A Legendre spectral element model for sloshing and acoustic analysis in nearly incompressible fluids

A new spectral finite element formulation is presented for modeling the sloshing and the acoustic waves in nearly incompressible fluids. The formulation makes use of the Legendre polynomials in deriving the finite element interpolation shape functions in the Lagrangian frame of reference. The formulated element uses Gauss-Lobatto-Legendre quadrature scheme for integrating the volumetric stiffness and the mass matrices while the conventional Gauss-Legendre quadrature scheme is used on the rotational stiffness matrix to completely eliminate the zero energy modes, which are normally associated with the Lagrangian FE formulation. The numerical performance of the spectral element formulated here is examined by doing the inf-sup test oil a standard rectangular rigid tank partially filled with liquid The eigenvalues obtained from the formulated spectral element are compared with the conventional equally spaced node locations of the h-type Lagrangian finite element and the predicted results show that these spectral elements are more accurate and give superior convergence The efficiency and robustness of the formulated elements are demonstrated by solving few standard problems involving free vibration and dynamic response analysis with undistorted and distorted spectral elements. and the obtained results are compared with available results in the published literature (C) 2009 Elsevier Inc All rights reserved

Evidence for a thermally reversing window in bulk Ge-Te-Si glasses revealed by alternating differential scanning calorimetry

Experiments on Ge15Tc85-xSix glasses (2 <= x <= 12) using alternating differential scanning calorimetry (ADSC) indicate that these glasses exhibit one glass transition and two crystallization reactions upon heating. The glass transition temperature has been found to increase almost linearly with silicon content, in the entire composition tie-line. The first crystallization temperature (T-cl) exhibits an increase with silicon content for x<5; T-cl remains almost a constant in the composition range 5 < x <= 10 and it increases comparatively more sharply with silicon content thereafter. The specific heat change (Delta C-p) is found to decrease with an increase in silicon content, exhibiting a minimum at x=5 (average coordination number, (r) = 2.4); a continuous increase is seen in Delta C-p with silicon concentration above x = 5. The effects seen in the variation with composition of T-cl and Delta C-p at x=5, are the specific signatures of the mean-field stiffness threshold at (r) = 2.4. Furthermore, a broad trough is seen in the enthalpy change (Delta H-NR), which is indicative of a thermally reversing window in Ge15Te85-xSix glasses in the composition range 2 <= x <= 6 (2.34 <= (r) <= 2.42).

Simultaneous material selection and geometry design of statically determinate trusses using continuous optimization

In this work, we explore simultaneous geometry design and material selection for statically determinate trusses by posing it as a continuous optimization problem. The underlying principles of our approach are structural optimization and Ashby’s procedure for material selection from a database. For simplicity and ease of initial implementation, only static loads are considered in this work with the intent of maximum stiffness, minimum weight/cost, and safety against failure. Safety of tensile and compression members in the truss is treated differently to prevent yield and buckling failures, respectively. Geometry variables such as lengths and orientations of members are taken to be the design variables in an assumed layout. Areas of cross-section of the members are determined to satisfy the failure constraints in each member. Along the lines of Ashby’s material indices, a new design index is derived for trusses. The design index helps in choosing the most suitable material for any geometry of the truss. Using the design index, both the design space and the material database are searched simultaneously using gradient-based optimization algorithms. The important feature of our approach is that the formulated optimization problem is continuous, although the material selection from a database is an inherently discrete problem. A few illustrative examples are included. It is observed that the method is capable of determining the optimal topology in addition to optimal geometry when the assumed layout contains more links than are necessary for optimality.

Parametric finite element analyses of geocellsupported embankments

This paper presents the results from parametric finite element analyses of geocell-supported embankments constructed on weak foundation soils. A composite model is used to numerically simulate the improvement in the strength and stiffness of the soil as a result of geocell confinement. The shear strength of the geocell-encased soil is obtained as a function of the additional confining pressure due to the geocell encasement considering it as a thin cylinder subjected to internal pressure. The stiffness of the geocell-encased soil is obtained from the stiffness of the unreinforced soil and the tensile modulus of the geocell material using an empirical equation. The validity of the model is verified by simulating the laboratory experiments on model geocell-supported embankments. Parametric finite element analyses of the geocell-supported embankments are carried out by varying the dimensions of the geocell layer, the tensile strength of the material used for fabricating the geocell layer, the properties of the infill soil, and the depth of the foundation layer. Some important guidelines for selecting the geocell reinforcement to support embankments on weak foundation soils are established through these numerical studies.

