Abstract: A size-dependent Euler–Bernoulli beam model, which
accounts for nonlocal stress field, strain gradient field and higher
order inertia force field, is derived based on the nonlocal strain
gradient theory considering velocity gradient effect. The governing
equations and boundary conditions are derived both in dimensional
and dimensionless form by employed the Hamilton principle. The
analytical solutions based on different continuum theories are
compared. The effect of higher order inertia terms is extremely
significant in high frequency range. It is found that there exists
an asymptotic frequency for the proposed beam model, while for
the nonlocal strain gradient theory the solutions diverge. The effect
of strain gradient field in thickness direction is significant in low
frequencies domain and it cannot be neglected when the material
strain length scale parameter is considerable with beam thickness.
The influence of each of three size effect parameters on the natural
frequencies are investigated. The natural frequencies increase with
the increasing material strain gradient length scale parameter or
decreasing velocity gradient length scale parameter and nonlocal
parameter.
Abstract: Hydraulic structures such as gravity dams are classified as essential structures, and have the vital role in providing strong and safe water resource management. Three major aspects must be considered to achieve an effective design of such a structure: 1) The building cost, 2) safety, and 3) accurate analysis of seepage characteristics. Due to the complexity and non-linearity relationships of the seepage process, many approximation theories have been developed; however, the application of these theories results in noticeable errors. The analytical solution, which includes the difficult conformal mapping procedure, could be applied for a simple and symmetrical problem only. Therefore, the objectives of this paper are to: 1) develop a surrogate model based on numerical simulated data using SEEPW software to approximately simulate seepage process related to a hydraulic structure, 2) develop and solve a linked simulation-optimization model based on the developed surrogate model to describe the seepage occurring under a concrete gravity dam, in order to obtain optimum and safe design at minimum cost. The result shows that the linked simulation-optimization model provides an efficient and optimum design of concrete gravity dams.
Abstract: The present paper applies the optimal homotopy perturbation method (OHPM) and the optimal homotopy asymptotic method (OHAM) introduced recently to obtain analytic approximations of the non-linear equations modeling the flow of polymer in case of wire coating of a corotational Maxwell fluid. Expression for the velocity field is obtained in non-dimensional form. Comparison of the results obtained by the two methods at different values of non-dimensional parameter l10, reveal that the OHPM is more effective and easy to use. The OHPM solution can be improved even working in the same order of approximation depends on the choices of the auxiliary functions.
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: 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: Optimization is necessary for finding appropriate solutions to a range of real-life problems. In particular, genetic (or more generally, evolutionary) algorithms have proved very useful in solving many problems for which analytical solutions are not available. In this paper, we present an optimization algorithm called Dynamic Schema with Dissimilarity and Similarity of Chromosomes (DSDSC) which is a variant of the classical genetic algorithm. This approach constructs new chromosomes from a schema and pairs of existing ones by exploring their dissimilarities and similarities. To show the effectiveness of the algorithm, it is tested and compared with the classical GA, on 15 two-dimensional optimization problems taken from literature. We have found that, in most cases, our method is better than the classical genetic algorithm.
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: The exploitation of flow pulsation in micro- and
mini-channels is a potentially useful technique for enhancing cooling
of high-end photonics and electronics systems. It is thought that
pulsation alters the thickness of the hydrodynamic and thermal
boundary layers, and hence affects the overall thermal resistance
of the heat sink. Although the fluid mechanics and heat transfer
are inextricably linked, it can be useful to decouple the parameters
to better understand the mechanisms underlying any heat transfer
enhancement. Using two-dimensional, two-component particle image
velocimetry, the current work intends to characterize the heat transfer
mechanisms in pulsating flow with a mean Reynolds number of
48 by experimentally quantifying the hydrodynamics of a generic
liquid-cooled channel geometry. Flows circulated through the test
section by a gear pump are modulated using a controller to achieve
sinusoidal flow pulsations with Womersley numbers of 7.45 and
2.36 and an amplitude ratio of 0.75. It is found that the transient
characteristics of the measured velocity profiles are dependent on the
speed of oscillation, in accordance with the analytical solution for
flow in a rectangular channel. A large velocity overshoot is observed
close to the wall at high frequencies, resulting from the interaction
of near-wall viscous stresses and inertial effects of the main fluid
body. The steep velocity gradients at the wall are indicative of
augmented heat transfer, although the local flow reversal may reduce
the upstream temperature difference in heat transfer applications.
