Spatial Wavelet Approach to Local Matrix Crack Detection in Composite Beams with Ply Level Material Uncertainty

Wavelet coefficients based on spatial wavelets are used as damage indicators to identify the damage location as well as the size of the damage in a laminated composite beam with localized matrix cracks. A finite element model of the composite beam is used in conjunction with a matrix crack based damage model to simulate the damaged composite beam structure. The modes of vibration of the beam are analyzed using the wavelet transform in order to identify the location and the extent of the damage by sensing the local perturbations at the damage locations. The location of the damage is identified by a sudden change in spatial distribution of wavelet coefficients. Monte Carlo Simulations (MCS) are used to investigate the effect of ply level uncertainty in composite material properties such as ply longitudinal stiffness, transverse stiffness, shear modulus and Poisson's ratio on damage detection parameter, wavelet coefficient. In this study, numerical simulations are done for single and multiple damage cases. It is observed that spatial wavelets can be used as a reliable damage detection tool for composite beams with localized matrix cracks which can result from low velocity impact damage.

Closed-form solutions for non-uniform Euler-Bernoulli free-free beams

In this paper, the free vibration of a non-uniform free-free Euler-Bernoulli beam is studied using an inverse problem approach. It is found that the fourth-order governing differential equation for such beams possess a fundamental closed-form solution for certain polynomial variations of the mass and stiffness. An infinite number of non-uniform free-free beams exist, with different mass and stiffness variations, but sharing the same fundamental frequency. A detailed study is conducted for linear, quadratic and cubic variations of mass, and on how to pre-select the internal nodes such that the closed-form solutions exist for the three cases. A special case is also considered where, at the internal nodes, external elastic constraints are present. The derived results are provided as benchmark solutions for the validation of non-uniform free-free beam numerical codes. (C) 2013 Elsevier Ltd. All rights reserved.

A Guided Wave approach for the detection of damage in a structure having elements with periodic damage

A wave propagation based approach for the detection of damage in components of structures having periodic damage has been proposed. Periodic damage pattern may arise in a structure due to periodicity in geometry and in loading. The method exploits the Block-Floquet band formation mechanism, a feature specific to structures with periodicity, to identify propagation bands (pass bands) and attenuation bands (stop bands) at different frequency ranges. The presence of damage modifies the wave propagation behaviour forming these bands. With proper positioning of sensors a damage force indicator (DFI) method can be used to locate the defect at an accuracy level of sensor to sensor distance. A wide range of transducer frequency may be used to obtain further information about the shape and size of the damage. The methodology is demonstrated using a few 1-D structures with different kinds of periodicity and damage. For this purpose, dynamic stiffness matrix is formed for the periodic elements to obtain the dispersion relationship using frequency domain spectral element and spectral super element method. The sensitivity of the damage force indicator for different types of periodic damages is also analysed.

Effect of hinged leaflets on vortex pair generation

We experimentally study the effect of having hinged leaflets at the jet exit on the formation of a two-dimensional counter-rotating vortex pair. A piston-cylinder mechanism is used to generate a starting jet from a high-aspect-ratio channel into a quiescent medium. For a rigid exit, with no leaflets at the channel exit, the measurements at a central plane show that the trailing jet in the present case is never detached from the vortex pair, and keeps feeding into the latter, unlike in the axisymmetric case. Passive flexibility is introduced in the form of rigid leaflets or flaps that are hinged at the exit of the channel, with the flaps initially parallel to the channel walls. The experimental arrangement closely approximates the limiting case of a free-to-rotate rigid flap with negligible structural stiffness, damping and flap inertia, as these limiting structural properties permit the largest flap openings. Using this arrangement, we start the flow and measure the flap kinematics and the vorticity fields for different flap lengths and piston velocity programs. The typical motion of the flaps involves a rapid opening and a subsequent more gradual return to its initial position, both of which occur when the piston is still moving. The initial opening of the flaps can be attributed to an excess pressure that develops in the channel when the flow starts, due to the acceleration that has to be imparted to the fluid slug between the flaps. In the case with flaps, two additional pairs of vortices are formed because of the motion of the flaps, leading to the ejection of a total of up to three vortex pairs from the hinged exit. The flaps' length (L-f) is found to significantly affect flap motions when plotted using the conventional time scale L/d, where L is the piston stroke and d is the channel width. However, with a newly defined time scale based on the flap length (L/L-f), we find a good collapse of all the measured flap motions irrespective of flap length and piston velocity for an impulsively started piston motion. The maximum opening angle in all these impulsive velocity program cases, irrespective of the flap length, is found to be close to 15 degrees. Even though the flap kinematics collapses well with L/L-f, there are differences in the distribution of the ejected vorticity even for the same L/L-f. Such a redistribution of vorticity can lead to important changes in the overall properties of the flow, and it gives us a better understanding of the importance of exit flexibility in such flows.

