Wavelet based spectral finite element modelling and detection of de-lamination in composite beams

In this paper, a model for composite beam with embedded de-lamination is developed using the wavelet based spectral finite element (WSFE) method particularly for damage detection using wave propagation analysis. The simulated responses are used as surrogate experimental results for the inverse problem of detection of damage using wavelet filtering. The WSFE technique is very similar to the fast fourier transform (FFT) based spectral finite element (FSFE) except that it uses compactly supported Daubechies scaling function approximation in time. Unlike FSFE formulation with periodicity assumption, the wavelet-based method allows imposition of initial values and thus is free from wrap around problems. This helps in analysis of finite length undamped structures, where the FSFE method fails to simulate accurate response. First, numerical experiments are performed to study the effect of de-lamination on the wave propagation characteristics. The responses are simulated for different de-lamination configurations for both broad-band and narrow-band excitations. Next, simulated responses are used for damage detection using wavelet analysis.

Prediction of the stiffness of nanoclay-polypropylene composites using a monte carlo finite element analysis approach

The present work deals with the prediction of stiffness of an Indian nanoclay-reinforced polypropylene composite (that can be termed as a nanocomposite) using a Monte Carlo finite element analysis (FEA) technique. Nanocomposite samples are at first prepared in the laboratory using a torque rheometer for achieving desirable dispersion of nanoclay during master batch preparation followed up with extrusion for the fabrication of tensile test dog-bone specimens. It has been observed through SEM (scanning electron microscopy) images of the prepared nanocomposite containing a given percentage (3–9% by weight) of the considered nanoclay that nanoclay platelets tend to remain in clusters. By ascertaining the average size of these nanoclay clusters from the images mentioned, a planar finite element model is created in which nanoclay groups and polymer matrix are modeled as separate entities assuming a given homogeneous distribution of the nanoclay clusters. Using a Monte Carlo simulation procedure, the distribution of nanoclay is varied randomly in an automated manner in a commercial FEA code, and virtual tensile tests are performed for computing the linear stiffness for each case. Values of computed stiffness modulus of highest frequency for nanocomposites with different nanoclay contents correspond well with the experimentally obtained measures of stiffness establishing the effectiveness of the present approach for further applications.

Spectral finite element based on an efficient layerwise theory for wave propagation analysis of composite and sandwich beams

In this paper, we present a spectral finite element model (SFEM) using an efficient and accurate layerwise (zigzag) theory, which is applicable for wave propagation analysis of highly inhomogeneous laminated composite and sandwich beams. The theory assumes a layerwise linear variation superimposed with a global third-order variation across the thickness for the axial displacement. The conditions of zero transverse shear stress at the top and bottom and its continuity at the layer interfaces are subsequently enforced to make the number of primary unknowns independent of the number of layers, thereby making the theory as efficient as the first-order shear deformation theory (FSDT). The spectral element developed is validated by comparing the present results with those available in the literature. A comparison of the natural frequencies of simply supported composite and sandwich beams obtained by the present spectral element with the exact two-dimensional elasticity and FSDT solutions reveals that the FSDT yields highly inaccurate results for the inhomogeneous sandwich beams and thick composite beams, whereas the present element based on the zigzag theory agrees very well with the exact elasticity solution for both thick and thin, composite and sandwich beams. A significant deviation in the dispersion relations obtained using the accurate zigzag theory and the FSDT is also observed for composite beams at high frequencies. It is shown that the pure shear rotation mode remains always evanescent, contrary to what has been reported earlier. The SFEM is subsequently used to study wavenumber dispersion, free vibration and wave propagation time history in soft-core sandwich beams with composite faces for the first time in the literature. (C) 2014 Elsevier Ltd. All rights reserved.

Finite element analysis of free vibration of the delaminated composite plate with variable kinematic multilayered plate elements

Composite laminates are prone to delamination. Implementation of delamination in the Carrera Unified Formulation frame work using nine noded quadrilateral MITC9 element is discussed in this article. MITC9 element is devoid of shear locking and membrane locking. Delaminated as well as healthy structure is analyzed for free mode vibration. The results from the present work are compared with the available experimental or/and research article or/and the three dimensional finite element simulations. The effect of different kinds and different percentages of area of delamination on the first three natural frequencies of the structure is discussed. The presence of open-mode delamination mode shape for large delaminations within the first three natural frequencies is discussed. Also, the switching of places between the second bending mode, with that of the first torsional mode frequency is discussed. Results obtained from different ordered theories are compared in the presence of delamination. Advantage of layerwise theories as compared to equivalent single layer theories for very large delaminations is stated. The effect of different kinds of delamination and their effect on the second bending and first torsional mode shape is discussed. (C) 2014 Elsevier Ltd. All rights reserved.

