Finite element approximations of nonlinear eigenvalue problems in quantum physics

In this paper, we study finite element approximations of a class of nonlinear eigenvalue problems arising from quantum physics. We derive both a priori and a posteriori finite element error estimates and obtain optimal convergence rates for both linear and quadratic finite element approximations. In particular, we analyze the convergence and complexity of an adaptive finite element method. In our analysis, we utilize certain relationship between the finite element eigenvalue problem and the associated finite element boundary value approximations. We also present several numerical examples in quantum physics that support our theory.     

Investigation of knitting architecture on the impact behavior of glass/epoxy composites

In this study, the effect of impact and post-impact behavior of E-glass/epoxy composite plates having different knitted fabrics were investigated by considering energy profile diagram and the related load–deflection curves. Different impact energies (5–25 J) were subjected to the plates consisting of eight layers of Plain [P]₈, Milano [M]₈, and Rib [R]₈ knitted fabrics. The impact tests were continued until complete perforation of layer fabrics. The damage modes and damage processes of layer fabrics under varied impact energies were also discussed. At the end of the impact tests, the damaged samples were mounted into a compression apparatus to determine the Compression after Impact (CAI) strength of layer fabric samples. The results of these impact and post-impact tests showed that the maximum contact force was observed in the [R]₈ fabric and the minimum contact force was observed in the [P]₈ fabric and the CAI strength reduced by increasing the impact energy.     

Multi-species measurements in 1-butanol pyrolysis behind reflected shock waves

The kinetics of 1-butanol pyrolysis were investigated by measuring multi-species time histories using shock tube/laser absorption methods. Species time histories of OH, H₂O, C₂H₄, CO, and CH₄ were measured behind reflected shock waves using UV and IR laser absorption during the high-temperature decomposition of 1% 1-butanol/argon mixtures. Initial reflected shock temperatures and pressures for these experiments covered 1250–1650 K and 1.3–1.9 atm. Measured OH and H₂O time histories are in good agreement with previous experimental studies; measured C₂H₄, CO, and CH₄ time histories are the first reported for this fuel in shock tube experiments.Production pathways and sensitivities for the measured species are analyzed using the recent Sarathy et al. (2012) [37] detailed mechanism. Simulations using this mechanism underpredict H₂O, OH, and C₂H₄ mole fractions, overpredict CH₄ mole fractions, and significantly underpredict CO mole fractions at early times. As discussed in past papers and confirmed in this study, the branching ratios of H abstraction rates from 1-butanol, which are not precisely known, can significantly affect H₂O time history simulations. These simulations show that H₂O is produced primarily through H-atom abstraction from 1-butanol by OH, and therefore H₂O time histories are extremely sensitive to 1-butanol decomposition channels that contribute to the OH radical pool. Simulations also show that more C₂H₄ would be produced by faster decomposition of 1-butanol through several channels that also affect H₂O production. Finally, simulations show that CO time histories are strongly sensitive to 1-butanol decomposition into nC₃H₇ and CH₂OH, especially at early times. Evidence is presented that indicates this decomposition pathway is too slow in the simulations by a factor of three to five at conditions of the current study.     

Generation of correlated stress time histories from continuous turbulence Power Spectral Density for fatigue analysis of aircraft structures

The main purpose of the present work is to develop an efficient computational method for generating correlated stress time histories for aircraft structures under gust loads. Random gusts in any direction, which lead to random multiaxial loads on the aircraft structure are considered. A direct temporal simulation of stress using a finite element model is not possible due to computational burden. In order to overcome this, a new and efficient method based on Power Spectral Density functions (PSD) of stress is proposed. Since the PSD of the various stress components have not previously been correlated, a result enabling the direct generation of the correlation between them has been established, which is crucial for fatigue and damage tolerance analysis in several dimensions. Validation is performed by comparison with a direct (and costly) temporal simulation as well as Rice’s formulas. An example on a long range aircraft illustrates the relevance of the proposed approach. Although this method is presented with an application on a two dimensional stress tensor, it should be noted that it could be straightforwardly extended to any linear system with multiple input and output.     

