Abstract: This paper investigates the nature of the development
of two-dimensional laminar flow of an incompressible fluid at the
reversed stagnation-point. ". In this study, we revisit the problem
of reversed stagnation-point flow over a flat plate. Proudman and
Johnson (1962) first studied the flow and obtained an asymptotic
solution by neglecting the viscous terms. This is no true in neglecting
the viscous terms within the total flow field. In particular it is pointed
out that for a plate impulsively accelerated from rest to a constant
velocity V0 that a similarity solution to the self-similar ODE is
obtained which is noteworthy completely analytical.
Abstract: In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.
Abstract: Incompressible Navier-Stokes equations are reviewed
in this work. Three-dimensional Navier-Stokes equations are solved
analytically. The Mathematical derivation shows that the solutions
for the zero and constant pressure gradients are similar. Descriptions
of the proposed formulation and validation against two laminar
experiments and three different turbulent flow cases are reported in
this paper. Even though, the analytical solution is derived for nonreacting
flows, it could reproduce trends for cases including
combustion.
Abstract: In this paper, we have applied the homotopy perturbation
method (HPM) for obtaining the analytical solution of unsteady
flow of gas through a porous medium and we have also compared the
findings of this research with some other analytical results. Results
showed a very good agreement between results of HPM and the
numerical solutions of the problem rather than other analytical solutions
which have previously been applied. The results of homotopy
perturbation method are of high accuracy and the method is very
effective and succinct.
Abstract: In this article an isotropic linear elastic half-space with
a cylindrical cavity of finite length is considered to be under the
effect of a ring shape time-harmonic torsion force applied at an
arbitrary depth on the surface of the cavity. The equation of
equilibrium has been written in a cylindrical coordinate system. By
means of Fourier cosine integral transform, the non-zero
displacement component is obtained in the transformed domain. With
the aid of the inversion theorem of the Fourier cosine integral
transform, the displacement is obtained in the real domain. With the
aid of boundary conditions, the involved boundary value problem for
the fundamental solution is reduced to a generalized Cauchy singular
integral equation. Integral representation of the stress and
displacement are obtained, and it is shown that their degenerated
form to the static problem coincides with existing solutions in the
literature.
Abstract: This paper presents a simplified version of Data Envelopment Analysis (DEA) - a conventional approach to evaluating the performance and ranking of competitive objects characterized by two groups of factors acting in opposite directions: inputs and outputs. DEA with a Perfect Object (DEA PO) augments the group of actual objects with a virtual Perfect Object - the one having greatest outputs and smallest inputs. It allows for obtaining an explicit analytical solution and making a step to an absolute efficiency. This paper develops this approach further and introduces a DEA model with Partially Perfect Objects. DEA PPO consecutively eliminates the smallest relative inputs or greatest relative outputs, and applies DEA PO to the reduced collections of indicators. The partial efficiency scores are combined to get the weighted efficiency score. The computational scheme remains simple, like that of DEA PO, but the advantage of the DEA PPO is taking into account all of the inputs and outputs for each actual object. Firm evaluation is considered as an example.
Abstract: Analytical solution of the first-order and third-order
shear deformation theories are developed to study the free vibration
behavior of simply supported functionally graded plates. The
material properties of plate are assumed to be graded in the thickness
direction as a power law distribution of volume fraction of the
constituents. The governing equations of functionally graded plates
are established by applying the Hamilton's principle and are solved
by using the Navier solution method. The influence of side-tothickness
ratio and constituent of volume fraction on the natural
frequencies are studied. The results are validated with the known
data in the literature.
Abstract: The numerical simulation of the slip effect via
vicoelastic fluid for 4:1 contraction problem is investigated with
regard to kinematic behaviors of streamlines and stress tensor by
models of the Navier-Stokes and Oldroyd-B equations. Twodimensional
spatial reference system of incompressible creeping flow
with and without slip velocity is determined and the finite element
method of a semi-implicit Taylor-Galerkin pressure-correction is
applied to compute the problem of this Cartesian coordinate system
including the schemes of velocity gradient recovery method and the
streamline-Upwind / Petrov-Galerkin procedure. The slip effect at
channel wall is added to calculate after each time step in order to
intend the alteration of flow path. The result of stress values and the
vortices are reduced by the optimum slip coefficient of 0.1 with near
the outcome of analytical solution.
