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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.

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.

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.

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 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.

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...

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.

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).

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.

This paper deals with the construction of numerical methods of random initial value problems. Random linear multistep methods are presented and sufficient conditions for their mean square convergence are established. Main statistical properties of the approximations processes are computed in several illustrative examples. Copyright © 2010 John Wiley & Sons, Ltd., Thanks to the anonymous reviewer whose comments greatly enhanced the paper. This work has been partially supported by the Spanish M.E.C. and FEDER grants MTM2009-08587 and TRA2007-68006-C02-02, the Universidad Politecnica de Valencia grant PAID-06-09 (ref. 2588) and Mexican Conacyt.

This paper encompasses our first efforts towards the numerical simulation of friction stir welding by employing a Lagrangian approach. To this end, we have employed a meshless method, namely the Natural Element Method (NEM). Friction Stir welding is a welding process where the union between the work pieces is achieved through the extremely high deformation imposed by a rotating pin, which moves between the two pieces. This extremely high strain is the main responsible of the difficulties associated with the numerical simulation of this forming process. Eulerian and Arbitrary Lagrangian-Eulerian (ALE) frameworks encounter difficulties in some aspects of the simulation. For instance, these approaches need additional techniques for the description of the boundary between materials, such as level sets, boundary markers or similar. In this paper we address the issue of employing a Lagrangian framework, which adequately describes the evolution in time of the interphase. The meshless character of the technique also ensures that no degeneracy on the accuracy is obtained due to mesh distortion. Some examples are presented that show the potential of the technique in simulating such a process.

The numerical analysis of thermal damage process proceeding in biological tissue, containing blood vessel, during laser irradiation is presented. Heat transfer in the tissue is assumed to be transient and two-dimensional with perfusion coefficient dependent on tissue injury. The internal heat source resulting from the laser irradiation based on the solution of diffusion equation is taken into account. At the stage of numerical computations the boundary element method and the finite difference method have been used. In the final part of the paper the results obtained are shown.

This paper presents a simulation result of confinement loss in a specialty optical fiber. The optical fiber is designed to have a thin metal-layer in the optical fiber clad. The optimum distance of copper layer from fiber core is determined by calculating the confinement loss. The confinement losses are observed by varying the copper diameter from core. The COMSOL multi-physics 5.3 is used as the simulation tool. The proposed design may potentially pave a broad range of applications including high-sensitive plasmonic biosensor and filtering devices.

This paper reveals the physical properties of Jeffery nanofluid flow past a moving plate embedded in porous medium under the existence of radiation and thermal diffusion. The analysis is carried out in three cases of moving plate, namely stationary plate λ = 0, forth-moving plate λ = 1, back-moving plate λ = −1. Finite difference method is applied to solve the governing equations of the flow and pointed out the variations in velocity, temperature and concentration with the use of graphical presentations. The impact of several parameters on local skin friction, Nusselt number and Sherwood number is also noticed and discussed. Enhancement of velocity is observed under the impact of Jeffery parameter for the cases of stationary plate and back-moving plate, whereas reverse nature is found in the case of forth-moving plate. The velocity enhances as the values of porosity parameter increases for the case of stationary plate and forth-moving plate but a reverse nature is noticed in the case of back-moving plate.

The paper deals with buckling and post-buckling behaviour of thin-walled glass reinforced aluminium laminate (GLARE) members subjected to axial loading. Different open cross-section profiles were prepared by autoclave technique that provided a high-quality manufacturing. Symmetrical 3/2 lay-ups were analysed wherein 7 stacking sequences were distinguished based on the fibres alignment in the composite layer. Composite specimens were axially compressed in laboratory tests by means of static testing unit that provided displacement control loading. The behaviour of thin-walled GLARE members was investigated with main focus on post-buckling response together with various failure modes. First Ply Failure (FPF) analysis was carried out simultaneously by Tsai-Wu, Hashin and Puck failure criteria in order to detect a first failure occurrence. Numerical analysis included also an attempt to estimate particular regions of laminate's damage in post-buckling state. Predicted collapsed mode shapes of GLARE members were found to be in a good agreement with experimental results.

