On the velocity of buckle propagation in a beam on a nonlinear elastic-foundation

The paper revisits a simple beam model used by Chater et al. (1983, Proc. IUTAM Symp. Collapse, Cambridge University Press) to examine the dynamics of propagating buckles on it. It was found that, if a buckle is initiated at a constant pressure higher than the propagation pressure of the model (P-p), the buckle accelerates and gradually reaches a constant velocity which depends upon the pressure, while if it is initiated at P-p, the buckle propagates at a velocity which depends upon the initial imperfection. The causes for the difference are also investigated.

Effects of contact resistance on thermal-conductivity of composite media with a periodic structure

The thermal conductivity of periodic composite media with spherical or cylindrical inclusions embedded in a homogeneous matrix is discussed. Using Green functions, we show that the Rayleigh identity can be generalized to deal with thermal properties ot these systems. A new calculating method for effective conductivity of composite media is proposed. Useful formulae for effective thermal conductivity are derived, and meanings of contact resistance in engineering problems are explained.

Structures on sliding base subject to horizontal and vertical motions

In this paper particular investigation is directed towards the combined effects of horizontal and vertical motions of real earthquakes to structures resting on sliding base. A simplified method is presented to treat the nonlinear effects of time dependent frictional force of the sliding base as a function of the vertical reaction produced by the foundation. As an example, the El Centro 1940 earthquake record is used on a structural model to show the structural responses due to a sliding base with different frictional and stiffness characteristics. The study shows that vertical ground motion does affect both the superstructure response and the base sliding displacement. Nevertheless, the sliding base isolator is shown to be effective for the reduction of seismic response of a superstructure.

High-order asymptotic field of tensile plane-strain nonlinear crack problems

In this paper, the governing equations and the analytical method of the secondorder asymptotic field for the plane-straln crack problems of mode I have been presented. The numerical calculation has been carried out. The amplitude coefficients k2 of the second term of the asymptotic field have been determined after comparing the present results with some fine results of the finite element calculation. The variation of coefficients k2 with changes of specimen geometry and developments of plastic zone have been analysed. It is shown that the second term of the asymptotic field has significant influence on the near-crack-tip field. Therefore, we may reasonably argue that both the J-integral and the coefficient k2 can beeome two characterizing parameters for crack initiation.

Asymptotic solutions to a class of nonlinear oscillation systems

In this paper, we present an asymptotic method for the analysis of a class of strongly nonlinear oscillators, derive second-order approximate solutions to them expressed in terms of their amplitudes and phases, and obtain the equations governing the amplitudes and phases, by which the amplitudes of the corresponding limit cycles and their behaviour can be determined. As an example, we investigate the modified van der Pol oscillator and give the second-order approximate analytical solution of its limit cycle. The comparison with the numerical solutions shows that the two results agree well with each other.

Nonlinear Dynamic Response of Tension Leg Platform

Tension Leg Platform (TLP) is a typical compliant offshore structure for oil exploitation in deep water. Most of the existing mathematical models for analyzing the dynamic response of TLP are based on explicit or implicit assumptions that displacements (translations and rotations) are small magnitude. Herein a theoretical method for analyzing the nonlinear dynamic behavior of TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e. finite displacement, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. Using this theoretical model, we perform the numerical analysis of dynamic response of a representative TLP. The comparison between the degenerative linear solution of the proposed nonlinear model and the published one shows good agreements. Furthermore, numerical results are presented which illustrate that nonlinearities exert a distinct influence on the dynamic responses of the TLP.

Numerical Simulation of R-M Instability

In order to capture shock waves and contact discontinuities in the field and easy to program with parallel computation a new algorithm is developed to solve the N-S equations for simulation of R-M instability problems. The method with group velocity control is used to suppress numerical oscillations, and an adaptive non-uniform mesh is used to get fine resolution. Numerical results for cylindrical shock-cylindrical interface interaction with a shock Mach number Ms=1.2 and Atwood number A=0.818, 0.961, 0.980 (the interior density of the interface/outer density p(1)/p(2) = 10, 50, 100, respectively), and for the planar shock-spherical interface interaction with Ms=1.2 and p(1)/p(2) = 14.28are presented. The effect of Atwood number and multi-mode initial perturbation on the R-M instability are studied. Multi-collisions of the reflected shock with the interface is a main reason of nonlinear development of the interface instability and formation of the spike-bubble structures In simulation with double mode perturbation vortex merging and second instability are found. After second instability the small vortex structures near the interface produced. It is important factor for turbulent mixing.

