Abstract: The electrical interaction between two axisymmetric
spheroidal particles in an electrolyte solution is examined numerically.
A Galerkin finite element method combined with a Newton-Raphson
iteration scheme is proposed to evaluate the spatial variation in the
electrical potential, and the result obtained used to estimate the
interaction energy between two particles. We show that if the surface
charge density is fixed, the potential gradient is larger at a point, which
has a larger curvature, and if surface potential is fixed, surface charge
density is proportional to the curvature. Also, if the total interaction
energy against closest surface-to-surface curve exhibits a primary
maximum, the maximum follows the order (oblate-oblate) >
(sphere-sphere)>(oblate-prolate)>(prolate-prolate), and if the curve
has a secondary minimum, the absolute value of the minimum follows
the same order.
Abstract: In this paper, the dam-reservoir interaction is
analyzed using a finite element approach. The fluid is assumed to be
incompressible, irrotational and inviscid. The assumed boundary
conditions are that the interface of the dam and reservoir is vertical
and the bottom of reservoir is rigid and horizontal. The governing
equation for these boundary conditions is implemented in the
developed finite element code considering the horizontal and vertical
earthquake components. The weighted residual standard Galerkin
finite element technique with 8-node elements is used to discretize
the equation that produces a symmetric matrix equation for the damreservoir
system. A new boundary condition is proposed for
truncating surface of unbounded fluid domain to show the energy
dissipation in the reservoir, through radiation in the infinite upstream
direction. The Sommerfeld-s and perfect damping boundary
conditions are also implemented for a truncated boundary to compare
with the proposed far end boundary. The results are compared with
an analytical solution to demonstrate the accuracy of the proposed
formulation and other truncated boundary conditions in modeling the
hydrodynamic response of an infinite reservoir.
Abstract: The purpose of this study is to derive optimal shapes of
a body located in viscous flows by the finite element method using the
acoustic velocity and the four-step explicit scheme. The formulation
is based on an optimal control theory in which a performance function
of the fluid force is introduced. The performance function should be
minimized satisfying the state equation. This problem can be transformed
into the minimization problem without constraint conditions
by using the adjoint equation with adjoint variables corresponding to
the state equation. The performance function is defined by the drag
and lift forces acting on the body. The weighted gradient method
is applied as a minimization technique, the Galerkin finite element
method is used as a spatial discretization and the four-step explicit
scheme is used as a temporal discretization to solve the state equation
and the adjoint equation. As the interpolation, the orthogonal basis
bubble function for velocity and the linear function for pressure
are employed. In case that the orthogonal basis bubble function is
used, the mass matrix can be diagonalized without any artificial
centralization. The shape optimization is performed by the presented
method.
Abstract: The seismic response of steel shear wall system considering nonlinearity effects using finite element method is investigated in this paper. The non-linear finite element analysis has potential as usable and reliable means for analyzing of civil structures with the availability of computer technology. In this research the large displacements and materially nonlinear behavior of shear wall is presented with developing of finite element code. A numerical model based on the finite element method for the seismic analysis of shear wall is presented with developing of finite element code in this research. To develop the finite element code, the standard Galerkin weighted residual formulation is used. Two-dimensional plane stress model and total Lagrangian formulation was carried out to present the shear wall response and the Newton-Raphson method is applied for the solution of nonlinear transient equations. The presented model in this paper can be developed for analysis of civil engineering structures with different material behavior and complicated geometry.
Abstract: Both the minimum energy consumption and
smoothness, which is quantified as a function of jerk, are generally
needed in many dynamic systems such as the automobile and the
pick-and-place robot manipulator that handles fragile equipments.
Nevertheless, many researchers come up with either solely
concerning on the minimum energy consumption or minimum jerk
trajectory. This research paper considers the indirect minimum Jerk
method for higher order differential equation in dynamics
optimization proposes a simple yet very interesting indirect jerks
approaches in designing the time-dependent system yielding an
alternative optimal solution. Extremal solutions for the cost functions
of indirect jerks are found using the dynamic optimization methods
together with the numerical approximation. This case considers the
linear equation of a simple system, for instance, mass, spring and
damping. The simple system uses two mass connected together by
springs. The boundary initial is defined the fix end time and end
point. The higher differential order is solved by Galerkin-s methods
weight residual. As the result, the 6th higher differential order shows
the faster solving time.
Abstract: In this paper, a numerical solution based on sinc
functions is used for finding the solution of boundary value problems
which arise from the problems of calculus of variations. This
approximation reduce the problems to an explicit system of algebraic
equations. Some numerical examples are also given to illustrate the
accuracy and applicability of the presented method.