Dynamics of a flexible splitter plate in the wake of a circular cylinder

Rigid splitter plates in the wake of bluff bodies are known to suppress the primary vortex shedding. In the present work, we experimentally study the problem of a flexible splitter plate in the wake of a circular cylinder. In this case, the splitter plate is free to continuously deform along its length due to the fluid forces acting on it; the flexural rigidity (EI) of the plate being an important parameter. Direct visualizations of the splitter plate motions, for very low values of flexural rigidity (EI), indicate periodic traveling wave type deformations of the splitter plate with maximum tip amplitudes of the order of I cylinder diameter. As the Reynolds number based on cylinder diameter is varied, two regimes of periodic splitter plate motions are found that are referred to as mode I and mode II, with a regime of aperiodic motions between them. The frequency of plate motions in both periodic modes is found to be close to the plane cylinder Strouhal number of about 0.2, while the average frequencies in the non-periodic regime are substantially lower. The measured normalized phase speed of the traveling wave for both periodic modes is also close to the convection speed of vortices in the plane cylinder wake. As the flexural rigidity of the plate (EI) is increased, the response of the plate was found to shift to the right when plotted with flow speed or Re. To better capture the effect of varying EI, we define and use a non-dimensional bending stiffness, K*, similar to the ones used in the flag flutter problem, K*=EI/(0.5 rho(UL3)-L-2), where U is the free-stream velocity and L is the splitter plate length. Amplitude data for different EI cases when plotted against this parameter appear to collapse on to a single curve for a given splitter plate length. Measurements of the splitter plate motions for varying splitter plate lengths indicate that plates that are substantially larger than the formation length of the plane cylinder wake have similar responses, while shorter plates show significant differences.

Numerical analysis of geocell reinforced ballast overlying soft clay subgrade

Geotextiles and geogrids have been in use for several decades in variety of geo-structure applications including foundation of embankments, retaining walls, pavements. Geocells is one such variant in geosynthetic reinforcement of recent years, which provides a three dimensional confinement to the infill material. Although extensive research has been carried on geocell reinforced sand, clay and layered soil subgrades, limited research has been reported on the aggregates/ballast reinforced with geocells. This paper presents the behavior of a railway sleeper subjected to monotonic loading on geocell reinforced aggregates, of size ranging from 20 to 75 mm, overlying soft clay subgrades. Series of tests were conducted in a steel test tank of dimensions 700 mm x 300 mm x 700 mm. In addition to the laboratory model tests, numerical simulations were performed using a finite difference code to predict the behavior of geocell reinforced ballast. The results from numerical simulations were compared with the experimental data. The numerical and experimental results manifested the importance that the geocell reinforcement has a significant effect on the ballast behaviour. The results depicted that the stiffness of underlying soft clay subgrade has a significant influence on the behavior of the geocell-aggregate composite material in redistributing the loading system.

Partial delamination modeling in composite beams using a finite element method

A new method of modeling partial delamination in composite beams is proposed and implemented using the finite element method. Homogenized cross-sectional stiffness of the delaminated beam is obtained by the proposed analytical technique, including extension-bending, extension-twist and torsion-bending coupling terms, and hence can be used with an existing finite element method. A two noded C1 type Timoshenko beam element with 4 degrees of freedom per node for dynamic analysis of beams is implemented. The results for different delamination scenarios and beams subjected to different boundary conditions are validated with available experimental results in the literature and/or with the 3D finite element simulation using COMSOL. Results of the first torsional mode frequency for the partially delaminated beam are validated with the COMSOL results. The key point of the proposed model is that partial delamination in beams can be analyzed using a beam model, rather than using 3D or plate models. (c) 2013 Elsevier B.V. All rights reserved.