Mixed finite elements for electromagnetic analysis

The occurrence of spurious solutions is a well-known limitation of the standard nodal finite element method when applied to electromagnetic problems. The two commonly used remedies that are used to address this problem are (i) The addition of a penalty term with the penalty factor based on the local dielectric constant, and which reduces to a Helmholtz form on homogeneous domains (regularized formulation); (ii) A formulation based on a vector and a scalar potential. Both these strategies have some shortcomings. The penalty method does not completely get rid of the spurious modes, and both methods are incapable of predicting singular eigenvalues in non-convex domains. Some non-zero spurious eigenvalues are also predicted by these methods on non-convex domains. In this work, we develop mixed finite element formulations which predict the eigenfrequencies (including their multiplicities) accurately, even for nonconvex domains. The main feature of the proposed mixed finite element formulation is that no ad-hoc terms are added to the formulation as in the penalty formulation, and the improvement is achieved purely by an appropriate choice of finite element spaces for the different variables. We show that the formulation works even for inhomogeneous domains where `double noding' is used to enforce the appropriate continuity requirements at an interface. For two-dimensional problems, the shape of the domain can be arbitrary, while for the three-dimensional ones, with our current formulation, only regular domains (which can be nonconvex) can be modeled. Since eigenfrequencies are modeled accurately, these elements also yield accurate results for driven problems. (C) 2014 Elsevier Ltd. All rights reserved.

Finite Element Analysis of Stress Evolution in Al-Si Alloy

A 2D multi-particle model is carried out to understand the effect of microstructural variations and loading conditions on the stress evolution in Al-Si alloy under compression. A total of six parameters are varied to create 26 idealized microstructures: particle size, shape, orientation, matrix temper, strain rate, and temperature. The effect of these parameters is investigated to understand the fracture of Si particles and the yielding of Al matrix. The Si particles are modeled as a linear elastic solid and the Al matrix is modeled as an elasto-plastic solid. The results of the study demonstrate that the increase in particle size decreases the yield strength of the alloy. The particles with high aspect ratio and oriented at 0A degrees and 90A degrees to the loading axis show higher stress values. This implies that the particle shape and orientation are dominant factors in controlling particle fracture. The heat treatment of the alloy is found to increase the stress levels of both particles and matrix. Stress calculations also show that higher particle fracture and matrix yielding is expected at higher strain rate deformation. Particle fracture decreases with increase in temperature and the Al matrix plays an important role in controlling the properties of the alloy at higher temperatures. Further, this strain rate and temperature dependence is more pronounced in the heat-treated microstructure. These predictions are consistent with the experimentally observed Si particle fracture in real microstructure.

Numerical analysis of segmented-electrode Orbitraps

Simple geometries which are possible alternatives for the Orbitrap are studied in this paper. We have taken up for numerical investigation two segmented-electrode structures, ORB1 and ORB2, to mimic the electric field of the Orbitrap. In the ORB1, the inner spindle-like electrode and the outer barrel-like electrode of the Orbitrap have been replaced by 35 rings and 35 discs of fixed radii, respectively. In this structure two segmented end cap electrodes have been added. In this geometry, different potentials are applied to the different electrodes keeping top-bottom symmetry intact. In the second geometry, ORB2, the inner and outer electrodes of the Orbitrap were replaced by an approximate step structure which follows the profile of the Orbitrap electrodes. In the present study 45 steps have been used. In the ORB2, like the Orbitrap, the inner electrode is held at a negative potential and the outer electrode is at ground potential. For the purpose of comparing the performance of ORB1 and ORB2 with that of the Orbitrap, the following studies have been undertaken: (1) variation of electric potential, (2) computation of ion trajectories, (3) simulation of image currents. These studies have been carried out using both 2D and 3D Boundary Element Method (BEM), the 3D BEM was developed specifically for this study. It has been seen in these investigations that ORB1 and ORB2 have performance similar to that of the Orbitrap, with the performance of the ORB1 being seen to be marginally superior to that of the ORB2. It has been shown that with proper optimization, geometries containing far fewer electrodes can be used as mass analyzers. A novel technique of optimization of the electric field has been proposed with the objective of minimizing the dependence of axial frequency of ion motion on the initial position of an ion. The results on the optimization of 9 and 15 segmented-electrode traps having the same design as ORB1 show that it can provide accurate mass analysis. (C) 2015 Elsevier B.V. All rights reserved.

