle cloud as it reacts with the gas. A mathematical model is presented that bases on the Eulerian‐Lagrangian approach for the description of the both phases: solid and gas. Finally some results are shown: both snapshots of particle location as well statistics.

This paper presents a modified Thiele‐Werner algorithm to construct a kind of reliable vector‐valued rational interpolants (RVRIs) and then studies their existence. The reliability of this method means that if a solution of the basic vector‐valued rational interpolation problem exists, the method given in this paper finds it. Then a method for testing the existence for RVRIs and some methods for dealing with unattainable points for RVRIs are given.

To improve understanding of the mechanical behavior of granular materials it is important to be able to quantify the relative arrangement of the grains, i.e. the fabric. This can be done, for example, by measuring the orientations of the particles (e.g. the long axis orientation) or by considering the orientations of the vectors normal to each grain‐grain contact. In two dimensional (2D) analyses this information can be obtained by digital image analysis of images of thin sections obtained from an optical microscope. While such data is useful, granular materials of engineering interest are three dimensional (3D) materials and quantification of the 3D fabric is necessary. Micro Computed‐Tomography (μCT) together with 3D image analysis has emerged as a promising technique for obtaining the 3D data required. This paper aims to highlight the challenges associated with using image analysis to provide quantitative information on fabric. While automated image segmentation has proved to produce reasonable results in some cases, it is sometimes less successful when dealing with highly irregular and angular soil grains. This paper evaluates the effectiveness of 2D and 3D segmentation techniques that rely on the watershed segmentation algorithm. The primary material considered is Reigate Silver Sand, a natural quartzitic sand with grain diameters in the range of 150–300 μm. While the sand considered is primarily of interest to geotechnical engineers, the results of this study will be of interest to anyone seeking to quantify granular material fabric using either 2D microscopy data or μCT 3D data sets.

HMX‐based high explosive devices may unintentionally ignite and transit to deflagration or detonation during mechanical loadings such as low velocity impact. We focus our attention to ignition. The Browning and Scammon criterion is used in this study. A concrete like constitutive law is derived, with an up‐to‐date experimental characterization. These models have been implemented in the Abaqus/Explicit finite element code. Numerical simulations are compared to go/no go impact experiments in order to calibrate the threshold. This paper is about the influence of two major assumptions: (1) the behavior at finite strains and (2) the boundary conditions. This paper shows that ignition threshold evolves significantly due to these assumptions, leading to erroneous predictions.

The present paper refers to the numerical simulation of air velocity at open air spaces and the conducting thermal comfort after the evaluation of the examined space using CFD methods, taking into account bioclimatic principles at the architectural design. More specially, the paper draws attention to the physical procedures governing air movement at an open environment area in Athens (athletic park), named “Serafeio Athletic and Cultural Centre,” trying to form them in such way that will lead to the thermal comfort of the area’s visitors. The study presents a mathematical model, implemented in a general computer code that can provide detailed information on velocity, prevailing in three‐dimensional spaces of any geometrical complexity. Turbulent flow is simulated and buoyancy effects are taken into account. This modelling procedure is intended to contribute to the effort towards designing open areas, such as parks, squares or outdoor building environments, using thermal comfort criteria at the bioclimatic...

The paper gives Lyapunov type sufficient conditions for partial finite‐time and asymptotic stability in which some state variables converge to zero while the rest converge to constant values that possibly depend on the initial conditions. The paper then presents partially asymptotically stabilizing controllers for many nonlinear control systems for which continuous asymptotically stabilizing (in the usual sense) controllers are known not to exist.