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.

Elastic properties of fast ion conducting lithium based borate glasses

Elastic properties of Li2O-PbO-B2O3 glasses have been investigated using sound velocity measurements at 10 MHz. Four series of glasses have been investigated with different concentrations of Li2O, PbO and B2O3. The variations of molar volume have been examined for the influences of Li2O and PbO. The elastic moduli reveal trends in their compositional dependence. The bulk and shear modulus increases monotonically with increase in the concentration of tetrahedral boron which increases network dimensionality. The variation of bulk moduli has also been correlated to the variation in energy densities. The Poisson's ratio found to be insensitive to the concentration of tetrahedral boron in the structure. The experimental Debye temperatures are in good agreement with the expected theoretical values. Experimental observations have been examined in view, the presence of borate network and the possibility of non-negligible participation of lead in network formation. (c) 2005 Elsevier B.V. All rights reserved.

Surface instability of confined elastic bilayers: Theory and simulations

The surface of a soft elastic film becomes unstable and forms a self-organized undulating pattern because of adhesive interactions when it comes in contact proximity with a rigid surface. For a single film, the pattern length scale lambda, which is governed by the minimization of the elastic stored energy, gives lambda similar to 3h, where h is the film thickness. Based on a linear stability analysis and simulations of adhesion and debonding, we consider the contact instability of an elastic bilayer, which provides greater flexibility in the morphological control of interfacial instability. Unlike the case of a single film, the morphology of the contact instability patterns, debonding distance, and debonding force in a bilayer can be controlled in a nonlinear way by varying the thicknesses and shear moduli of the films. Interestingly, the pattern wavelength in a bilayer can be greatly increased or decreased compared to a single film when the adhesive contact is formed by the stiffer or the softer of the two films, respectively. In particular, lambda as small as 0.5h can be obtained. This indicates a new strategy for pattern miniaturization in elastic contact lithography.

Non-Linear vibration of an elastic string

Equations proposed in previous work on the non-linear motion of a string show a basic disagreement, which is here traced to an assumption about the longitudinal displacement u. It is shown that it is neither necessary nor justifiable to assume that u is zero; and also that the velocity of propagation of u disturbances in a string is different from that in an infinite medium, although this difference is usually negligible. After formulating the exact equations of motion for the string, a systematic procedure is described for obtaining approximations to these equations to any order, making only the assumption that the strain in the material of the string is small. The lowest order equations in this scheme are non-linear, and are used to describe the response of a string near resonance. Finally, it is shown that in the absence of damping, planar motion of a string is always unstable at sufficiently high amplitudes, the critical amplitude falling to zero at the natural frequency and its subharmonics. The effect of slight damping on this instability is also discussed.

A symmetric solution for a cylindrical shell enclosed in an elastic casing

The problem of a long, thin circular cylindrical shell enclosed in an elastic casing and subjected to a ring of radial load on the inner rim is solved using the Love function for the casing in conjunction with Flügge shell theory. Numerical work has been done with a digital computer and the results for stress and displacement fields are given for various values of the shell geometry parameters and material constants.

Elastic constants of triclinic copper sulphate pentahydrate crystals

Using an iterative technique to obtain the exact solutions of the cubic Christoffel equation, the 21 elastic constants of copper sulphate pentahydrate have been determined at 25°C by the ultrasonic pulse echo method. The elastic constants, referred to the IRE recommended system of axes, are c11=5·65, c12=2·65, c13=3·21, c14=−0·33, c15=−0·08, c16=−0·39, c22=4·33, c23=3·47, c24=−0·07, c25=−0·21, c26=0·02, c33=5·69, c34=−0·44, c35=−0·21, c36=−0·16, c44=1·73, c45=0·09, c46=0·03, c55=1·22, c56=−0·26 and c66=1·00 in units of 1010 N m−2.

The elastic properties of a group of optical glasses by the pulse echo set-up

The pulse-echo apparatus, designed and constructed by the author, has been used to reinvestigate the elastic properties of the eighteen optical glasses. The elastic constants are correct to 0·5%. The results are compared with the earlier investigation which utilised the optical method. The possible causes for large discrepancies observed are critically and briefly discussed. A qualitative interpretation of the results has been successfully attempted. The acoustic velocity increases with the decrease in lead and barium oxides and with increase in calcium oxide and boron trioxide components.

Elastic stress analysis of jointed half-planes

Using a Fourier-integral approach, the problem of stress analysis in a composite plane consisting of two half-planes of different elastic properties rigidly joined along their boundaries has been solved. The analysis is done for a force acting in one of the half-planes for both cases when the force acts parallel and perpendicular to the interface. As a particular case, the interface stresses are evaluated when the interface is smooth. Some properties of the normal stress at the interface are discussed both for plane stress and plane strain conditions.

Wave propagation in a micropolar fluid contained in a visco-elastic membrane

The aim of the paper is to investigate the propagation of a pulse in a micropolar fluid contained in a visco-elastic membrane. It was undertaken with a view to study how closely we can approximate the flow of blood in arteries by the above model. We find that for large Reynolds number, the effect of micropolarity is hardly perceptible, whereas for small Reynolds numbers it is of considerable importance.

A fourier-integral solution for the elastic quarter-plane

The problem of an elastic quarter-plane with arbitrary loadings on the boundaries has been solved using a Fourier-integral approach.

Elastic behaviour of matter under very high pressures - Uniform compression

In order to study the elastic behaviour of matter when subjected to very large pressures, such as occur for example in the interior of the earth, and to provide an explanation for phenomena like earthquakes, it is essential to be able to calculate the values of the elastic constants of a substance under a state of large initial stress in terms of the elastic constants of a natural or stress-free state. An attempt has been made in this paper to derive expressions for these quantities for a substance of cubic symmetry on the basis of non-linear theory of elasticity and including up to cubic powers of the strain components in the strain energy function. A simple method of deriving them directly from the energy function itself has been indicated for any general case and the same has been applied to the case of hydrostatic compression. The notion of an effective elastic energy-the energy require to effect an infinitesimal deformation over a state of finite strain-has been introduced, the coefficients in this expression being the effective elastic constants. A separation of this effective energy function into normal co-ordinates has been given for the particular case of cubic symmetry and it has been pointed out, that when any of such coefficients in this normal form becomes negative, elastic instability will set in, with associated release of energy.

A novel approach for large-scale polypeptide folding based on elastic networks using continuous optimization

We present a new computationally efficient method for large-scale polypeptide folding using coarse-grained elastic networks and gradient-based continuous optimization techniques. The folding is governed by minimization of energy based on Miyazawa–Jernigan contact potentials. Using this method we are able to substantially reduce the computation time on ordinary desktop computers for simulation of polypeptide folding starting from a fully unfolded state. We compare our results with available native state structures from Protein Data Bank (PDB) for a few de-novo proteins and two natural proteins, Ubiquitin and Lysozyme. Based on our simulations we are able to draw the energy landscape for a small de-novo protein, Chignolin. We also use two well known protein structure prediction software, MODELLER and GROMACS to compare our results. In the end, we show how a modification of normal elastic network model can lead to higher accuracy and lower time required for simulation.