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: Smoke discharging is a main reason of air pollution
problem from industrial plants. The obstacle of a building has an
affect with the air pollutant discharge. In this research, a mathematical
model of the smoke dispersion from two sources and one source with
a structural obstacle is considered. The governing equation of the
model is an isothermal mass transfer model in a viscous fluid. The
finite element method is used to approximate the solutions of the
model. The triangular linear elements have been used for discretising
the domain, and time integration has been carried out by semi-implicit
finite difference method. The simulations of smoke dispersion in
cases of one chimney and two chimneys are presented. The maximum
calculated smoke concentration of both cases are compared. It is then
used to make the decision for smoke discharging and air pollutant
control problems on industrial area.
Abstract: The effect of notch depth on the elastic new strainconcentration
factor (SNCF) of rectangular bars with single edge Unotch
under combined loading is studied here. The finite element
method (FEM) and super position technique are used in the current
study. This new SNCF under combined loading of static tension and
pure bending has been defined under triaxial stress state. The
employed specimens have constant gross thickness of 16.7 mm and
net section thickness varied to give net-to-gross thickness ratio ho/Ho
from 0.2 to 0.95. The results indicated that the elastic SNCF for
combined loading increases with increasing notch depth up to ho/Ho =
0.7 and sharply decreases with increasing notch depth. It is also
indicated that the elastic SNCF of combined loading is greater than
that of pure bending and less than that of the static tension for 0.2 ≤
ho/Ho ≤ 0.7. However, the elastic SNCF of combined loading is the
elastic SNCF for static tension and less than that of pure bending for
shallow notches (i.e. 0.8 ≤ ho/Ho ≤ 0.95).
Abstract: The aim of the current study is to develop a numerical
tool that is capable of achieving an optimum shape and design of
hyperbolic cooling towers based on coupling a non-linear finite
element model developed in-house and a genetic algorithm
optimization technique. The objective function is set to be the
minimum weight of the tower. The geometric modeling of the tower
is represented by means of B-spline curves. The finite element
method is applied to model the elastic buckling behaviour of a tower
subjected to wind pressure and dead load. The study is divided into
two main parts. The first part investigates the optimum shape of the
tower corresponding to minimum weight assuming constant
thickness. The study is extended in the second part by introducing the
shell thickness as one of the design variables in order to achieve an
optimum shape and design. Design, functionality and practicality
constraints are applied.
Abstract: Nowadays, engineering ceramics have significant
applications in different industries such as; automotive, aerospace,
electrical, electronics and even martial industries due to their
attractive physical and mechanical properties like very high hardness
and strength at elevated temperatures, chemical stability, low friction
and high wear resistance. However, these interesting properties plus
low heat conductivity make their machining processes too hard,
costly and time consuming. Many attempts have been made in order
to make the grinding process of engineering ceramics easier and
many scientists have tried to find proper techniques to economize
ceramics' machining processes. This paper proposes a new diamond
plunge grinding technique using ultrasonic vibration for grinding
Alumina ceramic (Al2O3). For this purpose, a set of laboratory
equipments have been designed and simulated using Finite Element
Method (FEM) and constructed in order to be used in various
measurements. The results obtained have been compared with the
conventional plunge grinding process without ultrasonic vibration
and indicated that the surface roughness and fracture strength
improved and the grinding forces decreased.
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.