Abstract: In this paper, an advanced Nonlinear Exponential
Model (NEM), able to simulate the uniaxial dynamic behavior of
seismic isolators having a continuously decreasing tangent stiffness
with increasing displacement in the relatively large displacements
range and a hardening or softening behavior at large displacements, is
presented. The mathematical model is validated by comparing the
experimental force-displacement hysteresis loops obtained during
cyclic tests, conducted on a helical wire rope isolator and a recycled
rubber-fiber reinforced bearing, with those predicted analytically.
Good agreement between the experimental and simulated results
shows that the proposed model can be an effective numerical tool to
predict the force-displacement relationship of seismic isolation
devices within the large displacements range. Compared to the
widely used Bouc-Wen model, unable to simulate the response of
seismic isolators at large displacements, the proposed one allows to
avoid the numerical solution of a first order nonlinear ordinary
differential equation for each time step of a nonlinear time history
analysis, thus reducing the computation effort. Furthermore, the
proposed model can simulate the smooth transition of the hysteresis
loops from small to large displacements by adopting only one set of
five parameters determined from the experimental hysteresis loops
having the largest amplitude.
Abstract: In this paper, a one-dimensional (1d) Parallel Elasto-
Plastic Model (PEPM), able to simulate the uniaxial dynamic
behavior of seismic isolators having a continuously decreasing
tangent stiffness with increasing displacement, is presented. The
parallel modeling concept is applied to discretize the continuously
decreasing tangent stiffness function, thus allowing to simulate the
dynamic behavior of seismic isolation bearings by putting linear
elastic and nonlinear elastic-perfectly plastic elements in parallel. The
mathematical model has been validated by comparing the
experimental force-displacement hysteresis loops, obtained testing a
helical wire rope isolator and a recycled rubber-fiber reinforced
bearing, with those predicted numerically. Good agreement between
the simulated and experimental results shows that the proposed
model can be an effective numerical tool to predict the forcedisplacement
relationship of seismic isolators within relatively large
displacements. Compared to the widely used Bouc-Wen model, the
proposed one allows to avoid the numerical solution of a first order
ordinary nonlinear differential equation for each time step of a
nonlinear time history analysis, thus reducing the computation effort,
and requires the evaluation of only three model parameters from
experimental tests, namely the initial tangent stiffness, the asymptotic
tangent stiffness, and a parameter defining the transition from the
initial to the asymptotic tangent stiffness.
Abstract: Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.
Abstract: The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.
Abstract: In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.
Abstract: This study presents a quasi-zero stiffness (QZS) vibration isolator using flexure-based spring mechanisms which afford both negative and positive stiffness elements, which enable self-adjustment. The QZS property of the isolator is achieved at the equilibrium position. A nonlinear mathematical model is then developed, based on the pre-compression of the flexure-based spring mechanisms. The dynamics are further analyzed using the Harmonic Balance method. The vibration attention efficiency is illustrated using displacement transmissibility, which is then compared with the corresponding linear isolator. The effects of parameters on performance are also investigated by numerical solutions. The flexure-based spring mechanisms are subsequently designed using the concept of compliant mechanisms, with evaluation by ANSYS software, and simulations of the QZS isolator.
Abstract: Recently, advanced geotechnical engineering problems
related to soil movement, particle loss, and modeling of local failure
(i.e. discontinua) as well as modeling the in-contact structures (i.e.
continua) are of the great interest among researchers. The aim of this
research is to meet the requirements with respect to the modeling
of the above-mentioned two different domains simultaneously. To
this end, a coupled numerical method is introduced based on
Discrete Element Method (DEM) and eXtended-Finite Element
Method (X-FEM). In the coupled procedure, DEM is employed to
capture the interactions and relative movements of soil particles as
discontinua, while X-FEM is utilized to model in-contact structures as
continua, which may consist of different types of discontinuities. For
verification purposes, the new coupled approach is utilized to examine
benchmark problems including different contacts between/within
continua and discontinua. Results are validated by comparison with
those of existing analytical and numerical solutions. This study
proves that extended-finite-discrete element method can be used
to robustly analyze not only contact problems, but also other
types of discontinuities in continua such as (i) crack formations
and propagations, (ii) voids and bimaterial interfaces, and (iii)
combination of previous cases. In essence, the proposed method
can be used vastly in advanced soil-structure interaction problems to
investigate the micro and macro behaviour of the surrounding soil and
the response of the embedded structure that contains discontinuities.