The partition of unity finite element method for elastic wave propagation in Reissner-Mindlin plates

This paper reports a numerical method for modelling the elastic wave propagation in plates. The method is based on the partition of unity approach, in which the approximate spectral properties of the infinite dimensional system are embedded within the space of a conventional finite element method through a consistent technique of waveform enrichment. The technique is general, such that it can be applied to the Lagrangian family of finite elements with specific waveform enrichment schemes, depending on the dominant modes of wave propagation in the physical system. A four-noded element for the Reissner-indlin plate is derived in this paper, which is free of shear locking. Such a locking-free property is achieved by removing the transverse displacement degrees of freedom from the element nodal variables and by recovering the same through a line integral and a weak constraint in the frequency domain. As a result, the frequency-dependent stiffness matrix and the mass matrix are obtained, which capture the higher frequency response with even coarse meshes, accurately. The steps involved in the numerical implementation of such element are discussed in details. Numerical studies on the performance of the proposed element are reported by considering a number of cases, which show very good accuracy and low computational cost. Copyright (C)006 John Wiley & Sons, Ltd.

Rendering stiffer walls: a hybrid haptic system using continuous and discrete time feedback

Instability in conventional haptic rendering destroys the perception of rigid objects in virtual environments. Inherent limitations in the conventional haptic loop restrict the maximum stiffness that can be rendered. In this paper we present a method to render virtual walls that are much stiffer than those achieved by conventional techniques. By removing the conventional digital haptic loop and replacing it with a part-continuous and part-discrete time hybrid haptic loop, we were able to render stiffer walls. The control loop is implemented as a combinational logic circuit on an field-programmable gate array. We compared the performance of the conventional haptic loop and our hybrid haptic loop on the same haptic device, and present mathematical analysis to show the limit of stability of our device. Our hybrid method removes the computer-intensive haptic loop from the CPU-this can free a significant amount of resources that can be used for other purposes such as graphical rendering and physics modeling. It is our hope that, in the future, similar designs will lead to a haptics processing unit (HPU).

On the effect of matrix cracks in composite helicopter rotor blade

This paper investigates the feasibility of an on-line damage detection capability for helicopter main rotor blades made of composite material. Damage modeled in the composite is matrix cracking. A box-beam with stiffness properties similar to a hingeless rotor blade is designed using genetic algorithm for the typical [+/-theta(m)/90(n)](s) family of composites. The effect of matrix cracks is included in an analytical model of composite box-beam. An aeroelastic analysis of the helicopter rotor based on finite elements in space and time is used to study the effects of matrix cracking in the rotor blade in forward flight. For global fault detection, rotating frequencies, tip bending and torsion response, and blade root loads are studied. It is observed that the effect of matrix cracking on lag bending and elastic twist deflection at the blade tip and blade root yawing moment is significant and these parameters can be monitored for online health monitoring. For implementation of local fault detection technique, the effect on axial and shear strain, for matrix cracks in the whole blade as well as matrix cracks occurring locally is studied. It is observed that using strain measurement along the blade it is possible to locate the matrix cracks as well as to predict density of matrix cracks. (C) 2004 Elsevier Ltd. All rights reserved.

Self-regularized pseudo time-marching schemes for structural system identification with static measurements

We explore the application of pseudo time marching schemes, involving either deterministic integration or stochastic filtering, to solve the inverse problem of parameter identification of large dimensional structural systems from partial and noisy measurements of strictly static response. Solutions of such non-linear inverse problems could provide useful local stiffness variations and do not have to confront modeling uncertainties in damping, an important, yet inadequately understood, aspect in dynamic system identification problems. The usual method of least-square solution is through a regularized Gauss-Newton method (GNM) whose results are known to be sensitively dependent on the regularization parameter and data noise intensity. Finite time,recursive integration of the pseudo-dynamical GNM (PD-GNM) update equation addresses the major numerical difficulty associated with the near-zero singular values of the linearized operator and gives results that are not sensitive to the time step of integration. Therefore, we also propose a pseudo-dynamic stochastic filtering approach for the same problem using a parsimonious representation of states and specifically solve the linearized filtering equations through a pseudo-dynamic ensemble Kalman filter (PD-EnKF). For multiple sets of measurements involving various load cases, we expedite the speed of thePD-EnKF by proposing an inner iteration within every time step. Results using the pseudo-dynamic strategy obtained through PD-EnKF and recursive integration are compared with those from the conventional GNM, which prove that the PD-EnKF is the best performer showing little sensitivity to process noise covariance and yielding reconstructions with less artifacts even when the ensemble size is small.

