Abstract: Fiber Reinforced Polymer (FRP) composites enjoy an array of applications ranging from aerospace, marine and military to automobile, recreational and civil industry due to their outstanding properties. A structural glass fiber reinforced polymer (GFRP) composite sandwich panel made from E-glass fiber skin and a modified phenolic core has been manufactured in Australia for civil engineering applications. One of the major mechanisms of damage in FRP composites is skin-core debonding. The presence of debonding is of great concern not only because it severely affects the strength but also it modifies the dynamic characteristics of the structure, including natural frequency and vibration modes. This paper deals with the investigation of the dynamic characteristics of a GFRP beam with single and multiple debonding by finite element based numerical simulations and analyses using the STRAND7 finite element (FE) software package. Three-dimensional computer models have been developed and numerical simulations were done to assess the dynamic behavior. The FE model developed has been validated with published experimental, analytical and numerical results for fully bonded as well as debonded beams. A comparative analysis is carried out based on a comprehensive parametric investigation. It is observed that the reduction in natural frequency is more affected by single debonding than the equally sized multiple debonding regions located symmetrically to the single debonding position. Thus it is revealed that a large single debonding area leads to more damage in terms of natural frequency reduction than isolated small debonding zones of equivalent area, appearing in the GFRP beam. Furthermore, the extents of natural frequency shifts seem mode-dependent and do not seem to have a monotonous trend of increasing with the mode numbers.
Abstract: Free vibration analysis of homogenous and axially functionally graded simply supported beams within the context of Euler-Bernoulli beam theory is presented in this paper. The material properties of the beams are assumed to obey the linear law distribution. The effective elastic modulus of the composite was predicted by using the rule of mixture. Here, the complexities which appear in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using a relatively new approach called the Differential Transformation Method. This technique is applied for solving differential equation of transverse vibration of axially functionally graded beams. Natural frequencies and corresponding normalized mode shapes are calculated for different Young’s modulus ratios. MATLAB code is designed to solve the transformed differential equation of the beam. Comparison of the present results with the exact solutions proves the effectiveness, the accuracy, the simplicity, and computational stability of the differential transformation method. The effect of the Young’s modulus ratio on the normalized natural frequencies and mode shapes is found to be very important.
Abstract: This paper deals with a nonlinear finite element analysis to examine the behavior up to failure of cantilever composite steel-concrete beams which are prestressed externally. 'Pre-' means stressing the high strength external tendons in the steel beam section before the concrete slab is added. The composite beam contains a concrete slab which is connected together with steel I-beam by means of perfect shear connectors between the concrete slab and the steel beam which is subjected to static loading. A finite element analysis will be done to study the effects of external prestressed tendons on the composite steel-concrete beams by locating the tendons in different locations (profiles). ANSYS version 12.1 computer program is being used to analyze the represented three-dimensional model of the cantilever composite beam. This model gives all these outputs, mainly load-displacement behavior of the cantilever end and in the middle span of the simple support part.
Abstract: The time delay and the structural stability are major issues in big size projects due to several factors. Improper planning and poor coordination lead to delay in construction, which sometimes result in reworking or rebuilding. This definitely increases the cost and time of project. This situation stresses the structural engineers to plan out of the limits of contemporary technology utilizing non-chronological approach with creative ideas. One of the strategies to solve this issue is through structural integrity solutions in a cost-effective way. We have faced several problems in a project worth 470 million USD, and one such issue is crane girder installation with composite steel beams. We have applied structural integrity approach with the proper and revised planning schedule to solve the problem efficiently with minimal expenses.
Abstract: In this paper, vibration of a nonlinear composite beam is analyzed and then an active controller is used to control the vibrations of the system. The beam is resting on a Winkler-Pasternak elastic foundation. The composite beam is reinforced by single walled carbon nanotubes. Using the rule of mixture, the material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are determined. The beam is cantilever and the free end of the beam is under follower force. Piezoelectric layers are attached to the both sides of the beam to control vibrations as sensors and actuators. The governing equations of the FG-CNTRC beam are derived based on Euler-Bernoulli beam theory Lagrange- Rayleigh-Ritz method. The simulation results are presented and the effects of some parameters on stability of the beam are analyzed.
