A two-dimensional elastic-plastic finite element analysis is performed for plane stress conditions with 4-node isoparametric elements to examine closure behaviour of fatigue cracks, giving special attention to the determination of the most appropriate mesh sizes. It is found that a smaller mesh size does not always give more accurate simulation results in the fatigue crack closure analysis, unlike a conventional structural analysis. A unique, most-appropriate mesh size exists for a given loading condition that will provide numerical results which agree well with experimental data. The most appropriate mesh size can be determined approximately in terms of the theoretical reversed plastic zone sue. In particular, the ratio of the most appropriate mesh size to the theoretical reversed plastic zone size is nearly constant for a given stress ratio in the so-called crack-length-fixed method proposed in this study. By using the concept of the most appropriate mesh size, the finite element analysis can predict fatigue crack closure behaviour very well.Keywords-Fatigue crack closure; Finite element method; Most-appropriate mesh size, Crack-lengthfixed method. NOMENCLATURE a, a, = half crack length and initial crack length da/dN = crack growth rate E = Young's modulus H' = linear strain hardening parameter (du/ds) K , , , K-= maximum and minimum stress intensity factors due to applied loading KO, = opening stress intensity factor R = stress ratio (= K-IK,,) U = crack opening ratio [=(K,, -Kop)/(Kpu. -K-)] Aa, Aa* = mesh size and most appropriate mesh sue u,,,, u,, = opening and closing stress urnax, u-=maximum and minimum applied stress ur = yield stress v = Poisson's ratio up, Aup = theoretical monotonic and reversed plastic zone sizes

We present the results of far ultraviolet (FUV) observations of the broad region around the Aquila Rift including the Galactic plane. As compared with various wavelength data sets, dust scattering is found to be the major origin of the diffuse FUV continuum in this region. The FUV intensity clearly correlates with the dust extinction level for E(B − V ) < 0.2, while this correlation disappears for E(B − V ) > 0.2 due to heavy dust extinction combined with the effect of nonuniform interstellar radiation fields. The FUV intensity also correlates well with Hα intensity, implying that at least some fraction of the observed Hα emission could be the dust-scattered light of Hα photons originating elsewhere in the Galaxy. Most of the Aquila Rift region is seen devoid of diffuse FUV continuum due to heavy extinction while strong emission is observed in the surrounding regions. Molecular hydrogen fluorescent emission lines are clearly seen in the spectrum of "Aquila-Serpens," while "Aquila-East" does not show any apparent line features. CO emission intensity is also found to be higher in the "Aquila-Serpens" region than in the "Aquila-East" region. In this regard, we note that regions of star formation have been found in "Aquila-Serpens" but not in "Aquila-East."

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