Abstract: Elastic compression stockings (ECSs) have been widely applied in prophylaxis and treatment of chronic venous insufficiency of lower extremities. The medical function of ECS is to improve venous return and increase muscular pumping action to facilitate blood circulation, which is largely determined by the complex interaction between the ECS and lower limb tissues. Understanding the mechanical transmission of ECS along the skin surface, deeper tissues, and vascular system is essential to assess the effectiveness of the ECSs. In this study, a three-dimensional (3D) finite element (FE) model of the leg-ECS system integrated with a 3D fluid-solid interaction (FSI) model of the leg-vein system was constructed to analyze the biomechanical properties of veins and soft tissues under different ECS compression. The Magnetic Resonance Imaging (MRI) of the human leg was divided into three regions, including soft tissues, bones (tibia and fibula) and veins (peroneal vein, great saphenous vein, and small saphenous vein). The ECSs with pressure ranges from 15 to 26 mmHg (Classes I and II) were adopted in the developed FE-FSI model. The soft tissue was assumed as a Neo-Hookean hyperelastic model with the fixed bones, and the ECSs were regarded as an orthotropic elastic shell. The interfacial pressure and stress transmission were simulated by the FE model, and venous hemodynamics properties were simulated by the FSI model. The experimental validation indicated that the simulated interfacial pressure distributions were in accordance with the pressure measurement results. The developed model can be used to predict interfacial pressure, stress transmission, and venous hemodynamics exerted by ECSs and optimize the structure and materials properties of ECSs design, thus improving the efficiency of compression therapy.
Abstract: The reinforcement and repair of concrete structures by bonding composite materials have become relatively common operations. Different types of composite materials can be used: carbon fiber reinforced polymer (CFRP), glass fiber reinforced polymer (GFRP) as well as functionally graded material (FGM). The development of analytical and numerical models describing the mechanical behavior of structures in civil engineering reinforced by composite materials is necessary. These models will enable engineers to select, design, and size adequate reinforcements for the various types of damaged structures. This study focuses on the free vibration behavior of orthotropic laminated composite plates using a refined shear deformation theory. In these models, the distribution of transverse shear stresses is considered as parabolic satisfying the zero-shear stress condition on the top and bottom surfaces of the plates without using shear correction factors. In this analysis, the equation of motion for simply supported thick laminated rectangular plates is obtained by using the Hamilton’s principle. The accuracy of the developed model is demonstrated by comparing our results with solutions derived from other higher order models and with data found in the literature. Besides, a finite-element analysis is used to calculate the natural frequencies of laminated composite plates and is compared with those obtained by the analytical approach.
Abstract: A laminated plate composite of graphite/epoxy has been analyzed dynamically in the present work by using a quadratic element (8-node diso-parametric), and by depending on 1st order shear deformation theory, every node in this element has 6-degrees of freedom (displacement in x, y, and z axis and twist about x, y, and z axis). The dynamic analysis in the present work covered parametric studies on a composite laminated plate (square plate) to determine its effect on the natural frequency of the plate. The parametric study is represented by set of changes (plate thickness, number of layers, support conditions, layer orientation), and the plates have been simulated by using ANSYS package 12. The boundary conditions considered in this study, at all four edges of the plate, are simply supported and fixed boundary condition. The results obtained from ANSYS program show that the natural frequency for both fixed and simply supported increases with increasing the number of layers, but this increase in the natural frequency for the first five modes will be neglected after 10 layers. And it is observed that the natural frequency of a composite laminated plate will change with the change of ply orientation, the natural frequency increases and it will be at maximum with angle 45 of ply for simply supported laminated plate, and maximum natural frequency will be with cross-ply (0/90) for fixed laminated composite plate. It is also observed that the natural frequency increase is approximately doubled when the thickness is doubled.
Abstract: In this study, fracture analysis of a fibrous composite
laminate with variable fiber spacing is carried out using Jk-integral
method. The laminate is assumed to be under thermal loading.
Jk-integral is formulated by using the constitutive relations of plane
orthotropic thermoelasticity. Developed domain independent form
of the Jk-integral is then integrated into the general purpose finite
element analysis software ANSYS. Numerical results are generated
so as to assess the influence of variable fiber spacing on mode I
and II stress intensity factors, energy release rate, and T-stress. For
verification, some of the results are compared to those obtained
using displacement correlation technique (DCT).
Abstract: Two micromechanical models for 3D smart composite
with embedded periodic or nearly periodic network of generally
orthotropic reinforcements and actuators are developed and applied to
cubic structures with unidirectional orientation of constituents.
