Analysis of transient response of saturated porous elastic soil under cyclic loading using element-free Galerkin method

A two-dimensional numerical procedure is presented to analyse the transient response of saturated porous elastic soil layer under cyclic loading. The procedure is based on the element-free Galerkin method and incorporated into the periodic conditions (temporal and spatial periodicity). Its shape function is constructed by moving least-square approximants, essential boundary conditions are implemented through Lagrange multipliers and the periodic conditions are implemented through a revised variational formulation. Time domain is discretized through the Crank–Nicolson scheme. Analytical solutions are developed to assess the effectiveness and accuracy of the current procedure in one and two dimensions. For only temporal periodic problems, a one-dimensional transient problem of finite thickness soil layer is analysed for sinusoidal surface loading. For both temporal and spatial periodic problems, a typical two-dimensional wave-induced transient problem with the seabed of finite thickness is analysed. Finally, a moving boundary problem is analysed. It is found that the current procedure is simple, efficient and accurate in predicting the response of soil layer under cyclic loading.     

Properties of the exact wave-type solutions in the theory of stratified flows

The general properties of the wave-type solutions in the theory of internal waves for flows in continuously stratified media are analysed. In addition to the well-known cases of the equivalence of the conditions for the summation of plane non-linear periodic waves and the principle of the superposition of linear waves, the conditions for the existence of wave-type solutions for non-stationary and attached waves in dissipative media are determined. The sets of relations of the physical parameters which can be used as expansion parameters when constructing approximate (asymptotic) solutions of the equations of internal waves in dissipative media are determined.     

Analysis of spectral characteristics for reflective tilted fiber gratings of uniform periods

On the basis of the coupled-mode theory, a detailed investigation of the optical spectral characteristics is presented for uniform tilted fiber gratings. Explicit expressions are derived for the spectral parameters of reflection and transmission spectra. Numerical simulations are carried on to show the dependences of grating spectral responses on the structural parameters, such as tilt angle, grating length, index modulation amplitude and polarization states. The effects of these parameters on shaping the grating spectra are discussed comprehensively. The physical mechanism and intuitive phase-matching vector model are provided to explain the unique behaviors of transmission loss spectra. The results are helpful for providing a better understanding of the spectral behavior of the tilted fiber grating.     

Mechanisms of stress transfer and interface integrity in carbon/epoxy composites under compression loading. Part II: Numerical approach

The finite element method is used to get an insight into the micromechanics of the compressive behaviour of carbon fibre composites. First the developed model is validated with existing experimental data and good agreement between predictions and experiments was found. Then the FE model is used to derive the complete stress field in the fibre and the matrix in the vicinity of a fibre fracture location. It was found that the perturbation of the stress field occurs mainly in the direction transverse to the fibre axis and this could explain the failure modes observed in composites tested in compression. Finally, a parametric study was performed on the effect of matrix modulus and matrix yield stress on the compressive fragmentation process.     

Elasto-plastic analysis of an internally pressurized thick-walled cylinder using a strain gradient plasticity theory

An analytical solution for the stress, strain and displacement fields in an internally pressurized thick-walled cylinder of an elastic strain-hardening plastic material in the plane strain state is presented. A strain gradient plasticity theory is used to describe the constitutive behavior of the material undergoing plastic deformations, whereas the generalized Hooke’s law is invoked to represent the material response in the elastic region. The solution gives explicit expressions for the stress, strain and displacement components. The inner radius of the cylinder enters these expressions not only in non-dimensional forms but also with its own dimensional identity, unlike classical plasticity-based solutions. As a result, the current solution can capture the size (strengthening) effect at the micron scale. The classical plasticity-based solution of the same problem is shown to be a special case of the present solution. Numerical results for the maximum effective stress in the cylinder wall are also provided to illustrate applications of the newly derived solution.     

