Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values

2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15

Experimental and numerical evaluation of composite repairs on wood beams damaged by cross-graining

An experimental and Finite Element study was performed on the bending behaviour of wood beams of the Pinus Pinaster species repaired with adhesively-bonded carbon–epoxy patches, after sustaining damage by cross-grain failure. This damage is characterized by crack growth at a small angle to the beams longitudinal axis, due to misalignment between the wood fibres and the beam axis. Cross-grain failure can occur in large-scale in a wood member when trees that have grown spirally or with a pronounced taper are cut for lumber. Three patch lengths were tested. The simulations include the possibility of cohesive fracture of the adhesive layer, failure within the wood beam in two propagation planes and patch interlaminar failure, by the use of cohesive zone modelling. The respective cohesive properties were estimated either by an inverse method or from the literature. The comparison with the tests allowed the validation of the proposed methodology, opening a good perspective for the reduction of costs in the design stages of these repairs due to extensive experimentation.

Numerical evaluation of three-dimensional scarf repairs in carbon-epoxy structures

The widespread employment of carbon-epoxy laminates in high responsibility and severely loaded applications introduces an issue regarding their handling after damage. Repair of these structures should be evaluated, instead of their disposal, for cost saving and ecological purposes. Under this perspective, the availability of efficient repair methods is essential to restore the strength of the structure. The development and validation of accurate predictive tools for the repairs behaviour are also extremely important, allowing the reduction of costs and time associated to extensive test programmes. Comparing with strap repairs, scarf repairs have the advantages of a higher efficiency and the absence of aerodynamic disturbance. This work reports on a numerical study of the tensile behaviour of three-dimensional scarf repairs in carbon-epoxy structures, using a ductile adhesive (Araldite® 2015). The finite elements analysis was performed in ABAQUS® and Cohesive Zone Modelling was used for the simulation of damage onset and growth in the adhesive layer. Trapezoidal cohesive laws in each pure mode were used to account for the ductility of the specific adhesive mentioned. A parametric study was performed on the repair width and scarf angle. The use of over-laminating plies covering the repaired region at the outer or both repair surfaces was also tested as an attempt to increase the repairs efficiency. The obtained results allowed the proposal of design principles for repairing composite structures.

Numerical Evaluation of Ventilation Performance in Children Day Care Centres

Modelling of ventilation is strongly dependent on the physical characteristics of the building of which precise evaluation is a complex and time consuming task. In the frame of a research project, two children day care centres (CDCC) have been selected in order to measure the envelope air permeability, the flow rate of mechanical ventilation systems and indoor and outdoor temperature. The data obtained was used as input to the computer code CONTAM for ventilation simulations. The results obtained were compared with direct measurements of ventilation flow from short term measurements with CO2 tracer gas and medium term measurements with perfluorocarbon tracer (PFT) gas decay method. After validation, in order to analyse the main parameters that affect ventilation, the model was used to predict the ventilation rates for a wide range of conditions. The purpose of this assessment was to find the best practices to improve natural ventilation. A simple analytical method to predict the ventilation flow rate of rooms is also presented. The method is based on the estimation of wind effect on the room through the evaluation of an average factor and on the assessment of relevant cross section of gaps and openings combined in series or in parallel. It is shown that it may be applied with acceptable accuracy for this type of buildings when ventilation is due essentially to wind action.

Numerical evaluation of the modulus of longitudinal elasticity in structural round timber elements of the Eucalyptus genus

Currently, the standards that deal with the determination of the properties of rigidity and strength for structural round timber elements do not take in consideration in their calculations and mathematical models the influence of the existing irregularities in the geometry of these elements. This study has as objective to determine the effective value of the modulus of longitudinal elasticity for structural round timber pieces of the Eucalyptus citriodora genus by a technique of optimization allied to the Inverse Analysis Method, to the Finite Element Method and the Least Square Method.

A generalization of Student’s t-distribution from the viewpoint of special functions

Student’s t-distribution has found various applications in mathematical statistics. One of the main properties of the t-distribution is to converge to the normal distribution as the number of samples tends to infinity. In this paper, by using a Cauchy integral we introduce a generalization of the t-distribution function with four free parameters and show that it converges to the normal distribution again. We provide a comprehensive treatment of mathematical properties of this new distribution. Moreover, since the Fisher F-distribution has a close relationship with the t-distribution, we also introduce a generalization of the F-distribution and prove that it converges to the chi-square distribution as the number of samples tends to infinity. Finally some particular sub-cases of these distributions are considered.