Self-regularized pseudo time-marching schemes for structural system identification with static measurements

We explore the application of pseudo time marching schemes, involving either deterministic integration or stochastic filtering, to solve the inverse problem of parameter identification of large dimensional structural systems from partial and noisy measurements of strictly static response. Solutions of such non-linear inverse problems could provide useful local stiffness variations and do not have to confront modeling uncertainties in damping, an important, yet inadequately understood, aspect in dynamic system identification problems. The usual method of least-square solution is through a regularized Gauss-Newton method (GNM) whose results are known to be sensitively dependent on the regularization parameter and data noise intensity. Finite time, recursive integration of the pseudo-dynamical GNM (PD-GNM) update equation addresses the major numerical difficulty associated with the near-zero singular values of the linearized operator and gives results that are not sensitive to the time step of integration. Therefore, we also propose a pseudo-dynamic stochastic filtering approach for the same problem using a parsimonious representation of states and specifically solve the linearized filtering equations through apseudo-dynamic ensemble Kalman filter (PD-EnKF). For multiple sets ofmeasurements involving various load cases, we expedite the speed of the PD-EnKF by proposing an inner iteration within every time step. Results using the pseudo-dynamic strategy obtained through PD-EnKF and recursive integration are compared with those from the conventional GNM, which prove that the PD-EnKF is the best performer showing little sensitivity to process noise covariance and yielding reconstructions with less artifacts even when the ensemble size is small. Copyright (C) 2009 John Wiley & Sons, Ltd.

A particle filtering approach for structural system identification in vehicle–structure interaction problems

The problem of identification of parameters of a beam-moving oscillator system based on measurement of time histories of beam strains and displacements is considered. The governing equations of motion here have time varying coefficients. The parameters to be identified are however time invariant and consist of mass, stiffness and damping characteristics of the beam and oscillator subsystems. A strategy based on dynamic state estimation method, that employs particle filtering algorithms, is proposed to tackle the identification problem. The method can take into account measurement noise, guideway unevenness, spatially incomplete measurements, finite element models for supporting structure and moving vehicle, and imperfections in the formulation of the mathematical models. Numerical illustrations based on synthetic data on beam-oscillator system are presented to demonstrate the satisfactory performance of the proposed procedure.

Advanced transmission electron microscope triboprobe with automated closed-loop nanopositioning

Here the design and operation of a novel transmission electron microscope (TEM) triboprobe instrument with real-time vision control for advanced in situ electron microscopy is demonstrated. The NanoLAB triboprobe incorporates a new high stiffness coarse slider design for increased stability and positioning performance. This is linked with an advanced software control system which introduces both new and flexible in situ experimental functional testing modes, plus an automated vision control feedback system. This advancement in instrumentation design unlocks new possibilities of performing a range of new dynamical nanoscale materials tests, including novel friction and fatigue experiments inside the electron microscope.

The fracture toughness of bulk metallic glasses

Stiffness, strength, and toughness are the three primary attributes of a material, in terms of its mechanical properties. Bulk metallic glasses (BMGs) are known to exhibit elastic moduli at a fraction lower than crystalline alloys and have extraordinary strength. However, the reported values of fracture toughness of BMGs are highly variable; some BMGs such as the Zr-based ones have toughness values that are comparable to some high strength steels and titanium alloys, whereas there are also BMGs that are almost as brittle as silicate glasses. Invariably, monolithic BMGs exhibit no or low crack growth resistance and tend to become brittle upon structural relaxation. Despite its critical importance for the use of BMGs as structural materials, the fracture toughness of BMGs is relatively poorly understood. In this paper, we review the available literature to summarize the current understanding of the mechanics and micromechanisms of BMG toughness and highlight the needs for future research in this important area.