Analytical formulas for the effective piezothermoelastic coefficients
are derived using the Asymptotic Homogenization Method (AHM).
Finite Element Analysis (FEA) is subsequently developed and used
to examine the aforementioned periodic 3D network reinforced smart
structures. The deformation responses from the FE simulations are
used to extract effective coefficients. The results from both
techniques are compared. This work considers piezoelectric materials
that respond linearly to changes in electric field, electric
displacement, mechanical stress and strain and thermal effects. This
combination of electric fields and thermo-mechanical response in
smart composite structures is characterized by piezoelectric and
thermal expansion coefficients. The problem is represented by unitcell
and the models are developed using the AHM and the FEA to
determine the effective piezoelectric and thermal expansion
coefficients. Each unit cell contains a number of orthotropic
inclusions in the form of structural reinforcements and actuators.
Using matrix representation of the coupled response of the unit cell,
the effective piezoelectric and thermal expansion coefficients are
calculated and compared with results of the asymptotic
homogenization method. A very good agreement is shown between
these two approaches.
Abstract: This paper describes the design optimization of ferrocement-laminated plate made up of reinforcing steel wire mesh(es) and cement mortar. For the improvement of the designing process, the plate is modeled as a multi-layer medium, dividing the ferrocement plate into layers of mortar and ferrocement. The mortar layers are assumed to be isotropic in nature and the ferrocement layers are assumed to be orthotropic. The ferrocement layers are little stiffer, but much more costlier, than the mortar layers due the presence of steel wire mesh. The optimization is performed for minimum weight design of the laminate using a genetic algorithm. The optimum designs are discussed for different plate configurations and loadings, and it is compared with the worst designs obtained at the final generation. The paper provides a procedure for the designers in decision-making process.
Abstract: This paper is concerned with an investigation into the
localized non-stability of a thin elastic orthotropic semi-infinite plate.
In this study, a semi-infinite plate, simply supported on two edges
and different boundary conditions, clamped, hinged, sliding contact
and free on the other edge, are considered. The mathematical model
is used and a general solution is presented the conditions under which
localized solutions exist are investigated.
Abstract: An accurate procedure to determine free vibrations of
beams and plates is presented.
The natural frequencies are exact solutions of governing vibration
equations witch load to a nonlinear homogeny system.
The bilinear and linear structures considered simulate a bridge.
The dynamic behavior of this one is analyzed by using the theory of
the orthotropic plate simply supported on two sides and free on the
two others. The plate can be excited by a convoy of constant or
harmonic loads. The determination of the dynamic response of the
structures considered requires knowledge of the free frequencies and
the shape modes of vibrations. Our work is in this context. Indeed,
we are interested to develop a self-consistent calculation of the Eigen
frequencies.
The formulation is based on the determination of the solution of
the differential equations of vibrations. The boundary conditions
corresponding to the shape modes permit to lead to a homogeneous
system. Determination of the noncommonplace solutions of this
system led to a nonlinear problem in Eigen frequencies.
We thus, develop a computer code for the determination of the
eigenvalues. It is based on a method of bisection with interpolation
whose precision reaches 10 -12. Moreover, to determine the
corresponding modes, the calculation algorithm that we develop uses
the method of Gauss with a partial optimization of the "pivots"
combined with an inverse power procedure. The Eigen frequencies
of a plate simply supported along two opposite sides while
considering the two other free sides are thus analyzed. The results
could be generalized with the case of a beam by regarding it as a
plate with low width.
We give, in this paper, some examples of treated cases. The
comparison with results presented in the literature is completely
satisfactory.
Abstract: Analysis for the propagation of elastic waves in
arbitrary anisotropic plates is investigated, commencing with a
formal analysis of waves in a layered plate of an arbitrary anisotropic
media, the dispersion relations of elastic waves are obtained by
invoking continuity at the interface and boundary of conditions on
the surfaces of layered plate. The obtained solutions can be used for
material systems of higher symmetry such as monoclinic,
orthotropic, transversely isotropic, cubic, and isotropic as it is
contained implicitly in the analysis. The cases of free layered plate
and layered half space are considered separately. Some special cases
have also been deduced and discussed. Finally numerical solution of
the frequency equations for an aluminum epoxy is carried out, and
the dispersion curves for the few lower modes are presented. The
results obtained theoretically have been verified numerically and
illustrated graphically.