The paper presents the research of tension process of elastomeric fiber gained from the Helical Auxetic Yarn structure. Experimental tests of static tension were carried out, and then used for the numerical model validation. Numerical analyses were conducted in the LS-Dyna software using the Finite Element Method. MAT_24_PIECEWISE_LINEAR_PLASTICITY material model, in which a curve from experimental research was implemented, was used. The adopted numerical model showed good compatibility with the results of experimental tests.

The packaging involve package cushioning to protect products from impact damage. The most common protection is trapezoidal cross-section PE foam cushioning. The paper covers the numerical analysis of the effect of the inclination angle of the trapezoidal walls on the maximum acceleration of the dropping platen as a result of impact with cushioning material. The research results show that for the angle of inclination of the side walls up to 15°, a similar product acceleration can be recorded as using the same volume cuboid sample.

In developed countries, shallow geothermal energy piles have become an innovative and sustainable technology in energy geotechnics. However the concept on shallow geothermal energy pile from design solutions, its operations and soil-pile interactions are still less understood. This paper aims to understand the general review on application in energy geotechnic, thermal properties and numerical studies of shallow geothermal energy pile. There are factors that need to be considered in early steps of numerical analysis which are geometry model, input data (thermal and soil properties), boundary conditions, elements discretization and type of analysis. Many previous studies show the three dimensional geometry problems are modelled in finite element computer modelling. Assumptions between soil and pile interaction are made and properties of soil and pile are identified in the studies. Results from previous studies indicate similar conclusion where W-shaped pipe typed configuration from various types of energy pile is the most efficient tool and it supplies moderate flow rate at the reference level.

The paper deals with numerical analysis of the DCB test configuration together with the data reduction scheme described in the ASTM D 5528 Standard for determination of the mode I fracture toughness in case of the laminated composites with mechanical couplings. Numerical analysis based on the FEM approach was performed with the Abaqus software exploiting the VCCT technique. The experiments on the DCB beams made of coupled laminates were also performed. The results show, that the distribution of the Strain Energy Release Rate can be asymmetric. A need for appropriate data reduction schemes has been revealed.

The numerical method to solve multimaterial topology optimization problems for elastic bodies in unilateral contact with Tresca friction is developed in the paper. The displacement of the elastic body in contact is governed by elliptic equation with inequality boundary conditions. The body is assumed to consists from more than two distinct isotropic elastic materials. The materials distribution function is chosen as the design variable. Since high contact stress appears during the contact phenomenon the aim of the structural optimization problem is to find such topology of the domain occupied by the body that the normal contact stress along the boundary of the body is minimized. The original cost functional is regularized using the multiphase volume constrained Ginzburg-Landau energy functional rather than the perimeter functional. The first order necessary optimality condition is recalled and used to formulate the generalized gradient flow equations of Allen–Cahn type. The optimal topology is obtained as...

The Rim-driven Thruster (RDT) integrates the thrust motor and the propeller, which can effectively reduce the space occupied by the propulsion system, improve the propulsion efficiency, and thus has important research value and broad market prospects. The Halbach Permanent Magnet Rim Thrust Motor (HPMRTM) can improve the torque density of the propulsion motor by utilizing the unilateral magnetic field of the Halbach array. In this paper, the numerical method is used to study the electromagnetic performance of the motor under different Halbach array parameters. The relationship between motor parameters such as air-gap flux density, electromagnetic torque and Halbach array parameters is obtained, and then the motor structure is optimized. By comparing with Common Permanent Magnet RTM, the advantages of HPMRTM are verified.

The paper presents the results of testing the strength of butt joints welded with the GMAW method. The base material of the joints was high-strength ferritic steel. The research program included experimental and computational part. In experimental studies, precise hardness distribution measurements were carried out to determine the extent of zones in joints. On the basis of the hardness of the material, its strength characteristics were defined in the relevant sections of the welded joint analyzed. Defining material properties and geometry of zones allowed to create a numerical model of the specimen. Based on the numerical analysis of the specimen load, the most stressed areas in the welded joint were determined. The results of numerical computations were verified by experimental methods. The correctness of the numerical model was checked by comparing the strain distributions on the surface of the specimen obtained FEM and measured using the Aramis video system.