Abstract: We develop a method based on polynomial quintic
spline for numerical solution of fourth-order non-homogeneous
parabolic partial differential equation with variable coefficient. By
using polynomial quintic spline in off-step points in space and
finite difference in time directions, we obtained two three level
implicit methods. Stability analysis of the presented method has been
carried out. We solve four test problems numerically to validate the
derived method. Numerical comparison with other methods shows
the superiority of presented scheme.
Abstract: This paper presents an investigation of the fabrication of the optical devices in terms of their characteristics based on the use of the electromagnetic waves. Planar waveguides are used to examine the field modes (bound modes) and the parameters required for this structure. The modifications are conducted on surface plasmons based waveguides. Simple symmetric dielectric slab structure is used and analyzed in terms of transverse electric mode (TE-Mode) and transverse magnetic mode (TM-Mode. The paper presents mathematical and numerical solutions for solving simple symmetric plasmons and provides simulations of surface plasmons for field confinement. Asymmetric TM-mode calculations for dielectric surface plasmons are also provided.
Abstract: Most of the building materials are considered porous, and composed of solid matrix and pores. In the pores, the moisture can be existed in two phases: liquid and vapor. Thus, the mass balance equation is comprised of various moisture driving potentials that translate the movement of the different existing phases occupying pores and the hygroscopic behavior of a porous construction material. This study suggests to resolve a hygrothermal mathematical model of heat and mass transfers in different porous building materials by a numerical investigation. Thereby, the evolution of temperature and moisture content fields has been processed. So, numerous series of hygrothermal calculation on several cases of wall are exposed. Firstly, a case of monolayer wall of massive wood has been treated. In this part, we have compared the numerical solution of the model on one and two dimensions and the effect of dimensional space has been evaluated. In the second case, three building materials (concrete, wood fiberboard and wooden insulation) are tested separately with the same boundary conditions and their hygrothermal behavior are compared. The evaluation of the exchange of heat and air at the interface between the wall and the interior ambiance is carried.
Abstract: In designing a low-energy-consuming buildings, the heat transfer through a large glass or wall becomes critical. Multiple layers of the window glasses and walls are employed for the high insulation. The gravity driven air flow between window glasses or wall layers is a natural heat convection phenomenon being a key of the heat transfer. For the first step of the natural heat transfer analysis, in this study the development and application of a finite volume method for the numerical computation of viscous incompressible flows is presented. It will become a part of the natural convection analysis with high-order scheme, multi-grid method, and dual-time step in the future. A finite volume method based on a fully-implicit second-order is used to discretize and solve the fluid flow on unstructured grids composed of arbitrary-shaped cells. The integrations of the governing equation are discretised in the finite volume manner using a collocated arrangement of variables. The convergence of the SIMPLE segregated algorithm for the solution of the coupled nonlinear algebraic equations is accelerated by using a sparse matrix solver such as BiCGSTAB. The method used in the present study is verified by applying it to some flows for which either the numerical solution is known or the solution can be obtained using another numerical technique available in the other researches. The accuracy of the method is assessed through the grid refinement.