Abstract: This paper revisits the free vibration problem of delaminated composite beams. It is shown that during the vibration of composite beams the delaminated parts are subjected to the parametric excitation. This can lead to the dynamic buckling during the motion of the structure. The equation of motion includes time-dependent stiffness and so it leads to a system of Mathieu-Hill differential equations. The free vibration analysis of beams is carried out in the usual way by using beam finite elements. The dynamic buckling problem is investigated locally, and the critical buckling forces are determined by the modified harmonic balance method by using an imposed time function of the motion. The stability diagrams are created, and the numerical predictions are compared to experimental results. The most important findings are the critical amplitudes at which delamination buckling takes place, the stability diagrams representing the instability of the system, and the realistic mode shape prediction in contrast with the unrealistic results of models available in the literature.
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: This paper studies a mathematical model based on the
integral equations for dynamic analyzes numerical investigations of a
non-uniform or multi-material composite beam. The beam is
subjected to a sub-tangential follower force and elastic foundation.
The boundary conditions are represented by generalized
parameterized fixations by the linear and rotary springs. A
mathematical formula based on Euler-Bernoulli beam theory is
presented for beams with variable cross-sections. The non-uniform
section introduces non-uniformity in the rigidity and inertia of beams
and consequently, more complicated equilibrium who governs the
equation. Using the boundary element method and radial basis
functions, the equation of motion is reduced to an algebro-differential
system related to internal and boundary unknowns. A generalized
formula for the deflection, the slope, the moment and the shear force
are presented. The free vibration of non-uniform loaded beams is
formulated in a compact matrix form and all needed matrices are
explicitly given. The dynamic stability analysis of slender beam is
illustrated numerically based on the coalescence criterion. A realistic
case related to an industrial chimney is investigated.
Abstract: An experimental and analytical research on shear
buckling of a comparably large polymer composite I-section is
presented. It is known that shear buckling load of a large span
composite beam is difficult to determine experimentally. In order to
sensitively detect shear buckling of the tested I-section, twenty strain
rosettes and eight displacement sensors were applied and attached on
the web and flange surfaces. The tested specimen was a pultruded
composite beam made of vinylester resin, E-glass, carbon fibers and
micro-fillers. Various coupon tests were performed before the shear
buckling test to obtain fundamental material properties of the Isection.
An asymmetric four-point bending loading scheme was
utilized for the shear test. The loading scheme resulted in a high shear
and almost zero moment condition at the center of the web panel. The
shear buckling load was successfully determined after analyzing the
obtained test data from strain rosettes and displacement sensors. An
analytical approach was also performed to verify the experimental
results and to support the discussed experimental program.
Abstract: Composite materials, due to their unique properties
such as high strength to weight ratio, corrosion resistance, and impact
resistance have huge potential as structural materials in automotive,
construction and transportation applications. However, these
properties often come at higher cost owing to complex design
methods, difficult manufacturing processes and raw material cost.
Traditionally, tapered laminated composite structures are
manufactured using autoclave manufacturing process by ply drop off
technique. Autoclave manufacturing though very powerful suffers
from high capital investment and higher energy consumption. As per
the current trends in composite manufacturing, Out of Autoclave
(OoA) processes are looked as emerging technologies for
manufacturing the structural composite components for aerospace
and defense applications. However, there is a need for improvement
among these processes to make them reliable and consistent. In this
paper, feasibility of using out of autoclave process to manufacture the
variable thickness cantilever beam is discussed. The minimum weight
design for the composite beam is obtained using constant stress beam
concept by tailoring the thickness of the beam. Ply drop off
techniques was used to fabricate the variable thickness beam from
glass/epoxy prepregs. Experiments were conducted to measure
bending stresses along the span of the cantilever beam at different
intervals by applying the concentrated load at the free end.
