VAM applied to dimensional reduction of non-linear hyperelastic plates

This work aims at dimensional reduction of non-linear isotropic hyperelastic plates in an asymptotically accurate manner. The problem is both geometrically and materially non-linear. The geometric non-linearity is handled by allowing for finite deformations and generalized warping while the material non-linearity is incorporated through hyperelastic material model. The development, based on the Variational Asymptotic Method (VAM) with moderate strains and very small thickness to shortest wavelength of the deformation along the plate reference surface as small parameters, begins with three-dimensional (3-D) non-linear elasticity and mathematically splits the analysis into a one-dimensional (1-D) through-the-thickness analysis and a two-dimensional (2-D) plate analysis. Major contributions of this paper are derivation of closed-form analytical expressions for warping functions and stiffness coefficients and a set of recovery relations to express approximately the 3-D displacement, strain and stress fields. Consistent with the 2-D non-linear constitutive laws, 2-D plate theory and corresponding finite element program have been developed. Validation of present theory is carried out with a standard test case and the results match well. Distributions of 3-D results are provided for another test case. (c) 2012 Elsevier Ltd. All rights reserved.

1-D Hydrogen bonded water in Cu(II)-picolinate coordination polymer: synthesis, crystal structure, and thermogravimetric analysis

A new Cu(II)-picolinate complex was synthesized and characterized by single crystal X-ray crystallography. The complex crystallizes in the centrosymmetric triclinic space group P (1) over bar (no. 2). Picolinate in the complex extends the neutral unit into a 1-D chain through mu(2)-bridging carboxylate. The complex has a hydrogen bonding acceptor in the second coordination sphere allowing lattice water to assemble neighboring chains. Water self-assembles to form a zig-zag 1-D chain. The adjacent chains are assembled by C-H center dot center dot center dot O interactions result in the formation 2-D hydrogen bonded network. The overall hydrogen bonding between water chain and Cu-picolinate network yields a 3-D hydrogen bonded coordination network. X-ray structural analysis, FTIR and thermal analysis have been used to characterize the reported compound in the solid state.

Coupled polynomial field approach for elimination of flexure and torsion locking phenomena in the Timoshenko and Euler-Bernoulli curved beam elements

The curvature related locking phenomena in the out-of-plane deformation of Timoshenko and Euler-Bernoulli curved beam elements are demonstrated and a novel approach is proposed to circumvent them. Both flexure and Torsion locking phenomena are noticed in Timoshenko beam and torsion locking phenomenon alone in Euler-Bernoulli beam. Two locking-free curved beam finite element models are developed using coupled polynomial displacement field interpolations to eliminate these locking effects. The coupled polynomial interpolation fields are derived independently for Timoshenko and Euler-Bernoulli beam elements using the governing equations. The presented of penalty terms in the couple displacement fields incorporates the flexure-torsion coupling and flexure-shear coupling effects in an approximate manner and produce no spurious constraints in the extreme geometric limits of flexure, torsion and shear stiffness. the proposed couple polynomial finite element models, as special cases, reduce to the conventional Timoshenko beam element and Euler-Bernoulli beam element, respectively. These models are shown to perform consistently over a wide range of flexure-to-shear (EI/GA) and flexure-to-torsion (EI/GJ) stiffness ratios and are inherently devoid of flexure, torsion and shear locking phenomena. The efficacy, accuracy and reliability of the proposed models to straight and curved beam applications are demonstrated through numerical examples. (C) 2012 Elsevier B.V. All rights reserved.

Wave propagation in stiffened structures using spectrally formulated finite element

In this work, the wave propagation analysis of built-up composite structures is performed using frequency domain spectral finite elements, to study the high frequency wave responses. The paper discusses basically two methods for modeling stiffened structures. In the first method, the concept of assembly of 2D spectral plate elements is used to model a built-up structure. In the second approach, spectral finite element method (SFEM) model is developed to model skin-stiffener structures, where the skin is considered as plate element and the stiffener as beam element. The SFEM model developed using the plate-beam coupling approach is then used to model wave propagation in a multiple stiffened structure and also extended to model the stiffened structures with different cross sections such as T-section, I-section and hat section. A number of parametric studies are performed to capture the mode coupling, that is, the flexural-axial coupling present in the wave responses.