A nanoindentation study of thick cBN films prepared by chemical vapor deposition

The mechanical properties of high-quality cubic boron nitride (cBN) films were systematically investigated by nanoindentation measurements performed in both cross-sectional and plan-view directions. The large film thickness (∼5 μm) allows the effective ruling out of both substrate and indenter size effects. The hardness and elastic modulus values were found to be 70 and 800 GPa, respectively, which are the highest values ever obtained on cBN films deposited by either PVD or CVD methods so far (comparable to those reported for cBN crystals synthesized by high-pressure high-temperature methods). The variation of hardness across the cBN film thickness was investigated. In conjunction with the transmission electron microscopic observations, the relationship of the hardness measured with the crystallinity and crystal size/grain boundaries was discussed.     

Deployment of tensegrity structures

In this paper we present a strategy for tensegrity structures deployment. The main idea is to use a certain set of equilibria to which the undeployed and deployed configurations belong. In the state space this set is represented by an equilibrium manifold. The deployment is conducted such that the deployment trajectory is close to this equilibrium manifold.     

Nonlinear interactions in the planar dynamics of cable-stayed beam

An analytical model is proposed to study the nonlinear interactions between beam and cable dynamics in stayed-systems. The integro-differential problem, describing the in-plane motion of a simple cable-stayed beam, presents quadratic and cubic nonlinearities both in the cable equation and at the boundary conditions. Mainly studied are the effects of quadratic interactions, appearing at relatively low oscillation amplitude. To this end an analysis of the sensitivity of modal properties to parameter variations, in intervals of technical interest, has evidenced the occurrence of one-to-two and two-to-one internal resonances between global and local modes. The interactions between the resonant modes evidences two different sources of oscillation in cables, illustrated by simple 2dof discrete models.In the one-to-two global–local resonance, a novel mechanism is analyzed, by which cable undergoes large periodic and chaotic oscillations due to an energy transfer from the low-global to high-local frequencies.In two-to-one global–local resonance, the well-known parametric-induced cable oscillation in stayed-systems is correctly reinterpreted through the autoparametric resonance between a global and a local mode. Increasing the load the saturation of the global oscillations evidences the energy transfer from high-global to low-local frequencies, producing large cable oscillations. In both cases, the effects of detuning from internal and external resonance are presented.     

Circular inclusions in anti-plane strain couple stress elasticity

The solution for a circular inclusion with a prescribed anti-plane eigenstrain is derived. It is shown that the components of the Eshelby tensor within the inclusion, corresponding to a uniform eigenstrain, can be either uniform or non-uniform, depending on the imposed interface conditions. The stress amplification factors due to circular void or rigid inclusion in an infinite medium under remote anti-plane shear stress are calculated. The failure of the couple stress elasticity to reproduce the classical elasticity solution in the limit of vanishingly small characteristic length is indicated for a particular type of boundary conditions. The solution for a circular inhomogeneity in an infinitely extended matrix subjected to remote shear stress is then derived. The effects of the imposed interface conditions, the shear stress and couple stress discontinuities, and the relationship between the inhomogeneity and its equivalent eigenstrain inclusion problem are discussed.     

A unified periodical boundary conditions for representative volume elements of composites and applications

An explicit unified form of boundary conditions for a periodic representative volume element (RVE) is presented which satisfies the periodicity conditions, and is suitable for any combination of multiaxial loads. Starting from a simple 2-D example, we demonstrate that the “homogeneous boundary conditions” are not only over-constrained but they may also violate the boundary traction periodicity conditions. Subsequently, the proposed method is applied to: (a) the simultaneous prediction of nine elastic constants of a unidirectional laminate by applying multiaxial loads to a cubic unit cell model; (b) the prediction of in-plane elastic moduli for [±θ]_n angle-ply laminates. To facilitate the analysis, a meso/micro rhombohedral RVE model has been developed for the [±θ]_n angle-ply laminates. The results obtained are in good agreement with the available theoretical and experimental results.