Abstract: A formulation of postbuckling analysis of end supported rods under self-weight has been presented by the variational method. The variational formulation involving the strain energy due to bending and the potential energy of the self-weight, are expressed in terms of the intrinsic coordinates. The variational formulation is accomplished by introducing the Lagrange multiplier technique to impose the boundary conditions. The finite element method is used to derive a system of nonlinear equations resulting from the stationary of the total potential energy and then Newton-Raphson iterative procedure is applied to solve this system of equations. The numerical results demonstrate the postbluckled configurations of end supported rods under self-weight. This finite element method based on variational formulation expressed in term of intrinsic coordinate is highly recommended for postbuckling analysis of end-supported rods under self-weight.
Abstract: In this study, the different approaches currently followed by design codes to assess the stability of buildings utilizing concrete moment resisting frames structural system are evaluated. For such purpose, a parametric study was performed. It involved analyzing group of concrete moment resisting frames having different slenderness ratios (height/width ratios), designed for different lateral loads to vertical loads ratios and constructed using ordinary reinforced concrete and high strength concrete for stability check and overall buckling using code approaches and computer buckling analysis. The objectives were to examine the influence of such parameters that directly linked to frames’ lateral stiffness on the buildings’ stability and evaluates the code approach in view of buckling analysis results. Based on this study, it was concluded that, the most susceptible buildings to instability and magnification of second order effects are buildings having high aspect ratios (height/width ratio), having low lateral to vertical loads ratio and utilizing construction materials of high strength. In addition, the study showed that the instability limits imposed by codes are mainly mathematical to ensure reliable analysis not a physical ones and that they are in general conservative. Also, it has been shown that the upper limit set by one of the codes that second order moment for structural elements should be limited to 1.4 the first order moment is not justified, instead, the overall story check is more reliable.
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: In this paper the problem of buckling of plates on foundation of finite length and with different side support is studied.
The Finite Strip Method is used as tool for the analysis. This method uses finite strip elastic, foundation, and geometric matrices to build the assembly matrices for the whole structure, then after introducing boundary conditions at supports, the resulting reduced matrices is transformed into a standard Eigenvalue-Eigenvector problem. The solution of this problem will enable the determination of the buckling load, the associated buckling modes and the buckling wave length.
To carry out the buckling analysis starting from the elastic, foundation, and geometric stiffness matrices for each strip a computer program FORTRAN list is developed.
Since stiffness matrices are function of wave length of buckling, the computer program used an iteration procedure to find the critical buckling stress for each value of foundation modulus and for each boundary condition.
The results showed the use of elastic medium to support plates subject to axial load increase a great deal the buckling load, the results found are very close with those obtained by other analytical methods and experimental work.
The results also showed that foundation compensates the effect of the weakness of some types of constraint of side support and maximum benefit found for plate with one side simply supported the other free.
Abstract: A continuum model is presented to study vdW
interaction on buckling analysis of multi-walled walled carbon
nanotube. In previous studies, only the vdW interaction between
adjacent two layers was considered and the vdW interaction between
the other two layers was neglected. The results show that the vdW
interaction cofficients are dependent on the change of interlayer
spacing and the radii of tubes. With increase of radii the vdW
coefficients approach a constant value. The numerical results show
that the effect of vdW interaction on the critical strain for a doublewalled
CNT is negligible when the radius is large enough for the
both the cases of before and after buckling.
Abstract: In this study, a vibration analysis was carried out of
symmetric angle-ply laminated composite plates with and without
square hole when subjected to compressive loads, numerically. A
buckling analysis is also performed to determine the buckling load of
laminated plates. For each fibre orientation, the compression load is
taken equal to 50% of the corresponding buckling load. In the
analysis, finite element method (FEM) was applied to perform
parametric studies, the effects of degree of orthotropy and stacking
sequence upon the fundamental frequencies and buckling loads are
discussed. The results show that the presence of a constant
compressive load tends to reduce uniformly the natural frequencies
for materials which have a low degree of orthotropy. However, this
reduction becomes non-uniform for materials with a higher degree of
orthotropy.
Abstract: In the traditional buckling analysis of rectangular
plates the classical thin plate theory is generally applied, so
neglecting the plating shear deformation. It seems quite clear that this
method is not totally appropriate for the analysis of thick plates, so
that in the following the two variable refined plate theory proposed
by Shimpi (2006), that permits to take into account the transverse
shear effects, is applied for the buckling analysis of simply supported
isotropic rectangular plates, compressed in one and two orthogonal
directions.
The relevant results are compared with the classical ones and, for
rectangular plates under uniaxial compression, a new direct
expression, similar to the classical Bryan-s formula, is proposed for
the Euler buckling stress.
As the buckling analysis is a widely diffused topic for a variety of
structures, such as ship ones, some applications for plates uniformly
compressed in one and two orthogonal directions are presented and
the relevant theoretical results are compared with those ones obtained
by a FEM analysis, carried out by ANSYS, to show the feasibility of
the presented method.
Abstract: Mechanical buckling analysis of rectangular plates
with central circular cutout is performed in this paper. The finiteelement
method is used to study the effects of plate-support
conditions, aspect ratio, and hole size on the mechanical buckling
strength of the perforated plates subjected to linearly varying loading.
Results show that increasing the hole size does not necessarily reduce
the mechanical buckling strength of the perforated plates. It is also
concluded that the clamped boundary condition increases the
mechanical buckling strength of the perforated plates more than the
simply-supported boundary condition and the free boundary
conditions enhance the mechanical buckling strength of the
perforated plates more effectively than the fixed boundary conditions.
Furthermore, for the bending cases, the critical buckling load of
perforated plates with free edges is less than perforated plates with
fixed edges.
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: In the classical buckling analysis of rectangular plates
subjected to the concurrent action of shear and uniaxial forces, the
Euler shear buckling stress is generally evaluated separately, so that
no influence on the shear buckling coefficient, due to the in-plane
tensile or compressive forces, is taken into account.
In this paper the buckling problem of simply supported rectangular
plates, under the combined action of shear and uniaxial forces, is
discussed from the beginning, in order to obtain new project formulas
for the shear buckling coefficient that take into account the presence
of uniaxial forces.
Furthermore, as the classical expression of the shear buckling
coefficient for simply supported rectangular plates is considered only
a “rough" approximation, as the exact one is defined by a system of
intersecting curves, the convergence and the goodness of the classical
solution are analyzed, too.
Finally, as the problem of the Euler shear buckling stress
evaluation is a very important topic for a variety of structures, (e.g.
ship ones), two numerical applications are carried out, in order to
highlight the role of the uniaxial stresses on the plating scantling
procedures and the goodness of the proposed formulas.