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.

Horizontal pullout resistance of a group of two vertical anchors in sand

The horizontal pullout capacity of a group of two vertical strip anchors placed along the same vertical plane in sand has been determined by using the upper bound finite elements limit analysis. The variation of the efficiency factor (xi (gamma) ) with changes in clear spacing (S) between the anchors has been established to evaluate the total group failure load for different values of (i) embedment ratio (H/B), (ii) soil internal friction angle (phi), and (iii) anchor-soil interface friction angle (delta). The total group failure load, for a given H/B, becomes always maximum corresponding to a certain optimal spacing (S-opt). The value of S-opt/B was found to lie in a range of 0.5-1.4. The maximum magnitude of xi (gamma) increases generally with increases in H/B, phi and delta.

Model domains in C-3 with abelian automorphism group

It is shown that every hyperbolic rigid polynomial domain in C-3 of finite-type, with abelian automorphism group is equivalent to a domain that is balanced with respect to some weight.

Automatic finite element formulation and assembly of hyperelastic higher order structural models

The formulation of higher order structural models and their discretization using the finite element method is difficult owing to their complexity, especially in the presence of non-linearities. In this work a new algorithm for automating the formulation and assembly of hyperelastic higher-order structural finite elements is developed. A hierarchic series of kinematic models is proposed for modeling structures with special geometries and the algorithm is formulated to automate the study of this class of higher order structural models. The algorithm developed in this work sidesteps the need for an explicit derivation of the governing equations for the individual kinematic modes. Using a novel procedure involving a nodal degree-of-freedom based automatic assembly algorithm, automatic differentiation and higher dimensional quadrature, the relevant finite element matrices are directly computed from the variational statement of elasticity and the higher order kinematic model. Another significant feature of the proposed algorithm is that natural boundary conditions are implicitly handled for arbitrary higher order kinematic models. The validity algorithm is illustrated with examples involving linear elasticity and hyperelasticity. (C) 2013 Elsevier Inc. All rights reserved.

Wave propagation analysis in laminated composite plates with transverse cracks using the wavelet spectral finite element method

This paper presents a newly developed wavelet spectral finite element (WFSE) model to analyze wave propagation in anisotropic composite laminate with a transverse surface crack penetrating part-through the thickness. The WSFE formulation of the composite laminate, which is based on the first-order shear deformation theory, produces accurate and computationally efficient results for high frequency wave motion. Transverse crack is modeled in wavenumber-frequency domain by introducing bending flexibility of the plate along crack edge. Results for tone burst and impulse excitations show excellent agreement with conventional finite element analysis in Abaqus (R). Problems with multiple cracks are modeled by assembling a number of spectral elements with cracks in frequency-wavenumber domain. Results show partial reflection of the excited wave due to crack at time instances consistent with crack locations. (C) 2014 Elsevier B.V. All rights reserved.

Precoding-Based Network Alignment Using Transform Approach for Acyclic Networks With Delay

