Biaxial-load effects on isopachics for a crack at the interface of dissimilar media

The plane problem of two dissimilar materials, bonded together and containing a crack along their common interface, which were subjected to a biaxial load at infinity, is examined by giving a closed-form expression for the first stress invariant of the normal stresses, which is equally valid everywhere, near to, and far from, the crack-tip region. This exact expression for the first-stress invariant is compared by constructing the respective isopachic-fringe patterns, to the approximate expression with non-singular terms, due to the biaxiality factor, for the same quantity. Significant differences between respective isopachic-patterns were found and their dependence on the elastic properties of both materials and the applied loads was demonstrated. The relative errors between the computedK I - andK II -components by using the approximate expression for the first stress-invariant and the accurate one, derived from closed-form solution along either isopachic-fringes or along circles and radii from the crack-tip have been given, indicating in some cases large discrepancies between exact and approximate solutions.

On a finite element model for the analysis of through cracks in laminated anisotropic cylindrical shells

A finite element model for the analysis of laminated composite cylindrical shells with through cracks is presented. The analysis takes into account anisotropic elastic behaviour, bending-extensional coupling and transverse shear deformation effects. The proposed finite element model is based on the approach of dividing a cracked configuration into triangular shaped singular elements around the crack tip with adjoining quadrilateral shaped regular elements. The parabolic isoparametric cylindrical shell elements (both singular and regular) used in this model employ independent displacement and rotation interpolation in the shell middle surface. The numerical comparisons show the evidence to the conclusion that the proposed model will yield accurate stress intensity factors from a relatively coarse mesh. Through the analysis of a pressurised fibre composite cylindrical shell with an axial crack, the effect of material orthotropy on the crack tip stress intensity factors is shown to be quite significant.

Regularized numerical integration of multibody dynamics with the generalized alpha method*

This paper discusses the consistent regularization property of the generalized α method when applied as an integrator to an initial value high index and singular differential-algebraic equation model of a multibody system. The regularization comes from within the discretization itself and the discretization remains consistent over the range of values the regularization parameter may take. The regularization involves increase of the smallest singular values of the ill-conditioned Jacobian of the discretization and is different from Baumgarte and similar techniques which tend to be inconsistent for poor choice of regularization parameter. This regularization also helps where pre-conditioning the Jacobian by scaling is of limited effect, for example, when the scleronomic constraints contain multiple closed loops or singular configuration or when high index path constraints are present. The feed-forward control in Kane's equation models is additionally considered in the numerical examples to illustrate the effect of regularization. The discretization presented in this work is adopted to the first order DAE system (unlike the original method which is intended for second order systems) for its A-stability and same order of accuracy for positions and velocities.

Application of Artificial Viscosity in Establishing Supercritical Solutions to the Transonic Integra

The nonlinear singular integral equation of transonic flow is examined in the free-stream Mach number range where only solutions with shocks are known to exist. It is shown that, by the addition of an artificial viscosity term to the integral equation, even the direct iterative scheme, with the linear solution as the initial iterate, leads to convergence. Detailed tables indicating how the solution varies with changes in the parameters of the artificial viscosity term are also given. In the best cases (when the artificial viscosity is smallest), the solutions compare well with known results, their characteristic feature being the representation of the shock by steep gradients rather than by abrupt discontinuities. However, 'sharp-shock solutions' have also been obtained by the implementation of a quadratic iterative scheme with the 'artificial viscosity solution' as the initial iterate; the converged solution with a sharp shock is obtained with only a few more iterates. Finally, a review is given of various shock-capturing and shock-fitting schemes for the transonic flow equations in general, and for the transonic integral equation in particular, frequent comparisons being made with the approach of this paper.

Viscoelastic Properties of Nanocrystalline Films of Semiconducting Chalcogenides at Liquid/Liquid Interface

The interfacial shear rheological properties of a continuous single-crystalline film of CuS and a 3D particulate gel of CdS nanoparticles (3−5 nm in diameter) formed at toluene−water interfaces have been studied. The ultrathin films (50 nm in thickness) are formed in situ in the shear cell through a reaction at the toluene−water interface between a metal−organic compound in the organic layer and an appropriate reagent for sulfidation in the aqueous layer. Linear viscoelastic spectra of the nanofilms reveal solid-like rheological behavior with the storage modulus higher than the loss modulus over the range of angular frequencies probed. Large strain amplitude sweep measurements on the CdS nanofilms formed at different reactant concentrations suggest that they form a weakly flocculated gel. Under steady shear, the films exhibit a yield stress, followed by a steady shear thinning at high shear rates. The viscoelastic and flow behavior of these films that are in common with those of many 3D “soft” materials like gels, foams, and concentrated colloidal suspensions can be described by the “soft” glassy rheology model.