Behaviour of Bi-adhesive Joints

The use of relatively low modulus adhesive at the ends of overlap in a bi-adhesive bondline of a bonded joint can reduce the stress concentration significantly and, therefore, potentially lead to higher strength of the joint. This study presents the two-dimensional and three-dimensional nonlinear (geometric and material) finite element analyses of adhesively bonded single lap joints having modulus-graded bondline under monotonic loading conditions. The adhesives were modelled as an elasto-plastic multi-linear material, while the substrates were regarded as both linear elastic and bi-linear elasto-plastic material. The computational simulations have been performed to investigate the bondline behaviour by studying the stress and strain distributions both at the mid-plane as well as at the interface of the bondline. It has been observed that the static strength is higher for joints with bi-adhesive bondlines compared to those with single adhesives in bondline. Higher joint strength has also been observed for optimum bi-adhesive bondline ratio through parametric studies. Effects of load level, and bondline thickness on stress distribution in the bi-adhesive bondline have also been studied. 3D analysis results reveal the existence of complex multi-axial stress/strain state at the ends of the overlap in the bondline which cannot be observed in 2D plane strain analysis. About 1/3rd of the width of the joint from the free edge in the width direction has 3D stress state, especially in the compliant adhesive of the bondline. Magnitudes of longitudinal and lateral stress/strain components are comparable to peel stress/strain components. It has also been analytically shown that the in-plane global stiffness of the joint remains unaffected by modulus gradation of the bondline adhesive. (C) Koninklijke Brill NV, Leiden, 2010.

Extending lagrange interpolation to develop a 4-node quadrilateral element

Today finite element method is a well established tool in engineering analysis and design. Though there axe many two and three dimensional finite elements available, it is rare that a single element performs satisfactorily in majority of practical problems. The present work deals with the development of 4-node quadrilateral element using extended Lagrange interpolation functions. The classical univariate Lagrange interpolation is well developed for 1-D and is used for obtaining shape functions. We propose a new approach to extend the Lagrange interpolation to several variables. When variables axe more than one the method also gives the set of feasible bubble functions. We use the two to generate shape function for the 4-node arbitrary quadrilateral. It will require the incorporation of the condition of rigid body motion, constant strain and Navier equation by imposing necessary constraints. The procedure obviates the need for isoparametric transformation since interpolation functions are generated for arbitrary quadrilateral shapes. While generating the element stiffness matrix, integration can be carried out to the accuracy desired by dividing the quadrilateral into triangles. To validate the performance of the element which we call EXLQUAD4, we conduct several pathological tests available in the literature. EXLQUAD4 predicts both stresses and displacements accurately at every point in the element in all the constant stress fields. In tests involving higher order stress fields the element is assured to converge in the limit of discretisation. A method thus becomes available to generate shape functions directly for arbitrary quadrilateral. The method is applicable also for hexahedra. The approach should find use for development of finite elements for use with other field equations also.

Elastic property estimation using Ultrasound Assisted Optical Elastography through Remote Palpation - A simulation study - art. no. 61640Q

We propose an effective elastography technique in which an acoustic radiation force is used for remote palpation to generate localized tissue displacements, which are directly correlated to localized variations of tissue stiffness and are measured using a light probe in the same direction of ultrasound propagation. The experimental geometry has provision to input light beam along the ultrasound propagation direction, and hence it can be prealigned to ensure proper interception of the focal region by the light beam. Tissue-mimicking phantoms with homogeneous and isotropic mechanical properties of normal and malignant breast tissue are considered for the study. Each phantom is insonified by a focusing ultrasound transducer (1 MHz). The focal volume of the transducer and the ultrasound radiation force in the region are estimated through solving acoustic wave propagation through medium assuming average acoustic properties. The forward elastography problem is solved for the region of insonification assuming the Lame's parameters and Poisson's ratio, under Dirichlet boundary conditions which gives a distribution of displacement vectors. The direction of displacement, though presented spatial variation, is predominantly towards the ultrasound propagation direction. Using Monte Carlo (MC) simulation we have traced the photons through the phantom and collected the photons arriving at the detector on the boundary of the object in the direction of ultrasound. The intensity correlations are then computed from detected photons. The intensity correlation function computed through MC simulation showed a modulation whose strength is found to be proportional to the amplitude of displacement and inversely related to the storage (elastic) modulus. It is observed that when the storage modulus in the focal region is increased the computed displacement magnitude, as indicated by the depth of modulation in the intensity autocorrelation, decreased and the trend is approximately exponential.