Abstract: Responses of the dynamical systems are highly affected by the natural frequencies and it has a huge impact on design and operation of high-rise and high-speed elevators. In the present paper, the variational iteration method (VIM) is employed to investigate better understanding the dynamics of elevator cable as a single-degree-of-freedom (SDOF) swing system. Comparisons made among the results of the proposed closed-form analytical solution, the traditional numerical iterative time integration solution, and the linearized governing equations confirm the accuracy and efficiency of the proposed approach. Furthermore, based on the results of the proposed closed-form solution, the linearization errors in calculating the natural frequencies in different cases are discussed.
Abstract: A 3D simulation study for an incompressible
slip flow around a spherical aerosol particle was performed.
The full Navier-Stokes equations were solved and the velocity
jump at the gas-particle interface was treated numerically by
imposition of the slip boundary condition. Analytical solution
to the Stokesian slip flow past a spherical particle was used as
a benchmark for code verification, and excellent agreement
was achieved. The Simulation results showed that in addition
to the Knudsen number, the Reynolds number affects the slip
correction factor. Thus, the Cunningham-based slip corrections
must be augmented by the inclusion of the effect of
Reynolds number for application to Lagrangian tracking of
fine particles. A new expression for the slip correction factor
as a function of both Knudsen number and Reynolds number
was developed.
Abstract: In this paper, collocation based cubic B-spline and
extended cubic uniform B-spline method are considered for
solving one-dimensional heat equation with a nonlocal initial
condition. Finite difference and θ-weighted scheme is used for
time and space discretization respectively. The stability of the
method is analyzed by the Von Neumann method. Accuracy of
the methods is illustrated with an example. The numerical results
are obtained and compared with the analytical solutions.
Abstract: The analytical solution of functionally graded
piezoelectric hollow cylinder which is under radial electric potential
and non-axisymmetric thermo-mechanical loads, are presented in this
paper. Using complex Fourier series and estimation of power law for
variations of material characterizations through the thickness, the
electro thermo mechanical behavior of the FGPM cylinder is
obtained. The stress and displacement distributions and the effect of
electric potential field on the cylinder behavior are also presented and
some applicable results are offered at the end of the paper.
Abstract: In this paper, an analytical approach for free vibration
analysis of four edges simply supported rectangular Kirchhoff plates
is presented. The method is based on wave approach. From wave
standpoint vibration propagate, reflect and transmit in a structure.
Firstly, the propagation and reflection matrices for plate with simply
supported boundary condition are derived. Then, these matrices are
combined to provide a concise and systematic approach to free
vibration analysis of a simply supported rectangular Kirchhoff plate.
Subsequently, the eigenvalue problem for free vibration of plates is
formulated and the equation of plate natural frequencies is
constructed. Finally, the effectiveness of the approach is shown by
comparison of the results with existing classical solution.
Abstract: In this paper, we propose a novel adaptive voltage control strategy for boost converter via Inverse LQ Servo-Control. Our presented strategy is based on an analytical formula of Inverse Linear Quadratic (ILQ) design method, which is not necessary to solve Riccati’s equation directly. The optimal and adaptive controller of the voltage control system is designed. The stability and the robust control are analyzed. Whereas, we can get the analytical solution for the optimal and robust voltage control is achieved through the natural angular velocity within a single parameter and we can change the responses easily via the ILQ control theory. Our method provides effective results as the stable responses and the response times are not drifted even if the condition is changed widely.
Abstract: In this paper, the telegraph equation is solved numerically by cubic B-spline quasi-interpolation .We obtain the numerical scheme, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the temporal derivative of the dependent variable. The advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement. The results of numerical experiments are presented, and are compared with analytical solutions by calculating errors L2 and L∞ norms to confirm the good accuracy of the presented scheme.