The algebraic formulation for linear network coding in acyclic networks with the links having integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay assumed for the links, the output symbols at the sink nodes, at any given time instant, is a F(p)m-linear combination of the input symbols across different generations, where F(p)m denotes the field over which the network operates (p is prime and m is a positive integer). We use finite-field discrete Fourier transform to convert the output symbols at the sink nodes, at any given time instant, into a F(p)m-linear combination of the input symbols generated during the same generation without making use of memory at the intermediate nodes. We call this as transforming the acyclic network with delay into n-instantaneous networks (n is sufficiently large). We show that under certain conditions, there exists a network code satisfying sink demands in the usual (nontransform) approach if and only if there exists a network code satisfying sink demands in the transform approach. When the zero-interference conditions are not satisfied, we propose three precoding-based network alignment (PBNA) schemes for three-source three-destination multiple unicast network with delays (3-S 3-D MUN-D) termed as PBNA using transform approach and time-invariant local encoding coefficients (LECs), PBNA using time-varying LECs, and PBNA using transform approach and block time-varying LECs. We derive sets of necessary and sufficient conditions under which throughputs close to n' + 1/2n' + 1, n'/2n' + 1, and n'/2n' + 1 are achieved for the three source-destination pairs in a 3-S 3-D MUN-D employing PBNA using transform approach and time-invariant LECs, and PBNA using transform approach and block time-varying LECs, where n' is a positive integer. For PBNA using time-varying LECs, we obtain a sufficient condition under which a throughput demand of n(1)/n, n(2)/n, and n(3)/n can be met for the three source-destination pairs in a 3-S 3-D MUN-D, where n(1), n(2), and n(3) are positive integers less than or equal to the positive integer n. This condition is also necessary when n(1) + n(3) = n(1) + n(2) = n where n(1) >= n(2) >= n(3).

Dielectric elastomers: Asymptotically-correct three-dimensional displacement field

Asymptotically-accurate dimensional reduction from three to two dimensions and recovery of 3-D displacement field of non-prestretched dielectric hyperelastic membranes are carried out using the Variational Asymptotic Method (VAM) with moderate strains and very small ratio of the membrane thickness to its shortest wavelength of the deformation along the plate reference surface chosen as the small parameters for asymptotic expansion. Present work incorporates large deformations (displacements and rotations), material nonlinearity (hyperelasticity), and electrical effects. It begins with 3-D nonlinear electroelastic energy and mathematically splits the analysis into a one-dimensional (1-D) through-the-thickness analysis and a 2-D nonlinear plate analysis. Major contribution of this paper is a comprehensive nonlinear through-the-thickness analysis which provides a 2-D energy asymptotically equivalent of the 3-D energy, a 2-D constitutive relation between the 2-D generalized strain and stress tensors for the plate analysis and a set of recovery relations to express the 3-D displacement field. Analytical expressions are derived for warping functions and stiffness coefficients. This is the first attempt to integrate an analytical work on asymptotically-accurate nonlinear electro-elastic constitutive relation for compressible dielectric hyperelastic model with a generalized finite element analysis of plates to provide 3-D displacement fields using VAM. A unified software package `VAMNLM' (Variational Asymptotic Method applied to Non-Linear Material models) was developed to carry out 1-D non-linear analysis (analytical), 2-D non-linear finite element analysis and 3-D recovery analysis. The applicability of the current theory is demonstrated through an actuation test case, for which distribution of 3-D displacements are provided. (C) 2014 Elsevier Ltd. All rights reserved.

Wave propagation of phonon and phason displacement modes in quasicrystals: Determination of wave parameters

The paper presents the study of wave propagation in quasicrystals. Our interest is in the computation of the wavenumber (k(n)) and group speed (c(g)) of the phonon and phason displacement modes of one, two, and three dimensional quasicrystals. These wave parameter expressions are derived and computed using the elasto-hydrodynamic equations for quasicrystals. For the computation of the wavenumber and group speeds, we use Fourier transform approximation of the phonon and the phason displacement modes. The characteristic equations obtained are a polynomial equation of the wavenumber (k(n)), with frequency as a parameter. The corresponding group speeds (c(g)) for different frequencies are then computed from the wavenumber k(n). The variation of wavenumber and group speeds with frequency is plotted for the 1-D quasicrystal, 2-D decagonal Al-Ni-Co quasicrystals, and 3-D icosahedral Al-Pd-Mn and Zn-Mg-Sc quasicrystals. From the wavenumber and group speeds plots, we obtain the cut-off frequencies for different spatial wavenumber eta(m). The results show that for 1-D, 2-D, and 3-D quasicrystals, the phonon displacement modes are non-dispersive for low values of eta(m) and becomes dispersive for increasing values of eta(m). The cut-off frequencies are not observed for very low values of eta(m), whereas the cut-off frequency starts to appear with increasing eta(m). The group speeds of the phason displacement modes are orders of magnitude lower than that of the phonon displacement modes, showing that the phason modes do not propagate, and they are essentially the diffusive modes. The group speeds of the phason modes are also not influenced by eta(m). The group speeds for the 2-D quasicrystal at 35 kHz is also simulated numerically using Galerkin spectral finite element methods in frequency domain and is compared with the results obtained using wave propagation analysis. The effect of the phonon and phason elastic constants on the group speeds is studied using 3-D icosahedral Al-Pd-Mn and Zn-Mg-Sc quasicrystals. It is also shown that the phason elastic constants and the coupling coefficient do not affect the group speeds of the phonon displacement modes. (C) 2015 AIP Publishing LLC.