Experimental results showed that the stresses in the bean at different
intervals were constant. This proves the ability of OoA process to
manufacture the constant stress beam. Finite element model for the
constant stress beam was developed using commercial finite element
simulation software. It was observed that the simulation results
agreed very well with the experimental results and thus validated
design and manufacturing approach used.
Abstract: Well-designed composite steel and concrete structures
highlight the good material properties and lower the deficiencies of
steel and concrete, in particular they make use of high tensile strength
of steel and high stiffness of concrete. The most common composite
steel and concrete structure is a simply supported beam, which
concrete slab transferring the slab load to a beam is connected to the
steel cross-section. The aim of this paper is to find the most adequate
numerical model of a simply supported composite beam with the
cross-sectional and material parameters based on the results of a
processed parametric study and numerical analysis. The paper also
evaluates the suitability of using compact concrete with the
lightweight aggregates for composite steel and concrete beams. The
most adequate numerical model will be used in the resent future to
compare the results of laboratory tests.
Abstract: In this investigation an elastic stress analysis is carried out a woven steel fiber reinforced thermoplastic cantilever beam loaded uniformly at the upper surface. The composite beam material consists of low density polyethylene as a thermoplastic (LDFE, f.2.12) and woven steel fibers. Granules of the polyethylene are put into the moulds and they are heated up to 160°C by using electrical resistance. Subsequently, the material is held for 5min under 2.5 MPa at this temperature. The temperature is decreased to 30°C under 15 MPa pressure in 3min. Closed form solution is found satisfying both the governing differential equation and boundary conditions. We investigated orientation angle effect on stress distribution of composite cantilever beams. The results show that orientation angle play an important role in determining the responses of a woven steel fiber reinforced thermoplastic cantilever beams and an optimal design of these structures.
Abstract: This paper deals with the design of a periodic output
feedback controller for a flexible beam structure modeled with
Timoshenko beam theory, Finite Element Method, State space
methods and embedded piezoelectrics concept. The first 3 modes are
considered in modeling the beam. The main objective of this work is
to control the vibrations of the beam when subjected to an external
force. Shear piezoelectric sensors and actuators are embedded into
the top and bottom layers of a flexible aluminum beam structure, thus
making it intelligent and self-adaptive. The composite beam is
divided into 5 finite elements and the control actuator is placed at
finite element position 1, whereas the sensor is varied from position 2
to 5, i.e., from the nearby fixed end to the free end. 4 state space
SISO models are thus developed. Periodic Output Feedback (POF)
Controllers are designed for the 4 SISO models of the same plant to
control the flexural vibrations. The effect of placing the sensor at
different locations on the beam is observed and the performance of
the controller is evaluated for vibration control. Conclusions are
finally drawn.
Abstract: In this paper, an analytical approach is used to study the coupled lateral-torsional vibrations of laminated composite beam. It is known that in such structures due to the fibers orientation in various layers, any lateral displacement will produce a twisting moment. This phenomenon is modeled by the bending-twisting material coupling rigidity and its main feature is the coupling of lateral and torsional vibrations. In addition to the material coupling, the effects of shear deformation and rotary inertia are taken into account in the definition of the potential and kinetic energies. Then, the governing differential equations are derived using the Hamilton-s principle and the mathematical model matches the Timoshenko beam model when neglecting the effect of bending-twisting rigidity. The equations of motion which form a system of three coupled PDEs are solved analytically to study the free vibrations of the beam in lateral and rotational modes due to the bending, as well as the torsional mode caused by twisting. The analytic solution is carried out in three steps: 1) assuming synchronous motion for the kinematic variables which are the lateral, rotational and torsional displacements, 2) solving the ensuing eigenvalue problem which contains three coupled second order ODEs and 3) imposing different boundary conditions related to combinations of simply, clamped and free end conditions. The resulting natural frequencies and mode shapes are compared with similar results in the literature and good agreement is achieved.