A review of the CTOA/CTOD fracture criterion

The crack-tip-opening angle or displacement (CTOA/CTOD) fracture criterion is one of the oldest fracture criteria applied to fracture of metallic materials with cracks. During the past two decades, the use of elastic–plastic finite-element analyses to simulate fracture of laboratory specimens and structural components using the CTOA criterion has expanded rapidly. But the early applications were restricted to two-dimensional analyses, assuming either plane-stress or plane-strain behavior, which lead to generally non-constant values of CTOA, especially in the early stages of crack extension. Later, the non-constant CTOA values were traced to inappropriate state-of-stress (or constraint) assumptions in the crack-front region and severe crack tunneling in thin-sheet materials. More recently, the CTOA fracture criterion has been used with three-dimensional analyses to study constraint effects, crack tunneling, and the fracture process. The constant CTOA criterion (from crack initiation to failure) has been successfully applied to numerous structural applications, such as aircraft fuselages and pipelines. But why does the “constant CTOA” fracture criterion work so well? This paper reviews the results from several studies, discusses the issues of why CTOA works, and discusses its limitations.     

天然气成分波动对其预混火焰传播特性的影响

利用定容燃烧弹试验平台和CHEMKIN PRO气相化学动力学软件,研究了常温常压和化学计量比下天然气成分变化对其层流燃烧速度和火焰不稳定性的影响规律。结果表明,天然气的层流燃烧速度随乙烷、丙烷和正丁烷含量的增加而上升,且乙烷的影响效果最为显著。天然气-空气火焰的不稳定性随着乙烷、丙烷和正丁烷含量的增加而降低,正丁烷对火焰综合不稳定性的抑制能力与丙烷相近,且都强于乙烷。火焰结构分析表明,天然气成分波动时H基浓度峰值的变化最为显著,天然气的层流燃烧速度与火焰中OH基和H基浓度之和的最大值之间有较强的相关性。层流燃烧速度敏感性分析和净反应速率分析表明,天然气成分变化会影响其燃烧过程中重要基元反应的进行,通过正影响的基元反应和负影响的基元反应之间的竞争,火焰中H基的浓度峰值发生变化,乙烷含量变化对H基浓度的影响最大。     

The use of failure assessment diagrams to describe delayed hydride cracking initiation at a blunt flaw

Delayed hydride cracking (DHC) in Zr–2.5Nb alloy material is of interest to the CANadian Deuterium Uranium (CANDU)⁽¹⁾ industry in the context of the potential to initiate DHC at a blunt flaw in a CANDU reactor pressure tube. The existing CANDU blunt flaw DHC evaluation procedure is based on a threshold peak flaw-tip stress for DHC initiation that is independent of flaw geometry. Work is underway to improve the existing blunt flaw DHC evaluation procedure by developing a methodology that takes into account the effect of flaw geometry parameters. The methodology is based on representing the stress relaxation due to hydride formation and crack initiation by a process zone. A process-zone model was used to develop failure assessment diagrams in the conventional format of R6 as described in this paper, although the coordinates of the diagram have a different physical meaning. The failure assessment diagrams were shown to be independent of the scale of the configuration as well as specific values of material properties. The failure assessment curves as derived in the conventional R6 format exhibit a strong dependence on the geometry of the flaw due to the stress concentration and associated stress gradient. By redefining the ordinate of the failure assessment diagram in terms of peak flaw-tip stress the geometry dependence of the failure assessment curves was reduced significantly. This minimal geometry dependence of the failure assessment curves is valuable with regards to practical engineering flaw evaluations. Agreement between the failure assessment diagram predictions and experimental results is reasonable.     

Analytical study of stress distributions due to semi-elliptic notches in shafts under torsion loading

Closed form solutions for the stress fields created by a semi-elliptic circumferential notch in an axisymmetric shaft under torsional loading are developed. The boundary value problem has been formulated by an approach using complex potential functions and the natural elliptic coordinate system. The solutions obtained for the shear stresses have a wide range of applicability, both in terms of the size and shape of the notches and the diameter of the shafts.     

Reliability analysis of deflection — drift limited structures

Deflections, structural deteriorations, floor vibrations and other serviceability criteria are naturally random with respect to their magnitudes. A realistic analysis of serviceability limit states therefore requires the consideration of risk of unserviceability. Isosafety functions are proposed here for analyzing the influence of different parameters on the reliability levels with respect to limit states associated with deflection and drift conditions.