The following paper presents numerical analyses and laboratory tests used for analyzing the impact of exploitation damage to the main structural members of the scaffolding frame system. The presence of inevitable defects reduces the strength of material compared to the theoretical strength. Numerical analysis preceded by own laboratory research allows you to describe precisely the behavior of the element. Performing a series of calculations gives information on the impact of the damage size and location on the bearing capacity of the scaffolding frame.

We have worked on the development of a particle-based numerical model of a hydrogen Radio Frequency (RF) Inductively Coupled Plasma (ICP). In the previous work, it has been shown that the model is able to simulate the E-to-H discharge mode transition, which is one of the distinct features of RF ICP. The purpose of the present study is to investigate the E-to-H discharge mode transition of the hydrogen RF ICP by our numerical model. In particular, the spatiotemporal behavior of ions, which we have not investigated in the previous work, will be presented in this paper.

The numerical equilibrium path analysis of the material with random rheological properties by using standard procedures and specialist computer programs was not successful. The proper solution for the analysed heuristic model of the material was obtained on the base of chaos theory elements and neural networks. The paper deals with mathematical reasons of used computer programs and also are elaborated the properties of the attractor used in analysis. There are presented results of conducted numerical analysis both in a numerical and in graphical form for the used procedures.

The main aim of this paper is an experimental and numerical analysis of the dynamic behavior of an active rotor with three composite blades. The study focuses on developing an effective FE modeling technique of a macro fiber composite element (denoted as MFC or active element) for the dynamic tests of active structures. The active rotor under consideration consists of a hub with a drive shaft, three grips and three glass-epoxy laminate blades with embedded active elements. A simplified FE model of the macro fiber composite element exhibiting the d33 piezoelectric effect is developed using the Abaqus software package. The discussed transducer is modeled as quasi-homogeneous piezoelectric material, and voltage is applied to the opposite faces of the element. In this case, the effective (equivalent) piezoelectric constant d33* is specified. Both static and dynamic tests are performed to verify the proposed model. First, static deflections of the active blade caused by the voltage signal are determined by num...

International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) -- SEP 25-30, 2017 -- Thessaloniki, GREECE, WOS: 000445105400303, In this paper, the concept of a strongly lacunary delta(2) quasi-Cauchy sequence is introduced. We proved interesting theorems related to strongly lacunary delta(2) -quasi-Cauchy sequences. A real valued function f defined on a subset A of the set of real numbers, is strongly lacunary delta(2) ward continuous on A if it preserves strongly lacunary delta(2) quasi-Cauchy sequences of points in A, i.e. (f(alpha(k))) is a strongly lacunary delta(2) quasi-Cauchy sequence whenever (alpha(k)) is a strongly lacunary delta(2) quasi-Cauchy sequences of points in A, where a sequence (alpha(k)) is called strongly lacunary delta(2) quasi-Cauchy if (Delta(2)alpha(k)) is a strongly lacunary delta(2) quasi-Cauchy sequence where Delta(2)alpha(k) = alpha(k+2)-2 alpha(k+1)+ alpha(k) for each positive integer k.

The numerical analysis of thermal damage process proceeding in biological tissue during laser irradiation is presented. Heat transfer in the tissue is assumed to be transient and two-dimensional. The internal heat source resulting from the laser irradiation based on the solution of diffusion equation is taken into account. The tissue is regarded as a homogeneous domain with perfusion coefficient treated as dependent on tissue injury. At the stage of numerical computations the boundary element method and the finite difference method have been used. In the final part of the paper the results obtained are shown.

Model high-speed combustor on gaseous hydrocarbon fuel, prepared for experiments in T-131 wind tunnel of TsAGI, is presented. Experiments are projected to create an experimental database for validation of calculations and physical models of turbulence and combustion. Geometry of combustor and prepared measurements are described. The main subject of paper is preliminary calculations of this combustor. Numerical methods for 2D and 3D URANS calculations are described. Special attention is given to numerical techniques allowing fast calculations of 3D unsteady flow development in the combustor. Approach to parallel realization of Fractional Time Stepping (FTS) technology is described. One way of In Situ Adaptive Tabulation (ISAT) of kinetic equations solution during the calculation is presented. Possible gasdynamic structure of flow in the combustor with the flame stabilization both in subsonic and in supersonic regime is described. Asymmetrical stationary solution (for the symmetrically-expanding duct) and symmetrical solution with flame oscillations are found and analyzed.