Abstract: Efficient handoff algorithms are a cost-effective way
of enhancing the capacity and QoS of cellular system. The higher
value of hysteresis effectively prevents unnecessary handoffs but
causes undesired cell dragging. This undesired cell dragging causes
interference or could lead to dropped calls in microcellular
environment. The problems are further exacerbated by the corner
effect phenomenon which causes the signal level to drop by 20-30 dB
in 10-20 meters. Thus, in order to maintain reliable communication
in a microcellular system new and better handoff algorithms must be
developed. A fuzzy based handoff algorithm is proposed in this paper
as a solution to this problem. Handoff on the basis of ratio of slopes
of normal signal loss to the actual signal loss is presented. The fuzzy
based solution is supported by comparing its results with the results
obtained in analytical solution.
Abstract: The aim of this paper is to develop a new two dimensional time accurate Euler solver for shock tube applications. The solver was developed to study the performance of a newly built short-duration hypersonic test facility at Universiti Tenaga Nasional “UNITEN" in Malaysia. The facility has been designed, built, and commissioned for different values of diaphragm pressure ratios in order to get wide range of Mach number. The developed solver uses second order accurate cell-vertex finite volume spatial discretization and forth order accurate Runge-Kutta temporal integration and it is designed to simulate the flow process for similar driver/driven gases (e.g. air-air as working fluids). The solver is validated against analytical solution and experimental measurements in the high speed flow test facility. Further investigations were made on the flow process inside the shock tube by using the solver. The shock wave motion, reflection and interaction were investigated and their influence on the performance of the shock tube was determined. The results provide very good estimates for both shock speed and shock pressure obtained after diaphragm rupture. Also detailed information on the gasdynamic processes over the full length of the facility is available. The agreements obtained have been reasonable.
Abstract: The main goal of the present work is to decrease the
computational burden for optimum design of steel frames with
frequency constraints using a new type of neural networks called
Wavelet Neural Network. It is contested to train a suitable neural
network for frequency approximation work as the analysis program.
The combination of wavelet theory and Neural Networks (NN)
has lead to the development of wavelet neural networks.
Wavelet neural networks are feed-forward networks using
wavelet as activation function. Wavelets are mathematical
functions within suitable inner parameters, which help them to
approximate arbitrary functions. WNN was used to predict the
frequency of the structures. In WNN a RAtional function with
Second order Poles (RASP) wavelet was used as a transfer
function. It is shown that the convergence speed was faster
than other neural networks. Also comparisons of WNN with
the embedded Artificial Neural Network (ANN) and with
approximate techniques and also with analytical solutions are
available in the literature.
Abstract: This paper presents an analytical solution to get a reliable estimation of the hydrodynamic pressure on gravity dams induced by vertical component earthquake when solving the fluid and dam interaction problem. Presented analytical technique is presented for calculation of earthquake-induced hydrodynamic pressure in the reservoir of gravity dams allowing for water compressibility and wave absorption at the reservoir bottom. This new analytical solution can take into account the effect of bottom material on seismic response of gravity dams. It is concluded that because the vertical component of ground motion causes significant hydrodynamic forces in the horizontal direction on a vertical upstream face, responses to the vertical component of ground motion are of special importance in analysis of concrete gravity dams subjected to earthquakes.
Abstract: Based on the standard finite element method, a new
finite element method which is known as nonlocal finite element
method (NL-FEM) is numerically implemented in this article to
study the nonlocal effects for solving 1D nonlocal elastic problem.
An Eringen-type nonlocal elastic model is considered. In this model,
the constitutive stress-strain law is expressed interms of integral
equation which governs the nonlocal material behavior. The new
NL-FEM is adopted in such a way that the postulated nonlocal elastic
behavior of material is captured by a finite element endowed with a
set of (cross-stiffness) element itself by the other elements in mesh.
An example with their analytical solutions and the relevant numerical
findings for various load and boundary conditions are presented and
discussed in details. It is observed from the numerical solutions that
the torsional deformation angle decreases with increasing nonlocal
nanoscale parameter. It is also noted that the analytical solution fails
to capture the nonlocal effect in some cases where numerical
solutions handle those situation effectively which prove the
reliability and effectiveness of numerical techniques.