Abstract: A new numerical scheme based on the H1-Galerkin mixed finite element method for a class of second-order pseudohyperbolic equations is constructed. The proposed procedures can be split into three independent differential sub-schemes and does not need to solve a coupled system of equations. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one space dimension. And the proposed method dose not requires the LBB consistency condition. Finally, some numerical results are provided to illustrate the efficacy of our method.
Abstract: A biophysically based multilayer continuum model of the facial soft tissue composite has been developed for simulating wrinkle formation. The deformed state of the soft tissue block was determined by solving large deformation mechanics equations using the Galerkin finite element method. The proposed soft tissue model is composed of four layers with distinct mechanical properties. These include stratum corneum, epidermal-dermal layer (living epidermis and dermis), subcutaneous tissue and the underlying muscle. All the layers were treated as non-linear, isotropic Mooney Rivlin materials. Contraction of muscle fibres was approximated using a steady-state relationship between the fibre extension ratio, intracellular calcium concentration and active stress in the fibre direction. Several variations of the model parameters (stiffness and thickness of epidermal-dermal layer, thickness of subcutaneous tissue layer) have been considered.
Abstract: The objective of this research is to examine the shear thinning behaviour of mixing flow of non-Newtonian fluid like toothpaste in the dissolution container with rotating stirrer. The problem under investigation is related to the chemical industry. Mixing of fluid is performed in a cylindrical container with rotating stirrer, where stirrer is eccentrically placed on the lid of the container. For the simulation purpose the associated motion of the fluid is considered as revolving of the container, with stick stirrer. For numerical prediction, a time-stepping finite element algorithm in a cylindrical polar coordinate system is adopted based on semi-implicit Taylor-Galerkin/pressure-correction scheme. Numerical solutions are obtained for non-Newtonian fluids employing power law model. Variations with power law index have been analysed, with respect to the flow structure and pressure drop.
Abstract: In the present study, a numerical analysis is carried
out to investigate unsteady MHD (magneto-hydrodynamic) flow and
heat transfer of a non-Newtonian second grade viscoelastic fluid
over an oscillatory stretching sheet. The flow is induced due to an
infinite elastic sheet which is stretched oscillatory (back and forth) in
its own plane. Effect of viscous dissipation and joule heating are
taken into account. The non-linear differential equations governing
the problem are transformed into system of non-dimensional
differential equations using similarity transformations. A newly
developed meshfree numerical technique Element free Galerkin
method (EFGM) is employed to solve the coupled non linear
differential equations. The results illustrating the effect of various
parameters like viscoelastic parameter, Hartman number, relative
frequency amplitude of the oscillatory sheet to the stretching rate and
Eckert number on velocity and temperature field are reported in
terms of graphs and tables. The present model finds its application in
polymer extrusion, drawing of plastic films and wires, glass, fiber
and paper production etc.
Abstract: The transient thermoelastic response of thick hollow cylinder made of functionally graded material under thermal loading is studied. The generalized coupled thermoelasticity based on the Green-Lindsay model is used. The thermal and mechanical properties of the functionally graded material are assumed to be varied in the radial direction according to a power law variation as a function of the volume fractions of the constituents. The thermal and elastic governing equations are solved by using Galerkin finite element method. All the finite element calculations were done by using commercial finite element program FlexPDE. The transient temperature, radial displacement, and thermal stresses distribution through the radial direction of the cylinder are plotted.
Abstract: Wavelet transform or wavelet analysis is a recently
developed mathematical tool in applied mathematics. In numerical
analysis, wavelets also serve as a Galerkin basis to solve partial
differential equations. Haar transform or Haar wavelet transform has
been used as a simplest and earliest example for orthonormal wavelet
transform. Since its popularity in wavelet analysis, there are several
definitions and various generalizations or algorithms for calculating
Haar transform. Fast Haar transform, FHT, is one of the algorithms
which can reduce the tedious calculation works in Haar transform. In
this paper, we present a modified fast and exact algorithm for FHT,
namely Modified Fast Haar Transform, MFHT. The algorithm or
procedure proposed allows certain calculation in the process
decomposition be ignored without affecting the results.
Abstract: The Wavelet-Galerkin finite element method for
solving the one-dimensional heat equation is presented in this work.
Two types of basis functions which are the Lagrange and multi-level
wavelet bases are employed to derive the full form of matrix system.
We consider both linear and quadratic bases in the Galerkin method.
Time derivative is approximated by polynomial time basis that
provides easily extend the order of approximation in time space. Our
numerical results show that the rate of convergences for the linear
Lagrange and the linear wavelet bases are the same and in order 2
while the rate of convergences for the quadratic Lagrange and the
quadratic wavelet bases are approximately in order 4. It also reveals
that the wavelet basis provides an easy treatment to improve
numerical resolutions that can be done by increasing just its desired
levels in the multilevel construction process.