Mechanical and electronic properties of pristine and Ni-doped Si, Ge, and Sn sheets

Silicene, a graphene analogue of silicon, has been generating immense interest due to its potential for applications in miniaturized devices. Unlike planar graphene, silicene prefers a buckled structure. Here we explore the possibility of stabilizing the planar form of silicene by Ni doping using first principles density functional theory based calculations. It is found that planar as well as buckled structure is stable for Ni-doped silicene, but the buckled sheet has slightly lower total energy. The planar silicene sheet has unstable phonon modes. A comparative study of the mechanical properties reveals that the in-plane stiffness of both the pristine and the doped planar silicene is higher compared to that of the buckled silicene. This suggests that planar silicene is mechanically more robust. Electronic structure calculations of the planar and buckled Ni-doped silicene show that the energy bands at the Dirac point transform from linear behavior to parabolic dispersion. Furthermore, we extend our study to Ge and Sn sheets that are also stable and the trends of comparable mechanical stability of the planar and buckled phases remain the same.

Viscoelastic Behavior of Human Lamin A Proteins in the Context of Dilated Cardiomyopathy

Lamins are intermediate filament proteins of type V constituting a nuclear lamina or filamentous meshwork which lines the nucleoplasmic side of the inner nuclear membrane. This protein mesh provides a supporting scaffold for the nuclear envelope and tethers interphase chromosome to the nuclear periphery. Mutations of mainly A-type lamins are found to be causative for at least 11 human diseases collectively termed as laminopathies majority of which are characterised by aberrant nuclei with altered structural rigidity, deformability and poor mechanotransduction behaviour. But the investigation of viscoelastic behavior of lamin A continues to elude the field. In order to address this problem, we hereby present the very first report on viscoelastic properties of wild type human lamin A and some of its mutants linked with Dilated cardiomyopathy (DCM) using quantitative rheological measurements. We observed a dramatic strain-softening effect on lamin A network as an outcome of the strain amplitude sweep measurements which could arise from the large compliance of the quasi-cross-links in the network or that of the lamin A rods. In addition, the drastic stiffening of the differential elastic moduli on superposition of rotational and oscillatory shear stress reflect the increase in the stiffness of the laterally associated lamin A rods. These findings present a preliminary insight into distinct biomechanical properties of wild type lamin A protein and its mutants which in turn revealed interesting differences.

Closed-form nonlinear sectional analysis of pretwisted anisotropic beam with multiple delaminations

Fiber reinforced laminated composite open-section beams are widely used as bearingless rotor flex beams because of their high specific strength and stiffness as well as fatigue life. These laminated composite structures exhibit a number of different failure modes, including fiber-matrix debonding within individual layers, delamination or separation of the layers, transverse cracks through one or more layers and fiber fracture. Delamination is a predominant failure mode in continuous fiber reinforced laminated composites and often initiate near the free edges of the structure. The appearance of delaminations in the composite rotorcraft flexbeams can lead to deterioration of the mechanical properties and, in turn, the helicopter performance as well as safety. Understanding and predicting the influence of free-edge delamination on the overall behavior of the laminates will provide quantitative measures of the extent of the damage and help ensure their damage tolerance.

Evaluation of the accuracy of an impact load cell using lumped parameter modeling and analysis

The objective of the current study is to evaluate the fidelity of load cell reading during impact testing in a drop-weight impactor using lumped parameter modeling. For the most common configuration of a moving impactor-load cell system in which dynamic load is transferred from the impactor head to the load cell, a quantitative assessment is made of the possible discrepancy that can result in load cell response. A 3-DOF (degrees-of-freedom) LPM (lumped parameter model) is considered to represent a given impact testing set-up. In this model, a test specimen in the form of a steel hat section similar to front rails of cars is represented by a nonlinear spring while the load cell is assumed to behave in a linear manner due to its high stiffness. Assuming a given load-displacement response obtained in an actual test as the true behavior of the specimen, the numerical solution of the governing differential equations following an implicit time integration scheme is shown to yield an excellent reproduction of the mechanical behavior of the specimen thereby confirming the accuracy of the numerical approach. The spring representing the load cell, however,predicts a response that qualitatively matches the assumed load-displacement response of the test specimen with a perceptibly lower magnitude of load.

