Abstract: The modelling of physical phenomena, such as the
earth’s free oscillations, the vibration of strings, the interaction of
atomic particles, or the steady state flow in a bar give rise to Sturm-
Liouville (SL) eigenvalue problems. The boundary applications of
some systems like the convection-diffusion equation, electromagnetic
and heat transfer problems requires the combination of Dirichlet and
Neumann boundary conditions. Hence, the incorporation of Robin
boundary condition in the analyses of Sturm-Liouville problem. This
paper deals with the computation of the eigenvalues and
eigenfunction of generalized Sturm-Liouville problems with Robin
boundary condition using the finite element method. Numerical
solution of classical Sturm–Liouville problem is presented. The
results show an agreement with the exact solution. High results
precision is achieved with higher number of elements.
Abstract: In the present study we have investigated axial
buckling characteristics of nanocomposite beams reinforced by
single-walled carbon nanotubes (SWCNTs). Various types of beam
theories including Euler-Bernoulli beam theory, Timoshenko beam
theory and Reddy beam theory were used to analyze the buckling
behavior of carbon nanotube-reinforced composite beams.
Generalized differential quadrature (GDQ) method was utilized to
discretize the governing differential equations along with four
commonly used boundary conditions. The material properties of the
nanocomposite beams were obtained using molecular dynamic (MD)
simulation corresponding to both short-(10,10) SWCNT and long-
(10,10) SWCNT composites which were embedded by amorphous
polyethylene matrix. Then the results obtained directly from MD
simulations were matched with those calculated by the mixture rule
to extract appropriate values of carbon nanotube efficiency
parameters accounting for the scale-dependent material properties.
The selected numerical results were presented to indicate the
influences of nanotube volume fractions and end supports on the
critical axial buckling loads of nanocomposite beams relevant to
long- and short-nanotube composites.
Abstract: This paper presents a study on the effect of
second-order slip and jump on forced convection through a long
isothermally heated or cooled planar microchannel. The fully
developed solutions of thermal flow fields are analytically obtained on
the basis of the second-order Maxwell-Burnett slip and Smoluchowski
jump boundary conditions. Results reveal that the second-order term in
the Karniadakis slip boundary condition is found to contribute a
negative velocity slip and then to lead to a higher pressure drop as well
as a higher fluid temperature for the heated-wall case or to a lower
fluid temperature for the cooled-wall case. These findings are contrary
to predictions made by the Deissler model. In addition, the role of
second-order slip becomes more significant when the Knudsen
number increases.
Abstract: In this paper, analysis of an infinite beam resting on
multilayer tensionless extensible geosynthetic reinforced granular
fill-poor soil system overlying soft soil strata under moving load with
constant velocity is presented. The beam is subjected to a
concentrated load moving with constant velocity. The upper
reinforced granular bed is modeled by a rough membrane embedded
in Pasternak shear layer overlying a series of compressible nonlinear
winkler springs representing the underlying the very poor soil. The
multilayer tensionless extensible geosynthetic layer has been
assumed to deform such that at interface the geosynthetic and the soil
have some deformation. Nonlinear behaviour of granular fill and the
very poor soil has been considered in the analysis by means of
hyperbolic constitutive relationships. Governing differential
equations of the soil foundation system have been obtained and
solved with the help of appropriate boundary conditions. The solution
has been obtained by employing finite difference method by means of
Gauss-Siedal iterative scheme. Detailed parametric study has been
conducted to study the influence of various parameters on the
response of soil–foundation system under consideration by means of
deflection and bending moment in the beam and tension mobilized in
the geosynthetic layer. These parameters include magnitude of
applied load, velocity of load, damping, ultimate resistance of poor
soil and granular fill layer. Range of values of parameters has been
considered as per Indian Railway conditions. This study clearly
observed that the comparisons of multilayer tensionless extensible
geosynthetic reinforcement with poor foundation soil and magnitude
of applied load, relative compressibility of granular fill and ultimate
resistance of poor soil has significant influence on the response of
soil–foundation system.
Abstract: The quantitative study of cell mechanics is of
paramount interest, since it regulates the behaviour of the living cells
in response to the myriad of extracellular and intracellular
mechanical stimuli. The novel experimental techniques together with
robust computational approaches have given rise to new theories and
models, which describe cell mechanics as combination of
biomechanical and biochemical processes. This review paper
encapsulates the existing continuum-based computational approaches
that have been developed for interpreting the mechanical responses of
living cells under different loading and boundary conditions. The
salient features and drawbacks of each model are discussed from both
structural and biological points of view. This discussion can
contribute to the development of even more precise and realistic
computational models of cell mechanics based on continuum
approaches or on their combination with microstructural approaches,
which in turn may provide a better understanding of
mechanotransduction in living cells.
