Probabilistic crack growth analyses using a boundary element model: Applications in linear elastic fracture and fatigue problems

This paper addresses the numerical solution of random crack propagation problems using the coupling boundary element method (BEM) and reliability algorithms. Crack propagation phenomenon is efficiently modelled using BEM, due to its mesh reduction features. The BEM model is based on the dual BEM formulation, in which singular and hyper-singular integral equations are adopted to construct the system of algebraic equations. Two reliability algorithms are coupled with BEM model. The first is the well known response surface method, in which local, adaptive polynomial approximations of the mechanical response are constructed in search of the design point. Different experiment designs and adaptive schemes are considered. The alternative approach direct coupling, in which the limit state function remains implicit and its gradients are calculated directly from the numerical mechanical response, is also considered. The performance of both coupling methods is compared in application to some crack propagation problems. The investigation shows that direct coupling scheme converged for all problems studied, irrespective of the problem nonlinearity. The computational cost of direct coupling has shown to be a fraction of the cost of response surface solutions, regardless of experiment design or adaptive scheme considered. (C) 2012 Elsevier Ltd. All rights reserved.

The Poincaré polynomial for the Hilbert scheme of points of C^2

Questo lavoro prende in esame lo schema di Hilbert di punti di C^2, il quale viene descritto assieme ad alcune sue proprietà, ad esempio la sua struttura hyper-kahleriana. Lo scopo della tesi è lo studio del polinomio di Poincaré di tale schema di Hilbert: ciò che si ottiene è una espressione del tipo serie di potenze, la quale è un caso particolare di una formula molto più generale, nota con il nome di formula di Goettsche.

Analytical investigation of squeeze film dampers

Squeeze film damping effects naturally occur if structures are subjected to loading situations such that a very thin film of fluid is trapped within structural joints, interfaces, etc. An accurate estimate of squeeze film effects is important to predict the performance of dynamic structures. Starting from linear Reynolds equation which governs the fluid behavior coupled with structure domain which is modeled by Kirchhoff plate equation, the effects of nondimensional parameters on the damped natural frequencies are presented using boundary characteristic orthogonal functions. For this purpose, the nondimensional coupled partial differential equations are obtained using Rayleigh-Ritz method and the weak formulation, are solved using polynomial and sinusoidal boundary characteristic orthogonal functions for structure and fluid domain respectively. In order to implement present approach to the complex geometries, a two dimensional isoparametric coupled finite element is developed based on Reissner-Mindlin plate theory and linearized Reynolds equation. The coupling between fluid and structure is handled by considering the pressure forces and structural surface velocities on the boundaries. The effects of the driving parameters on the frequency response functions are investigated. As the next logical step, an analytical method for solution of squeeze film damping based upon Green’s function to the nonlinear Reynolds equation considering elastic plate is studied. This allows calculating modal damping and stiffness force rapidly for various boundary conditions. The nonlinear Reynolds equation is divided into multiple linear non-homogeneous Helmholtz equations, which then can be solvable using the presented approach. Approximate mode shapes of a rectangular elastic plate are used, enabling calculation of damping ratio and frequency shift as well as complex resistant pressure. Moreover, the theoretical results are correlated and compared with experimental results both in the literature and in-house experimental procedures including comparison against viscoelastic dampers.

Appendix A. Whole-rock major, trace and rare earth element analyses of the Ulubey volcanics, Appendix B. Analytical standards and detection limits for analyses