Abstract: With the presence of a uniform vertical magnetic field and suspended particles, thermocapillary instability in a horizontal liquid layer is investigated. The resulting eigenvalue is solved by the Galerkin technique for various basic temperature gradients. It is found that the presence of magnetic field always has a stability effect of increasing the critical Marangoni number.
Abstract: Modeling transfer phenomena in several chemical
engineering operations leads to the resolution of partial differential
equations systems. According to the complexity of the operations
mechanisms, the equations present a nonlinear form and analytical
solution became difficult, we have then to use numerical methods
which are based on approximations in order to transform a
differential system to an algebraic one.Finite element method is one
of numerical methods which can be used to obtain an accurate
solution in many complex cases of chemical engineering.The packed
columns find a large application like contactor for liquid-liquid
systems such solvent extraction. In the literature, the modeling of this
type of equipment received less attention in comparison with the
plate columns.A mathematical bidimensionnal model with radial and
axial dispersion, simulating packed tower extraction behavior was
developed and a partial differential equation was solved using the
finite element method by adopting the Galerkine model. We
developed a Mathcad program, which can be used for a similar
equations and concentration profiles are obtained along the column.
The influence of radial dispersion was prooved and it can-t be
neglected, the results were compared with experimental concentration
at the top of the column in the extraction system:
acetone/toluene/water.
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: This paper focuses on a technique for identifying the geological boundary of the ground strata in front of a tunnel excavation site using the first order adjoint method based on the optimal control theory. The geological boundary is defined as the boundary which is different layers of elastic modulus. At tunnel excavations, it is important to presume the ground situation ahead of the cutting face beforehand. Excavating into weak strata or fault fracture zones may cause extension of the construction work and human suffering. A theory for determining the geological boundary of the ground in a numerical manner is investigated, employing excavating blasts and its vibration waves as the observation references. According to the optimal control theory, the performance function described by the square sum of the residuals between computed and observed velocities is minimized. The boundary layer is determined by minimizing the performance function. The elastic analysis governed by the Navier equation is carried out, assuming the ground as an elastic body with linear viscous damping. To identify the boundary, the gradient of the performance function with respect to the geological boundary can be calculated using the adjoint equation. The weighed gradient method is effectively applied to the minimization algorithm. To solve the governing and adjoint equations, the Galerkin finite element method and the average acceleration method are employed for the spatial and temporal discretizations, respectively. Based on the method presented in this paper, the different boundary of three strata can be identified. For the numerical studies, the Suemune tunnel excavation site is employed. At first, the blasting force is identified in order to perform the accuracy improvement of analysis. We identify the geological boundary after the estimation of blasting force. With this identification procedure, the numerical analysis results which almost correspond with the observation data were provided.
Abstract: This paper is concerned with the numerical minimization
of energy functionals in BV (
) (the space of bounded variation
functions) involving total variation for gray-scale 1-dimensional inpainting
problem. Applications are shown by finite element method
and discontinuous Galerkin method for total variation minimization.
We include the numerical examples which show the different recovery
image by these two methods.
Abstract: A water surface slope limiting scheme is tested and
compared with the water depth slope limiter for the solution of one
dimensional shallow water equations with bottom slope source term.
Numerical schemes based on the total variation diminishing Runge-
Kutta discontinuous Galerkin finite element method with slope
limiter schemes based on water surface slope and water depth are
used to solve one-dimensional shallow water equations. For each
slope limiter, three different Riemann solvers based on HLL, LF, and
Roe flux functions are used. The proposed water surface based slope
limiter scheme is easy to implement and shows better conservation
property compared to the slope limiter based on water depth. Of the
three flux functions, the Roe approximation provides the best results
while the LF function proves to be least suitable when used with
either slope limiter scheme.
Abstract: In the analysis of structures, the nonlinear effects due to large displacement, large rotation and materially-nonlinear are very important and must be considered for the reliable analysis. The non-linear fmite element analysis has potential as usable and reliable means for analyzing of civil structures with the availability of computer technology. In this research the large displacements and materially nonlinear behavior of shear wall is presented with developing of fmite element code using the standard Galerkin weighted residual formulation. Two-dimensional plane stress model was carried out to present the shear wall response. Total Lagangian formulation, which is computationally more effective, is used in the formulation of stiffness matrices and the Newton-Raphson method is applied for the solution of nonlinear transient equations. The details of the program formulation are highlighted and the results of the analyses are presented, along with a comparison of the response of the structure with Ansys software results. The presented model in this paper can be developed for nonlinear analysis of civil engineering structures with different material behavior and complicated geometry.