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: In this paper, we introduced a gradient-based inverse
solver to obtain the missing boundary conditions based on the
readings of internal thermocouples. The results show that the method
is very sensitive to measurement errors, and becomes unstable when
small time steps are used. The artificial neural networks are shown to
be capable of capturing the whole thermal history on the run-out
table, but are not very effective in restoring the detailed behavior of
the boundary conditions. Also, they behave poorly in nonlinear cases
and where the boundary condition profile is different.
GA and PSO are more effective in finding a detailed
representation of the time-varying boundary conditions, as well as in
nonlinear cases. However, their convergence takes longer. A
variation of the basic PSO, called CRPSO, showed the best
performance among the three versions. Also, PSO proved to be
effective in handling noisy data, especially when its performance
parameters were tuned. An increase in the self-confidence parameter
was also found to be effective, as it increased the global search
capabilities of the algorithm. RPSO was the most effective variation
in dealing with noise, closely followed by CRPSO. The latter
variation is recommended for inverse heat conduction problems, as it
combines the efficiency and effectiveness required by these
problems.
Abstract: Recent perceived climate variability raises concerns
with unprecedented hydrological phenomena and extremes.
Distribution and circulation of the waters of the Earth become
increasingly difficult to determine because of additional uncertainty
related to anthropogenic emissions. The world wide observed
changes in the large-scale hydrological cycle have been related to an
increase in the observed temperature over several decades. Although
the effect of change in climate on hydrology provides a general
picture of possible hydrological global change, new tools and
frameworks for modelling hydrological series with nonstationary
characteristics at finer scales, are required for assessing climate
change impacts. Of the downscaling techniques, dynamic
downscaling is usually based on the use of Regional Climate Models
(RCMs), which generate finer resolution output based on atmospheric
physics over a region using General Circulation Model (GCM) fields
as boundary conditions. However, RCMs are not expected to capture
the observed spatial precipitation extremes at a fine cell scale or at a
basin scale. Statistical downscaling derives a statistical or empirical
relationship between the variables simulated by the GCMs, called
predictors, and station-scale hydrologic variables, called predictands.
The main focus of the paper is on the need for using statistical
downscaling techniques for projection of local hydrometeorological
variables under climate change scenarios. The projections can be then
served as a means of input source to various hydrologic models to
obtain streamflow, evapotranspiration, soil moisture and other
hydrological variables of interest.
Abstract: The effect of non-homogeneity on the free transverse vibration of thin rectangular plates of bilinearly varying thickness has been analyzed using generalized differential quadrature (GDQ) method. The non-homogeneity of the plate material is assumed to arise due to linear variations in Young’s modulus and density of the plate material with the in-plane coordinates x and y. Numerical results have been computed for fully clamped and fully simply supported boundary conditions. The solution procedure by means of GDQ method has been implemented in a MATLAB code. The effect of various plate parameters has been investigated for the first three modes of vibration. A comparison of results with those available in literature has been presented.
Abstract: The nonlinear self-interaction of an electrostatic surface wave on a semibounded quantum plasma with relativistic degeneracy is investigated by using quantum hydrodynamic (QHD) model and the Poisson’s equation with appropriate boundary conditions. It is shown that a part of the second harmonic generated through self-interaction does not have a true surface wave character but propagates obliquely away from the plasma-vacuum interface into the bulk of plasma.
Abstract: This paper presents a study on the effect of
second-order slip on forced convection through a long isoflux heated
or cooled planar microchannel. The fully developed solutions of flow
and thermal fields are analytically obtained on the basis of the
second-order Maxwell-Burnett slip and local heat flux boundary
conditions. Results reveal that when the average flow velocity
increases or the wall heat flux amount decreases, the role of thermal
creep becomes more insignificant, while the effect of second-order slip
becomes larger. The second-order term in the Deissler slip boundary
condition is found to contribute a positive velocity slip and then to lead
to a lower pressure drop as well as a lower temperature rise for the
heated-wall case or to a higher temperature rise for the cooled-wall
case. These findings are contrary to predictions made by the
Karniadakis slip model.