Constrained linear minimax filter for systems with large plant uncertainties

This paper presents a method of designing a minimax filter in the presence of large plant uncertainties and constraints on the mean squared values of the estimates. The minimax filtering problem is reformulated in the framework of a deterministic optimal control problem and the method of solution employed, invokes the matrix Minimum Principle. The constrained linear filter and its relation to singular control problems has been illustrated. For the class of problems considered here it is shown that the filter can he constrained separately after carrying out the mini maximization. Numorieal examples are presented to illustrate the results.

Resistance Minimum in Dilute Magnetic Alloys in the Absence of Impurity Moments

A possible mechanism for the resistance minimum in dilute alloys in which the localized impurity states are non-magnetic is suggested. The fact is considered that what is essential to the Kondo-like behaviour is the interaction of the conduction electron spin s with the internal dynamical degrees of freedom of the impurity centre. The necessary internal dynamical degrees of freedom are provided by the dynamical Jahn-Teller effect associated with the degenerate 3d-orbitals of the transition-metal impurities interacting with the surrounding (octahedral) complex of the nearest-neighbour atoms. The fictitious spin I characterizing certain low-lying vibronic states of the system is shown to couple with the conduction electron spin s via s-d mixing and spin-orbit coupling, giving rise to a singular temperature-dependent exchange-like interaction. The resistivity so calculated is in fair agreement with the experimental results of Cape and Hake for Ti containing 0.2 at% of Fe.

Two-dimensional heat conduction with phase change in a semi-infinite mould

Analytical solution of a 2-dimensional problem of solidification of a superheated liquid in a semi-infinite mould has been studied in this paper. On the boundary, the prescribed temperature is such that the solidification starts simultaneously at all points of the boundary. Results are also given for the 2-dimensional ablation problem. The solution of the heat conduction equation has been obtained in terms of multiple Laplace integrals involving suitable unknown fictitious initial temperatures. These fictitious initial temperatures have interesting physical interpretations. By choosing suitable series expansions for fictitious initial temperatures and moving interface boundary, the unknown quantities can be determined. Solidification thickness has been calculated for short time and effect of parameters on the solidification thickness has been shown with the help of graphs.

The jump in vorticity across a shock wave in relativistic hydrodynamics

Using the singular surface theory, an expression for the jump in vorticity across a shock wave of arbitrary shape propagating in a uniform, perfect fluid occupying the space-time of special relativity, has been derived. It has been shown that the jump in vorticity across a shock of given strength and curvature depends only on the velocity of the medium ahead of the shock.

Symmetries and constraints in generalized Hamiltonian dynamics

A general analysis of symmetries and constraints for singular Lagrangian systems is given. It is shown that symmetry transformations can be expressed as canonical transformations in phase space, even for such systems. The relation of symmetries to generators, constraints, commutators, and Dirac brackets is clarified.

Intermolecular potentials in the dimer, the excimers, and the dimer ions of ethylene

Calculations are reported on the interaction energies in the dimer, the excimers, and the dimer ions of ethylene. The various a- and u-electron terms for different conformations of the dimeric species are determined by using the exchange perturbation method. The results predict that the singlet excimer and the dimer cation are stable primarily because of the large magnitude of the exciton-resonance and charge-resonance terms, respectively, while the neutral dimer, the triplet excimer, and the dimer anion are weakly stable. The variations of the various energy terms with conformations suggest that these dimeric species cannot have identifical structure.

Axisymmetric stress distribution in a transversely isotropic thick plate with a circular hole

An exact solution for the stresses in a transversely isotropic infinite thick plate having a circular hole and subjected to axisymmetric uniformly distributed load on the plane surfaces has been given. The solution is in the form of Fourier-Bessel series and integrals. Numerical results for the stresses are given using the elastic constants for magnesium, and are compared with the isotropic case.

Discontinuities in an arbitrarily moving gas in special relativity

Singular surface theory and ray theory are used to study the propagation of a weak discontinuity in an arbitrarily moving gas within the framework of special relativity. A differential equation is obtained describing the variation of the strength of the discontinuity along rays.

Korteweg-De Vries Equation for Non-Linear Ion-Acoustic Waves in a Plasma with Negative Ions

The theoretical analysis, based on the perturbation technique, of ion-acoustic waves in the vicinity of a Korteweg-de Vries (K-dV) equation derived in a plasma with some negative ions has been made. The investigation shows that the negative ions in plasma with isothermal electrons introduced a critical concentration at which the ion-acoustic wave plays an important role of wave-breaking and forming a precursor while the plasma with non-isothermal electrons has no such singular behaviour of the wave. These two distinct features of ion waves lead to an overall different approach of present study of ion-waves. A distinct feature of non-uniform transition from the nonisothermal case to isothermal case has been shown. Few particular plasma models have been chosen to show the characteristics behaviour of the ion-waves existing in different cases

Scaling for binary liquid systems and ferromagnets under pressure

Scaling relations between the critical indices are derived for two similar systems exhibiting λ lines: binary liquid systems and ferromagnets under pressure. In addition to the usual scaling relations, this procedure gives information about other weakly divergent quantities like isothermal compressibility and thermal expansion. Suggestions for more detailed investigations are made.