Industrial applications of additively manufactured components are increasing quickly. Adequate quality control of the parts is necessary in ensuring safety when using these materials. Base material properties, surface conditions, as well as location and size of defects are some of the main targets for nondestructive evaluation of additively manufactured parts, and the problem of adequate characterization is compounded given the challenges of complex part geometry. Numerical modeling can allow the interplay of the various factors to be studied, which can lead to improved measurement design. This paper presents a finite element simulation verified by experimental results of ultrasonic waves scattering from flat bottom holes (FBH) in additive manufacturing materials. A focused beam immersion ultrasound transducer was used for both the modeling and simulations in the additive manufactured samples. The samples were SS17 4 PH steel samples made by laser sintering in a powder bed.

Laboratory tests of concrete composite concrete T-shaped beams with variously arranged interface were performed. In the particular series the interface between concrete parts was reinforced or non-reinforced. Additionally the interface conditions varied as follows: existence of adhesion in the interface, adhesion partly broken using chemical agent and adhesion completely broken with PVE membrane put in the interface. The paper presents the compiled results of all tests and the first stage of FEM analysis concerning the series of beams, where the adhesion was broken. Results of numerical analysis are compared with the crack pattern observed during tests.

This paper considers the relationship between a binary response and a circular predictor. It develops the logistic regression model by employing the linear-circular regression approach. The maximum likelihood method is used to estimate the parameters. The Newton-Raphson numerical method is used to find the estimated values of the parameters. A data set from weather records of Toowoomba city is analysed by the proposed methods. Moreover, a simulation study is considered. The R software is used for all computations and simulations.

In this paper we present a new numerical method for solving fractional differential equations (FDEs) based on Genocchi polynomials operational matrix through collocation method. The operational matrix of fractional integration in Riemann-Liouville sense is derived. The upper bound for the error of the operational matrix of fractional integration is also shown. The properties of Genocchi polynomials are utilized to reduce the given problems to a system of algebraic equations. Illustrative examples are finally given to show the simplicity, accuracy and applicability of the method.

The paper focuses on investigation of resonance regimes of a drill string nonlinear dynamics under the effect of a variable axial compressive force. The drill string is modelled in the form of a rotating elastic isotropic rod with hinged ends. Deformations of the drill string are assumed to be finite. Using Galerkin’s approach a mathematical model of the drill string lateral vibrations reduces to a nonlinear ordinary differential equation for the generalized time function. Applying the harmonic balance method, the amplitude-frequency characteristics of the resonances on basic and higher frequencies are determined. As a result of numerical analysis of the impact of the dynamic system parameters on the resonance curves, considerable nonlinear effects of the amplitude-frequency characteristics of the drill string vibrations are revealed. Recommendations to choose optimal constructive and dynamic characteristics of drill strings are provided.

In this paper, we reformulate the Vlasov-Maxwell equations based on the Morrison-Marsden-Weinstein Poisson bracket. In order to get the numerical solutions preserving the Poisson bracket, we split the Hamiltonian of the Vlasov-Maxwell equations into five parts. We construct the numerical methods for the time direction via composing the exact solutions of subsystems. By combining an appropriate spatial discretization, we can prove that the resulting numerical discretization preserves the discrete Poisson bracket. We present numerical simulations for the problems of Landau damping and two-stream stability.