Abstract: Coronary artery bypass grafts (CABG) are widely
studied with respect to hemodynamic conditions which play
important role in presence of a restenosis. However, papers which
concern with constitutive modeling of CABG are lacking in the
literature. The purpose of this study is to find a constitutive model for
CABG tissue. A sample of the CABG obtained within an autopsy
underwent an inflation–extension test. Displacements were
recoredered by CCD cameras and subsequently evaluated by digital
image correlation. Pressure – radius and axial force – elongation
data were used to fit material model. The tissue was modeled as onelayered
composite reinforced by two families of helical fibers. The
material is assumed to be locally orthotropic, nonlinear,
incompressible and hyperelastic. Material parameters are estimated
for two strain energy functions (SEF). The first is classical
exponential. The second SEF is logarithmic which allows
interpretation by means of limiting (finite) strain extensibility.
Presented material parameters are estimated by optimization based
on radial and axial equilibrium equation in a thick-walled tube. Both
material models fit experimental data successfully. The exponential
model fits significantly better relationship between axial force and
axial strain than logarithmic one.
Abstract: In the present paper, an improved initial value
numerical technique is presented to analyze the free vibration of
symmetrically laminated rectangular plate. A combination of the
initial value method (IV) and the finite differences (FD) devices is
utilized to develop the present (IVFD) technique. The achieved
technique is applied to the equation of motion of vibrating laminated
rectangular plate under various types of boundary conditions. Three
common types of laminated symmetrically cross-ply, orthotropic and
isotropic plates are analyzed here. The convergence and accuracy of
the presented Initial Value-Finite Differences (IVFD) technique have
been examined. Also, the merits and validity of improved technique
are satisfied via comparing the obtained results with those available
in literature indicating good agreements.
Abstract: A theoretical study of the rigidities of slabs with
circular voids oriented in the longitudinal and in the transverse
direction is discussed. Equations are presented for predicting the
bending and torsional rigidities of the voided slabs. This paper
summarizes the results of an extensive literature search and initial
review of the current methods of analyzing voided slab. The various
methods of calculating the equivalent plate parameters, which are
necessary for two-dimensional analysis, are also reviewed. Static
deflections on voided slabs are shown to be in good agreement with
proposed equation.
Abstract: Analysis for the generalized thermoelastic Lamb
waves, which propagates in anisotropic thin plates in generalized
thermoelasticity, is presented employing normal mode expansion
method. The displacement and temperature fields are expressed by a
summation of the symmetric and antisymmetric thermoelastic modes
in the surface thermal stresses and thermal gradient free orthotropic
plate, therefore the theory is particularly appropriate for waveform
analyses of Lamb waves in thin anisotropic plates. The transient
waveforms excited by the thermoelastic expansion are analyzed for
an orthotropic thin plate. The obtained results show that the theory
provides a quantitative analysis to characterize anisotropic
thermoelastic stiffness properties of plates by wave detection. Finally
numerical calculations have been presented for a NaF crystal, and the
dispersion curves for the lowest modes of the symmetric and
antisymmetric vibrations are represented graphically at different
values of thermal relaxation time. However, the methods can be used
for other materials as well
Abstract: A frictionless contact problem for a two-layer orthotropic elastic medium loaded through a rigid flat stamp is considered. It is assumed that tensile tractions are not allowed and only compressive tractions can be transmitted across the interface. In the solution, effect of gravity is taken into consideration. If the external load on the rigid stamp is less than or equal to a critical value, continuous contact between the layers is maintained. The problem is expressed in terms of a singular integral equation by using the theory of elasticity and the Fourier transforms. Numerical results for initial separation point, critical separation load and contact stress distribution are presented.
Abstract: A macroscopic constitutive equation is developed for a high-density cellulose insulation material with emphasis on the outof- plane stress relaxation behavior. A hypothesis is proposed where the total stress is additively composed by an out-of-plane visco-elastic isotropic contribution and an in-plane elastic orthotropic response. The theory is validated against out-of-plane stress relaxation, compressive experiments and in-plane tensile hysteresis, respectively. For large scale finite element simulations, the presented model provides a balance between simplicity and capturing the materials constitutive behaviour.
Abstract: In this paper, a plane-strain orthotropic elasto-plastic
dynamic constitutive model is established, and with this constitutive
model, the thermal shock wave induced by intense pulsed X-ray
radiation in cylinder shell composite is simulated by the finite element
code, then the properties of thermal shock wave propagation are
discussed. The results show that the thermal shock wave exhibit
different shapes under the radiation of soft and hard X-ray, and while
the composite is radiated along different principal axes, great
differences exist in some aspects, such as attenuation of the peak stress
value, spallation and so on.
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.