Abstract: The problem under research is that of unpredictable modes occurring in two-stage centrifugal hydraulic pump as a result of hydraulic processes caused by vibrations of structural components. Numerical, analytical and experimental approaches are considered. A hypothesis was developed that the problem of unpredictable pressure decrease at the second stage of centrifugal pumps is caused by cavitation effects occurring upon vibration. The problem has been studied experimentally and theoretically as of today. The theoretical study was conducted numerically and analytically. Hydroelastic processes in dynamic “liquid – deformed structure” system were numerically modelled and analysed. Using ANSYS CFX program engineering analysis complex and computing capacity of a supercomputer the cavitation parameters were established to depend on vibration parameters. An influence domain of amplitudes and vibration frequencies on concentration of cavitation bubbles was formulated. The obtained numerical solution was verified using CFM program package developed in PNRPU. The package is based on a differential equation system in hyperbolic and elliptic partial derivatives. The system is solved by using one of finite-difference method options – the particle-in-cell method. The method defines the problem solution algorithm. The obtained numerical solution was verified analytically by model problem calculations with the use of known analytical solutions of in-pipe piston movement and cantilever rod end face impact. An infrastructure consisting of an experimental fast hydro-dynamic processes research installation and a supercomputer connected by a high-speed network, was created to verify the obtained numerical solutions. Physical experiments included measurement, record, processing and analysis of data for fast processes research by using National Instrument signals measurement system and Lab View software. The model chamber end face oscillated during physical experiments and, thus, loaded the hydraulic volume. The loading frequency varied from 0 to 5 kHz. The length of the operating chamber varied from 0.4 to 1.0 m. Additional loads weighed from 2 to 10 kg. The liquid column varied from 0.4 to 1 m high. Liquid pressure history was registered. The experiment showed dependence of forced system oscillation amplitude on loading frequency at various values: operating chamber geometrical dimensions, liquid column height and structure weight. Maximum pressure oscillation (in the basic variant) amplitudes were discovered at loading frequencies of approximately 1,5 kHz. These results match the analytical and numerical solutions in ANSYS and CFM.
Abstract: Numerical approach based on the electrical simulation method is proposed to solve a nonlinear transient heat conduction problem with nonlinear boundary for a spherical body. This problem represents a strong nonlinearity in both the governing equation for temperature dependent thermal property and the boundary condition for combined convective and radiative cooling. By analysing the equivalent electrical model using the electrical circuit simulation program HSPICE, transient temperature and heat flux distributions at sphere can be obtained easily and fast. The solutions clearly illustrate the effect of the radiation-conduction parameter Nrc, the Biot number and the linear coefficient of temperature dependent conductivity and heat capacity. On comparing the results with corresponding numerical solutions, the accuracy and efficiency of this computational method is found to be good.
Abstract: This paper has focused on the most important parameters in the LSC uptake; inlet Re number and Sc number in the presence of non-uniform magnetic field. The magnetic field is arising from the thin wire with electric current placed vertically to the arterial blood vessel. According to the results of this study, applying magnetic field can be a treatment for atherosclerosis by reducing LSC along the vessel wall. Homogeneous porous layer as a arterial wall has been regarded. Blood flow has been considered laminar and incompressible containing Ferro fluid (blood and 4 % vol. Fe3O4) under steady state conditions. Numerical solution of governing equations was obtained by using the single-phase model and control volume technique for flow field.
Abstract: Journal bearings used in IC engines are prone to premature
failures and are likely to fail earlier than the rated life due to
highly impulsive and unstable operating conditions and frequent
starts/stops. Vibration signature extraction and wear debris analysis
techniques are prevalent in industry for condition monitoring of
rotary machinery. However, both techniques involve a great deal of
technical expertise, time, and cost. Limited literature is available on
the application of these techniques for fault detection in reciprocating
machinery, due to the complex nature of impact forces that
confounds the extraction of fault signals for vibration-based analysis
and wear prediction. In present study, a simulation model was developed to investigate
the bearing wear behaviour, resulting because of different operating
conditions, to complement the vibration analysis. In current
simulation, the dynamics of the engine was established first, based on
which the hydrodynamic journal bearing forces were evaluated by
numerical solution of the Reynold’s equation. In addition, the
essential outputs of interest in this study, critical to determine wear
rates are the tangential velocity and oil film thickness between the
journals and bearing sleeve, which if not maintained appropriately,
have a detrimental effect on the bearing performance. Archard’s wear prediction model was used in the simulation to
calculate the wear rate of bearings with specific location information
as all determinative parameters were obtained with reference to crank
rotation. Oil film thickness obtained from the model was used as a
criterion to determine if the lubrication is sufficient to prevent contact
between the journal and bearing thus causing accelerated wear. A
limiting value of 1 μm was used as the minimum oil film thickness
needed to prevent contact. The increased wear rate with growing
severity of operating conditions is analogous and comparable to the
rise in amplitude of the squared envelope of the referenced vibration
signals. Thus on one hand, the developed model demonstrated its
capability to explain wear behaviour and on the other hand it also
helps to establish a co-relation between wear based and vibration
based analysis. Therefore, the model provides a cost effective and
quick approach to predict the impending wear in IC engine bearings
under various operating conditions.