The present paper explores the effect of slip variation for Newtonian and non-Newtonian lubricants on textured slider bearing performance considering cavitation. Investigations are carried out by using a numerical method based on commercial CFD (computational fluid dynamic) software ANSYS for fluid flow phenomenon to assess the tribological characteristic (i.e. hydrodynamic pressure distribution) of a lubricated sliding contact. The Zwart-Gerber-Belamri model for cavitation is adopted. To model hydrophobicity, i.e. slippage, the enhanced user-defined-function (UDF) in the FLUENT® package is developed. The numerical results show that the cavitation modeling has a huge effect on the performance. Neglecting the cavitation leads to a less accurate result. Also, regarding the effect of slip variation, it is found that the single slip is the best pattern to improve the pressure profile.

In the proposed paper we continue the study of the diaphony, defined in b-adic number system, and we extend it in different directions. We investigate this diaphony as a tool for estimation of the pseudorandom properties of some of the most used random number generators. This is done by evaluating the distribution of specially constructed two-dimensional nets on the base of the obtained random numbers. The aim is to see how the generated numbers are suitable for calculations in some numerical methods (Monte Carlo etc.).

The dynamic force equilibrium equations of the cup of crowned tapered roller bearing under the combined loads condition are established in this paper, considering the centrifugal forces of each roller, the forces of the rib/roller end contact and the contact forces between crowned tapered roller and raceway. The equations are solved based on the Newton iteration method to analysis the dynamic load distribution of crowned tapered roller bearings. The load distribution and contact deformation of tapered roller bearing with three kinds of crowned rollers, such as rollers with straight profile, circular crowned profile and logarithmic crowned profile, are analyzed according to the Palmgren’s formula and the numerical method based on influence coefficient method respectively. The results show that the Almgren’s formula can be applied to calculation of the dynamic load distribution approximatively, while the numerical method must be used in contact deformation calculation for the crowned tapered roller bearing.

The three-blade planetary mixer is one of the important solid propellant mixing equipment, the layout of blades will affect the blades’ torque load and the power consumption. In this paper, the effects of the eccentric distance (Es=0∼16 mm), the solid blade form (two paddles, and four paddlers), and the blade arrangement (linear arrangement, triangle arrangement) on the blades’ torque load are investigated during the mixer stirring the solid propellant process.

In this paper, we simulate some of the benchmark problems proposed by the World Federation of Nondestructive Evaluation Centers (WFNDEC) using a full wave simulation model based on accurate solutions to the boundary integral equations for ultrasonic scattering. Much of the previous work on modeling these problems relied on the Kirch-hoff approximation to find the scattered fields from defects. Here we instead use a numerical method, called the Nystrom method, for finding the scattered fields more accurately by solving the boundary integral equations of scattering. We compare our model’s predictions with both measurements and Kirchhoff approximation based models. We expect the presented results to serve as a validation of our model as well as a comparison between the Kirchhoff approximation and the Nystrom method.

A flexural strength of composite beam designed as boxed shaped section comprised of lipped C-channel of cold-formed steel (CFS) facing each other with reinforcement bars is proposed in this paper. The boxed shaped is kept restrained in position by a profiled metal decking installed on top of the beam to form a slab system. This profiled decking slab is cast by using self-compacting concrete where the concrete is in compression when load is applied to the beam. Reinforcement bars are used as shear connector between slab and CFS as beam. A numerical analysis method proposed by EC4 is used to predict the flexural strength of the proposed composite beam. It was assumed that elasto-plastic behaviour is developed in the cross –sectional of the proposed beam. The calculated predicted flexural strength of the proposed beam shows reasonable flexural strength for cold-formed composite beam.

The Ahlfors map and Szego kernel are both classically related to each other. Ahlfors map can be computed using Szego kernel without relying on the zeros of Ahlfors map. The Szego kernel is a solution of a Fredholm integral equation of the second kind with the Kerzman-Stein kernel. The exact zeros of the Ahlfors map are unknown except for the annulus region. This paper presents a numerical method for computing the zeros of the Ahlfors map of any bounded doubly connected region. The method depends on the values of Szego kernel, its derivative and the derivative of boundary correspondence function of Ahlfors map. Using combination of Nystrom method, GMRES method, fast multiple method and Newton’s method, the numerical examples presented here prove the effectiveness of the proposed method.