Reply to Discussion on ``Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis'' Comput. Geotech. 70 (2015) 138-149]

A discussion has been provided for the comments raised by the discusser (Clausen, 2015)1] on the article recently published by the authors (Chakraborty and Kumar, 2015). The effect of exponent alpha for values of GSI approximately smaller than 30 becomes more critical. On the other hand, for greater values of GSI, the results obtained by the authors earlier remain primarily independent of alpha and can be easily used. (C) 2015 Elsevier Ltd. All rights reserved.

Numerical analysis of segmented-electrode Orbitraps

Simple geometries which are possible alternatives for the Orbitrap are studied in this paper. We have taken up for numerical investigation two segmented-electrode structures, ORB1 and ORB2, to mimic the electric field of the Orbitrap. In the ORB1, the inner spindle-like electrode and the outer barrel-like electrode of the Orbitrap have been replaced by 35 rings and 35 discs of fixed radii, respectively. In this structure two segmented end cap electrodes have been added. In this geometry, different potentials are applied to the different electrodes keeping top-bottom symmetry intact. In the second geometry, ORB2, the inner and outer electrodes of the Orbitrap were replaced by an approximate step structure which follows the profile of the Orbitrap electrodes. In the present study 45 steps have been used. In the ORB2, like the Orbitrap, the inner electrode is held at a negative potential and the outer electrode is at ground potential. For the purpose of comparing the performance of ORB1 and ORB2 with that of the Orbitrap, the following studies have been undertaken: (1) variation of electric potential, (2) computation of ion trajectories, (3) simulation of image currents. These studies have been carried out using both 2D and 3D Boundary Element Method (BEM), the 3D BEM was developed specifically for this study. It has been seen in these investigations that ORB1 and ORB2 have performance similar to that of the Orbitrap, with the performance of the ORB1 being seen to be marginally superior to that of the ORB2. It has been shown that with proper optimization, geometries containing far fewer electrodes can be used as mass analyzers. A novel technique of optimization of the electric field has been proposed with the objective of minimizing the dependence of axial frequency of ion motion on the initial position of an ion. The results on the optimization of 9 and 15 segmented-electrode traps having the same design as ORB1 show that it can provide accurate mass analysis. (C) 2015 Elsevier B.V. All rights reserved.

Numerical Analysis of Rainfall Infiltration in the Slope with a Fracture

With the finite volume method, a 2D numerical model for seepage in unsaturated soil has been established to study the rainfall infiltration in the fractured slope.The result shows that more rain may infiltrate into the slope due to existing fracture and then the pore pressure rises correspondingly. Very probably, it is one of the crucial factors accounting for slope failure. Furthermore a preliminary study has been conducted to investigate the influence of various fracture and rainfall factors such as the depth, width and location of a crack, surface condition, rainfall intensity and duration. Pore pressure and water volumetric content during the transient seepage are carefully examined to reveal the intrinsic mechanism.

Analysis of super compact finite difference method and application to simulation of vortex-shock interaction

Turbulence and aeroacoustic noise high-order accurate schemes are required, and preferred, for solving complex flow fields with multi-scale structures. In this paper a super compact finite difference method (SCFDM) is presented, the accuracy is analysed and the method is compared with a sixth-order traditional and compact finite difference approximation. The comparison shows that the sixth-order accurate super compact method has higher resolving efficiency. The sixth-order super compact method, with a three-stage Runge-Kutta method for approximation of the compressible Navier-Stokes equations, is used to solve the complex flow structures induced by vortex-shock interactions. The basic nature of the near-field sound generated by interaction is studied.

The application of B-P constitutive equations in finite element analysis of high velocity impact

We present in this paper the application of B-P constitutive equations in finite element analysis of high velocity impact. The impact process carries out in so quick time that the heat-conducting can be neglected and meanwhile, the functions of temperature in equations need to be replaced by functions of plastic work. The material constants in the revised equations can be determined by comparison of the one-dimensional calculations with the experiments of Hopkinson bar. It can be seen from the comparison of the calculation with the experiment of a tungsten alloy projectile impacting a three-layer plate that the B-P constitutive equations in that the functions of temperature were replaced by the functions of plastic work can be used to analysis of high velocity impact.

Effect of dentin tubules on the mechanical properties of dentin - part III: Numerical, analysis

Imitating a real tooth and the periodontal supporting tissues, we have established a 2D finite element model and carried out a numerical analysis based on the inhomogeneous and anisotropic (IA) stress-strain relation and strength model of dentin proposed in the preceding Parts I and II, and the conventional homogeneous and isotropic (III) model, respectively. Quite a few cases of loadings for a non-defected and a defected tooth are considered. The numerical results show that the stress level predicted by the IA model is remarkably higher than that by the III model, revealing that the effect of the dentin tubules should be taken into a serious consideration from the viewpoint of biomechanics.