Singular stresses at the tip of a crack terminating at frictional interface of fibre reinforced composites

The stress singularities at the tip of a crack that terminates at a frictional interface between two layers in anisotropic composites are investigated. The order of stress singularities is determined by solving the characteristic equations obtained from the boundary conditions and the frictional interface conditions for the cases concerned. The interface is assumed to be governed by Coulomb's law of friction. Numerical results are presented for the cases with a crack terminating at a frictional interface of a fibre reinforced composite, and it is shown that there is a big difference of stress singularities between cases with and without considering friction along the interface.

An extension of Purcell's vector method with applications to panel element equations

The classical Purcell's vector method, for the construction of solutions to dense systems of linear equations is extended to a flexible orthogonalisation procedure. Some properties are revealed of the orthogonalisation procedure in relation to the classical Gauss-Jordan elimination with or without pivoting. Additional properties that are not shared by the classical Gauss-Jordan elimination are exploited. Further properties related to distributed computing are discussed with applications to panel element equations in subsonic compressible aerodynamics. Using an orthogonalisation procedure within panel methods enables a functional decomposition of the sequential panel methods and leads to a two-level parallelism.

On the coupling of Navier–Stokes and linearised Euler equations for aeroacoustic simulation

Aerodynamic generation of sound is governed by the Navier–Stokes equations while acoustic propagation in a non-uniform medium is effectively described by the linearised Euler equations. Different numerical schemes are required for the efficient solution of these two sets of equations, and therefore, coupling techniques become an essential issue. Two types of one-way coupling between the flow solver and the acoustic solver are discussed: (a) for aerodynamic sound generated at solid surfaces, and (b) in the free stream. Test results indicate how the coupling achieves the necessary accuracy so that Computational Fluid Dynamics codes can be used in aeroacoustic simulations.

An improved result of exponential stability of stochastic semilinear evolution equations

Sufficient conditions for the exponential stability of a class ofnonlinear, non-autonomous stochastic differential equations in infinitedimensions are studied. The analysis consists of introducing a suitableapproximating solution systems and using a limiting argument to pass onstability of strong solutions to mild ones. As a consequence, the classicalcriteriaof stability in A. Ichikawa [8] are improved and extended to cover a class ofnon-autonomous stochastic evolution equations.Two examples are investigated to illustrate our theory.

Moment decay rates of solutions of stochastic differential equations

The objective of this paper is to investigate the p-ίh moment asymptotic stability decay rates for certain finite-dimensional Itό stochastic differential equations. Motivated by some practical examples, the point of our analysis is a special consideration of general decay speeds, which contain as a special case the usual exponential or polynomial type one, to meet various situations. Sufficient conditions for stochastic differential equations (with variable delays or not) are obtained to ensure their asymptotic properties. Several examples are studied to illustrate our theory.

On a flexible elimination algorithm with applications to panel element equations

A flexible elimination algorithm is presented and is applied to the solution of dense systems of linear equations. Properties of the algorithm are exploited in relation to panel element methods for potential flow and subsonic compressible flow. Further properties in relation to distributed computing are also discussed.

Investigation of wall-slip effect on paste release characteristic in flip-chip stencil printing process

As the trend toward further miniaturisation of pocket and handheld consumer electronic products continues apace, the requirements for even smaller solder joints will continue. With further reductions in the size of solder joints, the reliability of solder joints will become more and more critical to the long-term performance of electronic products. Solder joints play an important role in electronics packaging, serving both as electrical interconnections between the components and the board, and as mechanical support for components. With world-wide legislation for the removal/reduction of lead and other hazardous materials from electrical and electronic products, the electronics manufacturing industry has been faced with an urgent search for new lead-free solder alloy systems and other solder alternatives. In order to achieve high volume, low cost production, the stencil printing process and subsequent wafer bumping of solder paste has become indispensable. There is wide agreement in industry that the paste printing process accounts for the majority of assembly defects, and most defects originate from poor understanding of the effect of printing process parameters on printing performance. The printing of ICAs and lead-free solder pastes through the very small stencil apertures required for flip chip applications was expected to result in increased stencil clogging and incomplete transfer of paste to the printed circuit pads. Paste release from the stencil apertures is dependent on the interaction between the solder paste, surface pad and aperture wall; including its shape. At these very narrow aperture sizes the paste rheology becomes crucial for consistent paste withdrawal because for smaller paste volumes surface tension effects become dominant over viscous flow. Successful aperture filling and release will greatly depend on the rheology of the paste material. Wall-slip plays an important role in characterising the flow behaviour of solder paste materials. The wall- slip arises due to the various attractive and repulsive forces acting between the solder particles and the walls of the measuring geometry. These interactions could lead to the presence of a thin solvent layer adjacent to the wall, which gives rise to slippage. The wall slip effect can play an important role in ensuring successful paste release after the printing process. The aim of this study was to investigate the influence of the paste microstructure on slip formation for the paste materials (lead-free solder paste and isotropic conductive adhesives). The effect of surface roughness on the paste viscosity was investigated. It was also found that altering the surface roughness of the parallel plate measuring geometry did not significantly eliminate wall slip as was expected. But results indicate that the use of a relatively rough surface helps to increase paste adhesion to the plates, inducing structural breakdown of the paste. Most importantly, the study also demonstrated on how the wall slip formation in the paste material could be utilised for understanding of the paste microstructure and its flow behaviour