The Euler equations have been used to model gas dynamics for decades. They consist of mathematical equations for the conservation of mass, momentum, and energy of the gas. For a large time value, the solution may contain discontinuities, even when the initial condition is smooth. A standard finite volume numerical method is not able to give accurate solutions to the Euler equations around discontinuities. Therefore we solve the Euler equations using an adaptive mesh finite volume method. In this paper, we present a new construction of the adaptive mesh finite volume method with an efficient computation of the refinement indicator. The adaptive method takes action automatically at around places having inaccurate solutions. Inaccurate solutions are reconstructed to reduce the error by refining the mesh locally up to a certain level. On the other hand, if the solution is already accurate, then the mesh is coarsened up to another certain level to minimize computational efforts. We implement the numerical entropy production as the mesh refinement indicator. As a test problem, we take the Sod shock tube problem. Numerical results show that the adaptive method is more promising than the standard one in solving the Euler equations of gas dynamics.

When determining the characteristics of the fatigue crack growth rate, it is necessary, inter alia, to measure the crack length growth which must be combined with the number of accumulated load cycles. The length of the crack is determined using different testing methods. Recently, there is an increased interest in optical systems based on digital image correlation methods. These methods have however some limitations as regards, inter alia, the sharpness of pictures taken during tests e.g. at cryogenic temperatures. This paper presents a comparative analysis of the crack length “a” as a function of a crack-opening-displacement “δ” obtained by experimental and numerical method. The tests were performed under ambient temperature for CT type specimens made of Ti6Al4V titanium alloy. Numerical research was carried out by finite element method using ABAQUS software. Satisfactory results were obtained which gave the reasons for establishing a hybrid methods for the crack length determination.

One-step block method for solving linear Volterra integro-differential equations (VIDEs) is presented in this paper. In VIDEs, the unknown function appears in the form of derivative and under the integral sign. The popular methods for solving VIDEs are the method of quadrature or quadrature method combined with numerical method. The proposed block method will solve the ordinary differential equations (ODEs) part and Newton-Cotes quadrature rule is applied to calculate the integral part of VIDEs. Numerical problems are presented to illustrate the performance of the proposed method.

This paper proposes a wavelet based numerical method for the solution of elastoplastic problem. The method is based on the Lagrange variational equation of elastic static and the Haar wavelet transform of the components of deformation field. Some examples of analysis of multilevel deformation are shown for the demonstration of the method’s capabilities. Some differences in the wavelet spectrums of multilevel inhomogeneous media are shown and discussed.

A BGK-type model is a simplified model to the Boltzmann equation where the complicated collision integral is approximated using a simple relaxation term. In this paper, a generalized BGK-type model is proposed by combining the original BGK, Shakhov and ellipsoidal statistical models. To verify the new model, theoretical and numerical analysis is performed. The Chapman-Enskog expansion shows that the generalized model can recover the Navier-Stokes-Fourier and Burnett equations by choosing properly the introduced parameters. In addition, the collision term of the model is evaluated for several designed relaxation problems. Results show that the new model can match the results of third-order moments obtained with DSMC method by adjusting the free parameters.

We present a conservative spectral method for the fully nonlinear Boltzmann collision operator based on the weighted convolution structure in Fourier space developed by Gamba and Tharkabhushnanam. This method can simulate a broad class of collisions, including both elastic and inelastic collisions as well as angularly dependent cross sections in which grazing collisions play a major role. The extension presented in this paper consists of factorizing the convolution weight on quadrature points by exploiting the symmetric nature of the particle interaction law, which reduces the computational cost and memory requirements of the method to O(M2N4logN) from the O(N6) complexity of the original spectral method, where N is the number of velocity grid points in each velocity dimension and M is the number of quadrature points in the factorization, which can be taken to be much smaller than N. We present preliminary numerical results.

In this paper we present a new search direction known as the CG-BFGS method, which uses the search direction of the conjugate gradient method approach in the quasi-Newton methods. The new algorithm is compared with the quasi-Newton methods in terms of the number of iterations and CPU-time. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is used as an updating formula for the approximation of the Hessian for both methods. Our numerical analysis provides strong evidence that our CG-BFGS method is more efficient than the ordinary BFGS method. Besides, we also prove that the new algorithm is globally convergent.