The clinical evaluation of language functions (CELF): its applicability for hearing-impaired children

This paper discusses the diagnostic battery of the CELF in terms of construct validity and in administration of subtests.

Numerical evaluation of material model and thickness effect on LSP induced residual stresses

Laser Shock Peening (LSP) is a technological process used to improve mechanical properties in metallic components. When a short and intense laser pulse irradiates a metallic surface, high pressure plasma is generated on the treated surface; elasto-plastic waves, then, propagate inside the target and create plastic strain. This surface treatment induces a deep compressive residual stresses field on the treated area and through the thickness; such compressive residual stress is expected to increase the fatigue resistance, and reduce the detrimental effects of corrosion and stress corrosion cracking.

A bi-cubic transformation for the numerical evaluation of the Cauchy principal value integrals in boundary methods

The numerical strategies employed in the evaluation of singular integrals existing in the Cauchy principal value (CPV) sense are, undoubtedly, one of the key aspects which remarkably affect the performance and accuracy of the boundary element method (BEM). Thus, a new procedure, based upon a bi-cubic co-ordinate transformation and oriented towards the numerical evaluation of both the CPV integrals and some others which contain different types of singularity is developed. Both the ideas and some details involved in the proposed formulae are presented, obtaining rather simple and-attractive expressions for the numerical quadrature which are also easily embodied into existing BEM codes. Some illustrative examples which assess the stability and accuracy of the new formulae are included.

Numerical evaluation of the vibration reduction index for structural joints

The present paper addresses the analysis of structural vibration transmission in the presence of structural joints. The problem is tackled from a numerical point of view, analyzing some scenarios by using finite element models. The numerical results obtained making use of this process are then compared with those evaluated using the EN 12354 standard vibration reduction index concept. It is shown that, even for the simplest cases, the behavior of a structural joint is complex and evidences the frequency dependence. Comparison with results obtained by empirical formulas reveals that those of the standards cannot accurately reproduce the expected behavior, and thus indicate that alternative complementary calculation procedures are required. A simple methodology to estimate the difference between numerical and standard predictions is here proposed allowing the calculation of an adaptation term that makes both approaches converge. This term was found to be solution-dependent, and thus should be evaluated for each structure.

Application of continued fractions for fast evaluation of certain functions on a digital computer.

Bibliography: p. 23.

Evaluation of special consumer-homemaking programs in Illinois high schools /

"Prepared for and funded by the Board of Vocational Education and Rehabilitation, Division of Vocational and Technical Education, Special Programs Unit, Springfield, Illinois."

Numerical evaluation of three dimensional effects in planar flow birefringence

The influence of three dimensional effects on isochromatic birefringence is evaluated for planar flows by means of numerical simulation. Two fluid models are investigated in channel and abrupt contraction geometries. In practice, the flows are confined by viewing windows, which alter the stresses along the optical path. The observed optical properties differ therefore from their counterpart in an ideal two-dimensional flow. To investigate the influence of these effects, the stress optical rule and the differential propagation Mueller matrix are used. The material parameters are selected so that a retardation of multiple orders is achieved, as is typical for highly birefringent melts. Errors due to three dimensional effects are mainly found on the symmetry plane, and increase significantly with the flow rate. Increasing the geometric aspect ratio improve the accuracy provided that the error on the retardation is less than one order. (C) 2004 Elsevier B.V. All rights reserved.

Numerical evaluation of the fields induced by body motion in or near high-field MRI scanners

In modern magnetic resonance imaging, both patients and health care workers are exposed to strong. non-uniform static magnetic fields inside and outside of the scanner. In which body movement may be able to induce electric currents in tissues which could be potentially harmful. This paper presents theoretical investigations into the spatial distribution of induced E-fields in a tissue-equivalent human model when moving at various positions around the magnet. The numerical calculations are based on an efficient. quasi-static, finite-difference scheme. Three-dimensional field profiles from an actively shielded 4 T magnet system are used and the body model projected through the field profile with normalized velocity. The simulation shows that it is possible to induce E-fields/currents near the level of physiological significance under some circumstances and provides insight into the spatial characteristics of the induced fields. The methodology presented herein can be extrapolated to very high field strengths for the evaluation of the effects of motion at a variety of field strengths and velocities. (C) 2004 Elsevier Ltd. All rights reserved.