While unsteady effects remain evident at the lower frequency, the
annular effect subsides and retreats from the wall. The shear rate at
the wall is increased during the accelerating half-cycle and decreased
during deceleration compared to steady flow, suggesting that the flow
may experience both enhanced and diminished heat transfer during
a single period. Hence, the thickness of the hydrodynamic boundary
layer is reduced for positively moving flow during one half of the
pulsation cycle at the investigated frequencies. It is expected that the
size of the thermal boundary layer is similarly reduced during the
cycle, leading to intervals of heat transfer enhancement.
Abstract: Electro-osmosis in clayey soils and sediments, for
purposes of clay consolidation, dewatering, or cleanup, and electro
injection in porous media is widespread recent decades. It is
experimentally found that the chemical properties of porous media
especially PH change the characteristics of media. Electro-osmotic
conductivity is a function of soil and grout material chemistry,
altering with time. Many numerical approaches exist to simulate the
of electro kinetic flow rate considering chemical changes. This paper
presents a simplified analytical solution for constant flow rate based
on varying electro osmotic conductivity and time dependent viscosity
for injection of colloidal silica.
Abstract: To study the dynamic mechanics response of asphalt
pavement under the temperature load and vehicle loading, asphalt
pavement was regarded as multilayered elastic half-space system, and
theory analysis was conducted by regarding dynamic modulus of
asphalt mixture as the parameter. Firstly, based on the dynamic
modulus test of asphalt mixture, function relationship between the
dynamic modulus of representative asphalt mixture and temperature
was obtained. In addition, the analytical solution for thermal stress in
single layer was derived by using Laplace integral transformation and
Hankel integral transformation respectively by using thermal
equations of equilibrium. The analytical solution of calculation model
of thermal stress in asphalt pavement was derived by transfer matrix
of thermal stress in multilayer elastic system. Finally, the variation of
thermal stress in pavement structure was analyzed. The result shows
that there is obvious difference between the thermal stress based on
dynamic modulus and the solution based on static modulus. So the
dynamic change of parameter in asphalt mixture should be taken into
consideration when theoretical analysis is taken out.
Abstract: During welding or flame cutting of metals, the
prediction of heat affected zone (HAZ) is critical. There is need to
develop a simple mathematical model to calculate the temperature
variation in HAZ and derivative analysis can be used for this purpose.
This study presents analytical solution for heat transfer through
conduction in mild steel plate. The homogeneous and nonhomogeneous
boundary conditions are single variables. The full field
analytical solutions of temperature measurement, subjected to local
heating source, are derived first by method of separation of variables
followed with the experimental visualization using infrared imaging.
Based on the present work, it is suggested that appropriate heat input
characteristics controls the temperature distribution in and around
HAZ.
Abstract: This paper presents a fully Lagrangian coupled
Fluid-Structure Interaction (FSI) solver for simulations of
fluid-structure interactions, which is based on the Moving Particle
Semi-implicit (MPS) method to solve the governing equations
corresponding to incompressible flows as well as elastic structures.
The developed solver is verified by reproducing the high velocity
impact loads of deformable thin wedges with three different materials
such as mild steel, aluminium and tin during water entry. The present
simulation results for aluminium are compared with analytical solution
derived from the hydrodynamic Wagner model and linear Wan’s
theory. And also, the impact pressure and strain on the water entry
wedge with three different materials, such as mild steel, aluminium
and tin, are simulated and the effects of hydro-elasticity are discussed.
Abstract: A solution methodology without using integral
transformation is proposed to develop analytical solutions for
transient heat conduction in nonuniform hollow cylinders with
time-dependent boundary condition at the outer surface. It is shown
that if the thermal conductivity and the specific heat of the medium
are in arbitrary polynomial function forms, the closed solutions of the
system can be developed. The influence of physical properties on the
temperature distribution of the system is studied. A numerical
example is given to illustrate the efficiency and the accuracy of the
solution methodology.
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 paper, a new trend for improvement in semianalytical
method based on scale boundaries in order to solve the 2D
elastodynamic problems is provided. In this regard, only the
boundaries of the problem domain discretization are by specific subparametric
elements. Mapping functions are uses as a class of higherorder
Lagrange polynomials, special shape functions, Gauss-Lobatto-
Legendre numerical integration, and the integral form of the weighted
residual method, the matrix is diagonal coefficients in the equations
of elastodynamic issues. Differences between study conducted and
prior research in this paper is in geometry production procedure of
the interpolation function and integration of the different is selected.
