Abstract: In this paper, mesh-free element free Galerkin (EFG) method is extended to solve two-dimensional potential flow problems. Two ideal fluid flow problems (i.e. flow over a rigid cylinder and flow over a sphere) have been formulated using variational approach. Penalty and Lagrange multiplier techniques have been utilized for the enforcement of essential boundary conditions. Four point Gauss quadrature have been used for the integration on two-dimensional domain (Ω) and nodal integration scheme has been used to enforce the essential boundary conditions on the edges (┌). The results obtained by EFG method are compared with those obtained by finite element method. The effects of scaling and penalty parameters on EFG results have also been discussed in detail.
Abstract: MOC (method of cell) is a new method of investigating
wave propagating in material with periodic microstructure, and can
reflect the effect of microstructure. Wave propagation in periodically
laminated medium consisting of linearly elastic layers can be treated
as a special application of this method. In this paper, it was used to
simulate the dynamic response of carbon-phenolic to impulsive
loading under certain boundary conditions. From the comparison
between the results obtained from this method and the exact results
based on propagator matrix theory, excellent agreement is achieved.
Conclusion can be made that the oscillation periodicity is decided by
the thickness of sub-cells. In the end, the NHDMOC method, which
permits studying stress wave propagation with one dimensional strain,
was applied to study the one-dimensional stress wave propagation. In
this paper, the ZWT nonlinear visco-elastic constitutive relationship
with 7 parameters, NHDMOC, and corresponding equations were
deduced. The equations were verified, comparing the elastic stress
wave propagation in SHPB with, respectively, the elastic and the
visco-elastic bar. Finally the dispersion and attenuation of stress wave
in SHPB with visco-elastic bar was studied.
Abstract: New theory for functionally graded (FG) shell based on expansion of the equations of elasticity for functionally graded materials (GFMs) into Legendre polynomials series has been developed. Stress and strain tensors, vectors of displacements, traction and body forces have been expanded into Legendre polynomials series in a thickness coordinate. In the same way functions that describe functionally graded relations has been also expanded. Thereby all equations of elasticity including Hook-s law have been transformed to corresponding equations for Fourier coefficients. Then system of differential equations in term of displacements and boundary conditions for Fourier coefficients has been obtained. Cases of the first and second approximations have been considered in more details. For obtained boundary-value problems solution finite element (FE) has been used of Numerical calculations have been done with Comsol Multiphysics and Matlab.
Abstract: In this paper, the dynamic analysis of fuel storage
tanks has been studied and some equations are presented for the
created fluid waves due to storage tank motions. Also, the equations
for finite elements of fluid and structure interactions, and boundary
conditions dominant on structure and fluid, were researched. In this
paper, a numerical simulation is performed for the dynamic analysis
of a storage tank contained a fluid. This simulation has carried out by
ANSYS software, using FSI solver (Fluid and Structure Interaction
solver), and by considering the simulated fluid dynamic motions due
to earthquake loading, based on velocities and movements of
structure and fluid according to all boundary conditions dominant on
structure and fluid.
Abstract: The square-lattice Ising model is the simplest system
showing phase transitions (the transition between the paramagnetic
phase and the ferromagnetic phase and the transition between the
paramagnetic phase and the antiferromagnetic phase) and critical
phenomena at finite temperatures. The exact solution of the squarelattice
Ising model with free boundary conditions is not known for
systems of arbitrary size. For the first time, the exact solution of
the Ising model on the square lattice with free boundary
conditions is obtained after classifying all )
spin configurations with the microcanonical transfer matrix. Also, the
phase transitions and critical phenomena of the square-lattice Ising
model are discussed using the exact solution on the square
lattice with free boundary conditions.
Abstract: The present paper considers the steady free convection
boundary layer flow of a viscoelastic fluid on solid sphere with
Newtonian heating. The boundary layer equations are an order higher
than those for the Newtonian (viscous) fluid and the adherence
boundary conditions are insufficient to determine the solution of
these equations completely. Thus, the augmentation an extra
boundary condition is needed to perform the numerical
computational. The governing boundary layer equations are first
transformed into non-dimensional form by using special
dimensionless group and then solved by using an implicit finite
difference scheme. The results are displayed graphically to illustrate
the influence of viscoelastic K and Prandtl Number Pr parameters on
skin friction, heat transfer, velocity profiles and temperature profiles.
Present results are compared with the published papers and are found
to concur very well.
Abstract: This paper presents the buckling analysis of short and
long functionally graded cylindrical shells under thermal and
mechanical loads. The shell properties are assumed to vary
continuously from the inner surface to the outer surface of the shell.
The equilibrium and stability equations are derived using the total
potential energy equations, Euler equations and first order shear
deformation theory assumptions. The resulting equations are solved
for simply supported boundary conditions. The critical temperature
and pressure loads are calculated for both short and long cylindrical
shells. Comparison studies show the effects of functionally graded
index, loading type and shell geometry on critical buckling loads of
short and long functionally graded cylindrical shells.
Abstract: This paper deals with a numerical analysis of the
transient response of composite beams with strain rate dependent
mechanical properties by use of a finite difference method. The
equations of motion based on Timoshenko beam theory are derived.
The geometric nonlinearity effects are taken into account with von
Kármán large deflection theory. The finite difference method in
conjunction with Newmark average acceleration method is applied to
solve the differential equations. A modified progressive damage
model which accounts for strain rate effects is developed based on
the material property degradation rules and modified Hashin-type
failure criteria and added to the finite difference model. The
components of the model are implemented into a computer code in
Mathematica 6. Glass/epoxy laminated composite beams with
constant and strain rate dependent mechanical properties under
dynamic load are analyzed. Effects of strain rate on dynamic
response of the beam for various stacking sequences, load and
boundary conditions are investigated.
Abstract: The distributions of stresses and deflection in
rectangular isotropic and orthotropic plates with central
circular hole under transverse static loading have been studied
using finite element method. The aim of author is to analyze
the effect of D/A ratio (where D is hole diameter and A is plate
width) upon stress concentration factor (SCF) and deflection
in isotropic and orthotropic plates under transverse static
loading. The D/A ratio is varied from 0.01 to 0.9. The analysis
is done for plates of isotropic and two different orthotropic
materials. The results are obtained for three different boundary
conditions. The variations of SCF and deflection with respect
to D/A ratio are presented in graphical form and discussed.
The finite element formulation is carried out in the analysis
section of the ANSYS package.