Abstract: In this investigation an elastic stress analysis is carried out a woven steel fiber reinforced thermoplastic cantilever beam loaded uniformly at the upper surface. The composite beam material consists of low density polyethylene as a thermoplastic (LDFE, f.2.12) and woven steel fibers. Granules of the polyethylene are put into the moulds and they are heated up to 160°C by using electrical resistance. Subsequently, the material is held for 5min under 2.5 MPa at this temperature. The temperature is decreased to 30°C under 15 MPa pressure in 3min. Closed form solution is found satisfying both the governing differential equation and boundary conditions. We investigated orientation angle effect on stress distribution of composite cantilever beams. The results show that orientation angle play an important role in determining the responses of a woven steel fiber reinforced thermoplastic cantilever beams and an optimal design of these structures.
Abstract: This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y''' = f(x, y, y', y''), y(α)=y0, y'(α)=β, y''(α)=η with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non – stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.
Abstract: In order to study the free vibration of simply supported circular cylindrical shells; an analytical procedure is developed and discussed in detail. To identify its’ validity, the exact technique was applied to four different shell theories 1) Soedel, 2) Flugge, 3) Morley-Koiter, and 4) Donnell. The exact procedure was compared favorably with experimental results and those obtained using the numerical finite element method. A literature review reveals that beam functions are used extensively as an approximation for simply supported boundary conditions. The effects of this approximate method were also investigated on the natural frequencies by comparing results with those of the exact analysis.
Abstract: In this paper the influence of a vertical plate’s thermal capacity is numerically investigated in order to evaluate the evolution of the thermal boundary layer structure, as well as the convective heat transfer coefficient and the velocity and temperature profiles. Whereas the heat flux of the heated vertical plate is evaluated under time depending boundary conditions. The main important feature of this problem is the unsteadiness of the physical phenomena. A 2D CFD model is developed with the Ansys Fluent 14.0 environment and is validated using unsteady data obtained for plasterboard studied under a dynamic temperature evolution. All the phenomena produced in the vicinity of the thermal conductive vertical plate (plasterboard) are analyzed and discussed. This work is the first stage of a holistic research on transient free convection that aims, in the future, to study the natural convection in the vicinity of a vertical plate containing Phase Change Materials (PCM).
Abstract: We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.
Abstract: In the present work, study of the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. Material properties are graded in the thickness direction of the shell according to volume fraction power law distribution. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of boundary conditions on the natural frequencies of the FG cylindrical shell. The study is carried out using third order shear deformation shell theory. The governing equations of motion of FG cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of constituent volume fractions and the effects of free-free boundary conditions.
Abstract: In this paper, self-starting block hybrid method of
order (5,5,5,5)T is proposed for the solution of the special second
order ordinary differential equations with associated initial or
boundary conditions. The continuous hybrid formulations enable us
to differentiate and evaluate at some grids and off – grid points to
obtain four discrete schemes, which were used in block form for
parallel or sequential solutions of the problems. The computational
burden and computer time wastage involved in the usual reduction of
second order problem into system of first order equations are avoided
by this approach. Furthermore, a stability analysis and efficiency of
the block method are tested on stiff ordinary differential equations,
and the results obtained compared favorably with the exact solution.
Abstract: In this paper, free vibration analysis of carbon nanotube (CNT) reinforced laminated composite panels is presented. Three types of panels such as flat, concave and convex are considered for study. Numerical simulation is carried out using commercially available finite element analysis software ANSYS. Numerical homogenization is employed to calculate the effective elastic properties of randomly distributed carbon nanotube reinforced composites. To verify the accuracy of the finite element method, comparisons are made with existing results available in the literature for conventional laminated composite panels and good agreements are obtained. The results of the CNT reinforced composite materials are compared with conventional composite materials under different boundary conditions.
Abstract: Electro-hydraulic power steering (EHPS) system for
the fuel rate reduction and steering feel improvement is comprised of
ECU including the logic which controls the steering system and BL
DC motor and produces the best suited cornering force, BLDC motor,
high pressure pump integrated module and basic oil-hydraulic circuit
of the commercial HPS system.
Electro-hydraulic system can be studied in two ways such as
experimental and computer simulation. To get accurate results in
experimental study of EHPS system, the real boundary management is
necessary which is difficult task. And the accuracy of the experimental
results depends on the preparation of the experimental setup and
accuracy of the data collection. The computer simulation gives
accurate and reliable results if the simulation is carried out considering
proper boundary conditions. So, in this paper, each component of
EHPS was modeled, and the model-based analysis and control logic
was designed by using AMESim