Slope Stability Analysis Using Anisotropic and Nonlinear Failure Criteria

The shear strength of soils or rocks developed in a landslide usually exhibits anisotropic and nonlinear behavior. The process of sedimentation and subsequent consolidation can cause anisotropy of sedimentary soils or rocks, for instance. Nonlinearity of failure envelope could be attributed to "interlocking" or "dilatancy" of the material, which is generally dependent upon the stress level. An analytical method considering both anisotropy and nonlinearity of the failure envelops of soil and rocks is presented in the paper. The nonlinearfailure envelopes can be determined from routine triaxial tests. A spreadsheet program, which uses the Janbu's Generalized Procedure of Slice and incorporates anisotropic, illustrates the implementation of the approach and nonlinearfailure envelops. In the analysis, an equivalent Mohr-Coulomb linear failure criterion is obtained by drawing a tangent to the nonlinear envelope of an anisotropic soil at an appropriate stress level. An illustrative example is presented to show the feasibility and numerical efficiency of the method.

Short-Term Nonlinear Response of Tension Leg Platform in Random Sea Waves

Most of the existing mathematical models for analyzing the dynamic response of TLP are based on explicit or implicit assumptions that motions (translations and rotations) are small magnitude. However, when TLP works in severe adverse conditions, the a priori assumption on small displacements may be inadequate. In such situation, the motions should be regarded as finite magnitude. This paper will study stochastic nonlinear dynamic responses of TLP with finite displacements in random waves. The nonlinearities considered are: large amplitude motions, coupling the six degrees-of-freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. The nonlinear dynamic responses are calculated by using numerical integration procedure in the time domain. After the time histories of the dynamic responses are obtained, we carry out cycle counting of the stress histories of the tethers with rain-flow counting method to get the stress range distribution.

Relationships between Initial Unloading Slope, Contact Depth, and Mechanical Properties for Spherical Indentation in Linear Viscoelastic Solids

Using analytical and finite element modeling, we examine the relationships between initial unloading slope, contact depth, and mechanical properties for spherical indentation in viscoelastic solids with either displacement or load as the independent variable. We then investigate whether the Oliver-Pharr method for determining the contact depth and contact radius, originally proposed for indentation in elastic and elastic-plastic solids, is applicable to spherical indentation in viscoelastic solids. Finally, the analytical and numerical results are used to answer questions raised in recent literature about measuring viscoelastic properties from instrumented spherical indentation experiments.

Nonlinear Dynamic Responses of the Tensioned Tether under Parametric Excitations

The nonlinear dynamic responses of the tensioned tether subjected to combined surge and heave motions of floating platform are investigated using 2-D nonlinear beam model. It is shown that if the transverse-axial coupling of nonlinear beam model and the combined surge-heave motions of platform are considered, the governing equation is not Mathieu equation any more, it becomes nonlinear Hill equation. The Hill stability chart is obtained by using the Hill's infinite determinant and harmonic balance method. A parameter M, which is the function of tether length, the surge and heave amplitude of platform, is defined. The Hill stability chart is obviously different from Mathieu stability chart which is the specific case as M=0. Some case studies are performed by employing linear and nonlinear beam model respectively. It can be found that the results differences between nonlinear and linear model are apparent.

Contact pressure of porous Al2O3 probed by nanoindentations

Contact pressure of porous Al2O3 probed by nanoindentation was investigated by dimensional analysis with special attention paid to scaling effects in the mechanical behavior. It was found that, for sample containing small grains and interconnected pores, the contact pressure is manifest dominated by bonding strength of the porous alumina. Whereas the samples with coarse grain and various porous structures exhibit higher contact pressures and smaller residual deformations, which can be attributed to the mechanical response of the solid-phase under current limited peak loads.

Failure process analysis of cement under explosive loading with a generalized driven nonlinear threshold model

The microstructural heterogeneity and stress fluctuation play important roles in the failure process of brittle materials. In this paper, a generalized driven nonlinear threshold model with stress fluctuation is presented to study the effects of microstructural heterogeneity on continuum damage evolution. As an illustration, the failure process of cement material under explosive loading is analyzed using the model. The result agrees well with the experimental one, which proves the efficiency of the model.

Subsonic interface crack with crack face contact

A steady-state subsonic interface crack propagating between an elastic solid and a rigid substrate with crack face contact is studied. Two cases with respective to the contact length are considered, i.e., semi-infinite and finite crack face contact. Different from a stationary or an open subsonic interface crack, stress singularity at the crack tip in the present paper is found to be non-oscillatory. Furthermore, in the semi-infinite contact case, the singularity of the stress field near the crack tip is less than 1/2. In the finite contact case, no singularity exists near the crack tip, but less than 1/2 singularity does at the end of the contact zone. In both cases, the singularity depends on the linear contact coefficient and the crack speed. Asymptotic solutions near the crack tip are given and analyzed. In order to satisfy the contact conditions, reasonable region of the linear contact coefficient is found. In addition, the solution predicts a non-zero-energy dissipation rate due to crack face contact.