Singular Zone Research Articles

Self-similarity, renormalization, and phase space nonuniformity of Hamiltonian chaotic dynamics.

A detailed description of fractional kinetics is given in connection to islands' topology in the phase space of a system. The method of renormalization group is applied to the fractional kinetic equation in order to obtain characteristic exponents of the fractional space and time derivatives, and an analytic expression for the transport exponents. Numerous simulations for the web-map and standard map demonstrate different results of the theory. Special attention is applied to study the singular zone, a domain near the island boundary with a self-similar hierarchy of subislands. The birth and collapse of islands of different types are considered. (c) 1997 American Institute of Physics.

Finite-Element Analysis of Portland Cement Concrete Pavements with Cracks

It was verified that finite-element modeling could be successfully used to analyze concrete pavements with partial-depth cracks. An existing finite-element program, ILLI-SLAB, was modified (ILSL97) to allow for partial-depth crack analysis. To model a partial-depth crack, a special line spring element was added to the finite-element code. The line spring elements mimic the behavior of a crack by acting as a rotational hinge between two continuous slabs. By using available fracture mechanics techniques, a relationship was derived between the amount of moment load transfer across a crack and the crack depth. This analytical solution was then used to formulate the element stiffness matrix for the line spring element. The deflections predicted by the new finite-element program are correct, but the stresses in the vicinity of the crack tip needed to be corrected to match the stress singularity zone in front of cracks. Several example problems were used to verify the proposed finite-element model, and an example of a typical highway loading condition was analyzed.

Analysis of stress singular fields at a bimaterial wedge corner

The corner stress singularities at an adhesive interface have been investigated analytically for various butt joint geometries with different adhesive material behavior. Singularities for a rigid interface with elastic and elasto-plastic adhesives have been determined using finite element and finite element iterative methods. In addition, the singular zone geometries, the stress intensity factors and the plastic zone dimensions have been evaluated for the joints investigated. The results obtained in this study have shown excellent agreement with previously published analytical and numerical data. It has been found that the corner singularity becomes weaker as the plastic zone develops.

Singular stress behavior at an adhesive interface corner

The singular stress behavior at a bimaterial wedge corner was studied analytically using the Williams' Airy stress function approach. In addition, the Finite Element Method (FEM) and the Finite Element Iterative Method (FEIM) were used to investigate the asymptotic field in adhesive butt joints of various geometries. In particular, the singular power λ and the geometry of the singular stress zones in the joints were analyzed as a function of the elastic properties of the bonded materials. It was found that the singular power λ and the singular zone geometry at the interface corners in the joints are strongly dependent on the elastic properties of the adhesive and adherend. Moreover, the numerical results of the singular powers obtained from the FEIM analysis showed excellent agreement with previously published analytical data.

On mesh refinement methods of mixed‐hybrid finite elements for revealing the nature of the singularity in the free edge of a composite laminated plate

AbstractRefinement methods were applied in order to find the form of singularity in the free edge of a composite laminated plate. The application of a logarithmic stretched mesh in the past has led to problems by the creation of needle elements. Another disadvantage of this method has been the inability for self‐adaptation. In this work, two mesh‐refinement methods, employing rectangular elements, were applied in order to solve these problems. The first is the ‘interface constraints’ method, and the second is based on the use of a ‘new mixed‐hybrid transition element’. Although the first method is much simpler and almost no changes are needed in existing programs, it has a severe problem in that there is a shortage of degrees of freedom within the singularity zone. In our case this caused a totally incorrect solution. The second method needed a conceptual change in both program and analysis, but it gave accurate results.

A “buffer ring” for edge protection of high-purity germanium diodes

The electric field at the edge of the p +-type layer of a high-purity germanium diode was reduced by an additional electric singular zone, “buffer ring”, cut in the neighborhood of the edge where breakdown is unlikely to take place until a high field gradient occurs. The buffer ring successfully accomplished the edge protection, and greatly improved the volt-ampere characteristics and the stability of the diode.

A study of near and far field effects in photoelastic stress intensity determination

A technique known as the Taylor Series Correction Method (TSCM) for extracting the stress intensity factor from photoelastic data is reviewed. The need for ‘artificial’ flaws is identified and an approach due to Savin is used to near field effects of various practical flaw shapes upon the apparent stress intensity factor. Using the Sneddon-Srivastav solution for a line crack in a finite width plate, the constriction of the singular zone is demonstrated as the crack tip approaches the free edge. Results indicate that care must be taken in applying TSCM to obtain photoelastic data at appropriate distances from the crack tip.

IRREGULAR WAVE ATTACK ON A DOLOS BREAKWATER

The paper deals with two-dimensional tests on a scale model of a dolos breakwater. It is related with the construction of a large harbour at Sines for tankers with up to 1 million dwt, ore ships with up to 300,000 dwt, general cargo, etc. The main breakwater is design ed with 40 t dolos, in order to withstand waves with up to 1 1 m significant wave height(100 years return period). Considerations on wave data and on modelling the spectrum ( Pierson-Moskowitz ) precede the presentation of three sets of tests on LNEC's irregular wave flume. Main results are compared with those from regular wave tests. The most important conclusions are stressed: influence of pla_ cement on dolos damages, irrelevance of maintenance, importance of the singular zone of the dolos support base, disadjustment of Hudson's formula for calculation of dolos weight using H as significant wave height,and importance of individual movements for the risk of breaking of individual blocks.