VAM Applied to Dimensional Reduction of Nonlinear Multifunctional Film-fabric Laminates

This work aims at asymptotically accurate dimensional reduction of non-linear multi-functional film-fabric laminates having specific application in design of envelopes for High Altitude Airships (HAA). The film-fabric laminate for airship envelope consists of a woven fabric core coated with thin films on each face. These films provide UV protection and Helium leakage prevention, while the core provides required structural strength. This problem is both geometrically and materially non-linear. To incorporate the geometric non-linearity, generalized warping functions are used and finite deformations are allowed. The material non-linearity is handled by using hyper-elastic material models for each layer. The development begins with three-dimensional (3-D) nonlinear elasticity and mathematically splits the analysis into a one-dimensional through-the-thickness analysis and a two-dimensional (2-D) plate analysis. The through-the-thickness analysis provides the 2-D constitutive law which is then given as an input to the 2-D reference surface analysis. The dimensional reduction is carried out using Variational Asymptotic Method (VAM) for moderate strains and very small thickness-to-wavelength ratio. It features the identification and utilization of additional small parameters such as ratio of thicknesses and stiffness coefficients of core and films. Closed form analytical expressions for warping functions and 2-D constitutive law of the film-fabric laminate are obtained.

An Optical How Feature and McFIS Based Approach for 3-Dimensional Human Action Recognition

We propose to develop a 3-D optical flow features based human action recognition system. Optical flow based features are employed here since they can capture the apparent movement in object, by design. Moreover, they can represent information hierarchically from local pixel level to global object level. In this work, 3-D optical flow based features a re extracted by combining the 2-1) optical flow based features with the depth flow features obtained from depth camera. In order to develop an action recognition system, we employ a Meta-Cognitive Neuro-Fuzzy Inference System (McFIS). The m of McFIS is to find the decision boundary separating different classes based on their respective optical flow based features. McFIS consists of a neuro-fuzzy inference system (cognitive component) and a self-regulatory learning mechanism (meta-cognitive component). During the supervised learning, self-regulatory learning mechanism monitors the knowledge of the current sample with respect to the existing knowledge in the network and controls the learning by deciding on sample deletion, sample learning or sample reserve strategies. The performance of the proposed action recognition system was evaluated on a proprietary data set consisting of eight subjects. The performance evaluation with standard support vector machine classifier and extreme learning machine indicates improved performance of McFIS is recognizing actions based of 3-D optical flow based features.

Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis

The ultimate bearing capacity of a circular footing, placed over rock mass, is evaluated by using the lower bound theorem of the limit analysis in conjunction with finite elements and nonlinear optimization. The generalized Hoek-Brown (HB) failure criterion, but by keeping a constant value of the exponent, alpha = 0.5, was used. The failure criterion was smoothened both in the meridian and pi planes. The nonlinear optimization was carried out by employing an interior point method based on the logarithmic barrier function. The results for the obtained bearing capacity were presented in a non-dimensional form for different values of GSI, m(i), sigma(ci)/(gamma b) and q/sigma(ci). Failure patterns were also examined for a few cases. For validating the results, computations were also performed for a strip footing as well. The results obtained from the analysis compare well with the data reported in literature. Since the equilibrium conditions are precisely satisfied only at the centroids of the elements, not everywhere in the domain, the obtained lower bound solution will be approximate not true. (C) 2015 Elsevier Ltd. All rights reserved.