Abstract: This paper describes a new approach which can be
used to interpret the experimental creep deformation data obtained
from miniaturized thin plate bending specimen test to the
corresponding uniaxial data based on an inversed application of the
reference stress method. The geometry of the thin plate is fully
defined by the span of the support, l, the width, b, and the thickness,
d. Firstly, analytical solutions for the steady-state, load-line creep
deformation rate of the thin plates for a Norton’s power law under
plane stress (b→0) and plane strain (b→∞) conditions were obtained,
from which it can be seen that the load-line deformation rate of the
thin plate under plane-stress conditions is much higher than that
under the plane-strain conditions. Since analytical solution is not
available for the plates with random b-values, finite element (FE)
analyses are used to obtain the solutions. Based on the FE results
obtained for various b/l ratios and creep exponent, n, as well as the
analytical solutions under plane stress and plane strain conditions, an
approximate, numerical solutions for the deformation rate are
obtained by curve fitting. Using these solutions, a reference stress
method is utilised to establish the conversion relationships between
the applied load and the equivalent uniaxial stress and between the
creep deformations of thin plate and the equivalent uniaxial creep
strains. Finally, the accuracy of the empirical solution was assessed
by using a set of “theoretical” experimental data.
Abstract: In this study, one dimensional phase change problem
(a Stefan problem) is considered and a numerical solution of this
problem is discussed. First, we use similarity transformation to
convert the governing equations into ordinary differential equations
with its boundary conditions. The solutions of ordinary differential
equation with the associated boundary conditions and interface
condition (Stefan condition) are obtained by using a numerical
approach based on operational matrix of differentiation of shifted
second kind Chebyshev wavelets. The obtained results are compared
with existing exact solution which is sufficiently accurate.
Abstract: Reflux condensation occurs in vertical channels and tubes when there is an upward core flow of vapour (or gas-vapour mixture) and a downward flow of the liquid film. The understanding of this condensation configuration is crucial in the design of reflux condensers, distillation columns, and in loss-of-coolant safety analyses in nuclear power plant steam generators. The unique feature of this flow is the upward flow of the vapour-gas mixture (or pure vapour) that retards the liquid flow via shear at the liquid-mixture interface. The present model solves the full, elliptic governing equations in both the film and the gas-vapour core flow. The computational mesh is non-orthogonal and adapts dynamically the phase interface, thus produces a sharp and accurate interface. Shear forces and heat and mass transfer at the interface are accounted for fundamentally. This modeling is a big step ahead of current capabilities by removing the limitations of previous reflux condensation models which inherently cannot account for the detailed local balances of shear, mass, and heat transfer at the interface. Discretisation has been done based on finite volume method and co-located variable storage scheme. An in-house computer code was developed to implement the numerical solution scheme. Detailed results are presented for laminar reflux condensation from steam-air mixtures flowing in vertical parallel plate channels. The results include velocity and gas mass fraction profiles, as well as axial variations of film thickness.
Abstract: In this paper, the problem of steady laminar boundary
layer flow and heat transfer over a permeable exponentially
stretching/shrinking sheet with generalized slip velocity is
considered. The similarity transformations are used to transform the
governing nonlinear partial differential equations to a system of
nonlinear ordinary differential equations. The transformed equations
are then solved numerically using the bvp4c function in MATLAB.
Dual solutions are found for a certain range of the suction and
stretching/shrinking parameters. The effects of the suction parameter,
stretching/shrinking parameter, velocity slip parameter, critical shear
rate and Prandtl number on the skin friction and heat transfer
coefficients as well as the velocity and temperature profiles are
presented and discussed.
Abstract: Theory of interpretation of electromagnetic fields studied in the electrical prospecting with direct current is mainly developed for the case of a horizontal surface observation. However in practice we often have to work in difficult terrain surface. Conducting interpretation without the influence of topography can cause non-existent anomalies on sections. This raises the problem of studying the impact of different shapes of ground surface relief on the results of electrical prospecting's research. This research examines the numerical solutions of the direct problem of electrical prospecting for two-dimensional and three-dimensional media, taking into account the terrain. The problem is solved using the method of integral equations. The density of secondary currents on the relief surface is obtained.