Evaluation of the accuracy of an accelerometer response generated by axial impact loading

The basic objective in the present study is to show that for the most common configuration of an impactor system, an accelerometer cannot exactly reproduce the dynamic response of a specimen subject to impact loading. Assessment of the accelerometer mounted in a drop-weight impactor setup for an axially loaded specimen is done with the aid of an equivalent lumped parameter model (LPM) of the setup. A steel hat-type specimen under the impact loading is represented as a non-linear spring of varying stiffness, while the accelerometer is assumed to behave in a linear manner due to its high stiffness. A suitable numerical approach has been used to solve the non-linear governing equations for a 3 degrees-of-freedom system in a piece-wise linear manner. The numerical solution following an explicit time integration scheme is used to yield an excellent reproduction of the mechanical behavior of the specimen thereby confirming the accuracy of the numerical approach. The spring representing the accelerometer, however, predicts a response that qualitatively matches the assumed load–displacement response of the test specimen with a perceptibly lower magnitude of load.

Analysis of fatigue crack growth in reinforced concrete beams

Mechanical behavior of reinforced concrete members is influenced by the action of unknown crack bridging reactions of rebars. Under cyclic loading, due to progressive growth of cracks, this bridging action contributes to the overall strength, stiffness and hysteretic behavior of the member. In this work, fatigue behavior of reinforced concrete beams are studied using a crack propagation law, developed using dimensional analysis for plain concrete with the effect of reinforcement being simulated through constraint exerted on the crack opening. The parameters considered in the model are fracture toughness, crack length, loading ratio and structural size. A numerical procedure is followed to compute fatigue life of RC beams and the dissipated energy in the steel reinforcement due to the shake down phenomenon under cyclic loading. Through a sensitivity study, it is concluded that the structural size is the most sensitive parameter in the fatigue crack propagation phenomenon. Furthermore, the residual moment carrying capacity of an RC member is determined as a function of crack extension by including the bond-slip mechanism.

A parametric study on the buckling of functionally graded material plates with internal discontinuities using the partition of unity method

In this paper, the effect of local defects, viz., cracks and cutouts on the buckling behaviour of functionally graded material plates subjected to mechanical and thermal load is numerically studied. The internal discontinuities, viz., cracks and cutouts are represented independent of the mesh within the framework of the extended finite element method and an enriched shear flexible 4-noded quadrilateral element is used for the spatial discretization. The properties are assumed to vary only in the thickness direction and the effective properties are estimated using the Mori-Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation theory. The influence of various parameters, viz., the crack length and its location, the cutout radius and its position, the plate aspect ratio and the plate thickness on the critical buckling load is studied. The effect of various boundary conditions is also studied. The numerical results obtained reveal that the critical buckling load decreases with increase in the crack length, the cutout radius and the material gradient index. This is attributed to the degradation in the stiffness either due to the presence of local defects or due to the change in the material composition. (C) 2013 Elsevier Masson SAS. All rights reserved.

A finite element method for the Saint-Venant torsion and bending problems for prismatic beams

In this work, we present a finite element formulation for the Saint-Venant torsion and bending problems for prismatic beams. The torsion problem formulation is based on the warping function, and can handle multiply-connected regions (including thin-walled structures), compound and anisotropic bars. Similarly, the bending formulation, which is based on linearized elasticity theory, can handle multiply-connected domains including thin-walled sections. The torsional rigidity and shear centers can be found as special cases of these formulations. Numerical results are presented to show the good coarse-mesh accuracy of both the formulations for both the displacement and stress fields. The stiffness matrices and load vectors (which are similar to those for a variable body force in a conventional structural mechanics problem) in both formulations involve only domain integrals, which makes them simple to implement and computationally efficient. (C) 2014 Elsevier Ltd. All rights reserved.