Abstract: In this paper the Differential Quadrature Method (DQM) is employed to study the coupled lateral-torsional free vibration behavior of the laminated composite beams. In such structures due to the fiber orientations in various layers, the lateral displacement leads to a twisting moment. The coupling of lateral and torsional vibrations is modeled by the bending-twisting material coupling rigidity. In the present study, in addition to the material coupling, the effects of shear deformation and rotary inertia are taken into account in the definition of the potential and kinetic energies of the beam. The governing differential equations of motion which form a system of three coupled PDEs are solved numerically using DQ procedure under different boundary conditions consist of the combinations of simply, clamped, free and other end conditions. The resulting natural frequencies and mode shapes for cantilever beam are compared with similar results in the literature and good agreement is achieved.
Abstract: Eight steel reinforced concrete beams (SRC), were
fabricated and tested under earthquake type cyclic loading. The
effectiveness of intermediate stiffeners, such as mid-span stiffener and
plastic hinge zone stiffeners, in enhancing composite action and
ductility of SRC beams was investigated. The effectiveness of
strengthened beam-to-column (SBC) and weakened beam-to-column
(WBC) connections in enhancing beam ductility was also studied. It
was found that: (1) All the specimens possessed fairly high flexural
ductility and were found adequate for structures in high seismic zones.
(2) WBC connections induced stress concentration which caused extra
damage to concrete near the flange tapering zone. This extra damage
inhibited the flexural strength development and the ductility of the
specimens with WBC connections to some extent. (3) Specimens with
SBC connections demonstrated higher flexural strength and ductility
compared to specimens with WBC connections. (4) The intermediate
stiffeners, especially combination of plastic hinge zone stiffener and
mid span stiffeners, have an obvious effect in enhancing the ductility
of the beams with SBC connection.
Abstract: Researchers investigate arious strategies to develop composite beams and maximize the structural advantages. This study
attempted to conduct experiments and analysis of changes in the
neutral axis of positive moments of a Green Beam. Strain
compatibility analysis was used, and its efficiency was demonstrated
by comparing experimental and analytical values. In the comparison of
neutral axis, the difference between experimental and analytical values
was found to range from 8.8~26.2%. It was determined that strain
compatibility analysis can be useful for predicting the behaviors of
composite beams, with the ability to predict the behavior of not only
the elastic location of the composite member, but also of the plastic
location
Abstract: This work presents the mixed-mode II/III prestressed split-cantilever beam specimen for the fracture testing of composite materials. In accordance with the concept of prestressed composite beams one of the two fracture modes is provided by the prestressed state of the specimen, and the other one is increased up to fracture initiation by using a testing machine. The novel beam-like specimen is able to provide any combination of the mode-II and mode-III energy release rates. A simple closed-form solution is developed using beam theory as a data reduction scheme and for the calculation of the energy release rates in the new configuration. The applicability and the limitations of the novel fracture mechanical test are demonstrated using unidirectional glass/polyester composite specimens. If only crack propagation onset is involved then the mixed-mode beam specimen can be used to obtain the fracture criterion of transparent composite materials in the GII - GIII plane in a relatively simple way.
Abstract: The integral form of equations of motion of composite
beams subjected to varying time loads are discretized using a
developed finite element model. The model consists of a straight five
node twenty-two degrees of freedom beam element. The stability
analysis of the beams is studied by solving the matrix form
characteristic equations of the system. The principle of virtual work
and the first order shear deformation theory are employed to analyze
the beams with large deformation and small strains. The regions of
dynamic instability of the beam are determined by solving the
obtained Mathieu form of differential equations. The effects of nonconservative
loads, shear stiffness, and damping parameters on
stability and response of the beams are examined. Several numerical
calculations are presented to compare the results with data reported
by other researchers.
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.