Validity and accuracy of the present method are fully demonstrated
through two benchmark problems which are successfully modeled
using a few numbers of DOFs. The numerical results agree very well
with the analytical solutions and the results from other numerical
methods.
Abstract: This paper presents the application of the Discrete
Component Model for heating and evaporation to multi-component
biodiesel fuel droplets in direct injection internal combustion engines.
This model takes into account the effects of temperature gradient,
recirculation and species diffusion inside droplets. A distinctive
feature of the model used in the analysis is that it is based on the
analytical solutions to the temperature and species diffusion
equations inside the droplets. Nineteen types of biodiesel fuels are
considered. It is shown that a simplistic model, based on the
approximation of biodiesel fuel by a single component or ignoring
the diffusion of components of biodiesel fuel, leads to noticeable
errors in predicted droplet evaporation time and time evolution of
droplet surface temperature and radius.
Abstract: Nowadays, with the increasing of the wafer's size and
the decreasing of critical size of integrated circuit manufacturing in
modern high-tech, microelectronics industry needs a maximum
attention to challenge the contamination control. The move to 300
[mm] is accompanied by the use of Front Opening Unified Pods for
wafer and his storage. In these pods an airborne cross contamination
may occur between wafers and the pods. A predictive approach using
modeling and computational methods is very powerful method to
understand and qualify the AMCs cross contamination processes.
This work investigates the required numerical tools which are
employed in order to study the AMCs cross-contamination transfer
phenomena between wafers and FOUPs. Numerical optimization and
finite element formulation in transient analysis were established.
Analytical solution of one dimensional problem was developed and
the calibration process of physical constants was performed. The least
square distance between the model (analytical 1D solution) and the
experimental data are minimized. The behavior of the AMCs
intransient analysis was determined. The model framework preserves
the classical forms of the diffusion and convection-diffusion
equations and yields to consistent form of the Fick's law. The
adsorption process and the surface roughness effect were also
traduced as a boundary condition using the switch condition Dirichlet
to Neumann and the interface condition. The methodology is applied,
first using the optimization methods with analytical solution to define
physical constants, and second using finite element method including
adsorption kinetic and the switch of Dirichlet to Neumann condition.
Abstract: Numerical methods like binomial and trinomial trees and finite difference methods can be used to price a wide range of options contracts for which there are no known analytical solutions. American options are the most famous of that kind of options. Besides numerical methods, American options can be valued with the approximation formulas, like Bjerksund-Stensland formulas from 1993 and 2002. When the value of American option is approximated by Bjerksund-Stensland formulas, the computer time spent to carry out that calculation is very short. The computer time spent using numerical methods can vary from less than one second to several minutes or even hours. However to be able to conduct a comparative analysis of numerical methods and Bjerksund-Stensland formulas, we will limit computer calculation time of numerical method to less than one second. Therefore, we ask the question: Which method will be most accurate at nearly the same computer calculation time?
Abstract: Flood wave propagation in river channel flow can be enunciated by nonlinear equations of motion for unsteady flow. It is difficult to find analytical solution of these non-linear equations. Hence, in this paper verification of the finite element model has been carried out against available numerical predictions and field data. The results of the model indicate a good matching with both Preissmann scheme and HEC-RAS model for a river reach of 29km at both sites (15km from upstream and at downstream end) for discharge hydrographs. It also has an agreeable comparison with the Preissemann scheme for the flow depth (stage) hydrographs. The proposed model has also been applying to forecast daily discharges at 400km downstream in the Indus River from Sukkur barrage of Sindh, Pakistan, which demonstrates accurate model predictions with observed the daily discharges. Hence, this model may be utilized for flood warnings in advance.
Abstract: Athermal elastic stress analysis of steel fiber reinforced aluminum laminated composite plate is investigated. Four sides of the composite plate are clamped and subjected to a uniform temperature load. The analysis is performed both analytically and numerically. Laminated composite is manufactured via hot pressing method. The investigation of the effects of the orientation angle is provided. Different orientation angles are used such as [0°/90°]s, [30°/-30°]s, [45°/-45°]s, and [60/-60]s. The analytical solution is obtained via classical laminated composite theory and the numerical solution is obtained by applying finite element method via ANSYS.