Collisional and post-collisional volcanic rocks in the Ulubey (Ordu) area at the western edge of the Eastern Pontide Tertiary Volcanic Province (EPTVP) in NE Turkey are divided into four suites; Middle Eocene (49.4-44.6 Ma) aged Andesite-Trachyandesite (AT), Trachyandesite-Trachydacite-Rhyolite (TTR), Trachydacite-Dacite (TD) suites, and Middle Miocene (15.1 Ma) aged Trachybasalt (TB) suite. Local stratigraphy in the Ulubey area starts with shallow marine environment sediments of the Paleocene-Eocene time and then continues extensively with sub-aerial andesitic to rhyolitic and rare basaltic volcanism during Eocene and Miocene time, respectively. Petrographically, the volcanic rocks are composed primarily of andesites/trachyandesites, with minor trachydacites/rhyolites, basalts/trachybasalts and pyroclastics, and show porphyric, hyalo-microlitic porphyric and rarely glomeroporphyric, intersertal, intergranular, fluidal and sieve textures. The Ulubey (Ordu) volcanic rocks indicate magma evolution from tholeiitic-alkaline to calc-alkaline with medium-K contents. Primitive mantle normalized trace element and chondrite normalized rare earth element (REE) patterns show that the volcanic rocks have moderate light rare earth element (LREE)/heavy rare earth element (HREE) ratios relative to E-Type MORB and depletion in Nb, Ta and Ti. High Th/Yb ratios indicate parental magma(s) derived from an enriched source formed by mixing of slab and asthenospheric melts previously modified by fluids and sediments from a subduction zone. All of the volcanic rocks share similar incompatible element ratios (e.g., La/Sm, Zr/Nb, La/Nb) and chondrite-normalized REE patterns, indicating that the basic to acidic rocks originated from the same source. The volcanic rocks were produced by the slab dehydration-induced melting of an existing metasomatized mantle source, and the fluids from the slab dehydration introduced significant large ion lithophile element (LILE) and LREE to the source, masking its inherent HFSE-enriched characteristics. The initial 87Sr/86Sr (0.7044-0.7050) and eNd (-0.3 to +3.4) ratios of the volcanics suggest that they originated from an enriched lithospheric mantle source with low Sm/Nd ratios. Integration of the geochemical, petrological and isotopical with regional and local geological data suggest that the Tertiary volcanic rocks from the Ulubey (Ordu) area were derived from an enriched mantle, which had been previously metasomatized by fluids derived from subducted slab during Eocene to Miocene in collisional and post-collisional extension-related geodynamic setting following Late Mesozoic continental collision between the Eurasian plate and the Tauride-Anatolide platform.

Rhenium and platinum-group element concentrations and Os isotope data for Philippine Sea Plate basalts from DSDP Legs 31, 58, and 59

Platinum-group elements (PGE), rhenium and osmium isotope data are reported for basalts from Deep Sea Drilling Project cores in the Philippine Sea Plate (PSP). Lithophile trace element and isotopic characteristics indicate a range of source components including DMM, EMII and subduction-enriched mantle. MORB-like basalts possess smooth, inclined chondrite-normalised PGE patterns with high palladium-PGE/iridium-PGE ratios, consistent with previously published data for MORB, and with the inferred compatibility of PGE. In contrast, while basalts with EMII-type lithophile element chemistry possess high Pt/Ir ratios, many have much lower Pd/Ir and unusually high Ru/Ir of >10. Similarly, back-arc samples from the Shikoku and Parece-Vela basins have very high Ru/Ir ratios (>30) and Pd/Ir as low as 1.1. Such extreme Pd/Ir and Ru/Ir ratios have not been previously reported in mafic volcanic suites and cannot be easily explained by variable degrees of melting, fractional crystallisation or by a shallow-level process such as alteration or degassing. The data appear most consistent with sampling of at least two mantle components with distinct PGE compositions. Peridotites with the required PGE characteristics (i.e. low Pd, but relatively high Ru and Re) have not been documented in oceanic mantle, but have been found in sub-continental mantle lithosphere and are the result of considerable melt depletion and selective metasomatic enrichment (mainly Re). The long-term presence of subduction zones surrounding the Philippine Sea Plate makes this a prime location for metasomatic enrichment of mantle, either through fluid enrichment or infiltration by small melt fractions. The Re-Os isotope data are difficult to interpret with confidence due to low Os concentrations in most samples and the uncertainty in sample age. Data for Site 444A (Shikoku Basin) give an age of 17.7+/-1.3 Ma (MSWD = 14), consistent with the proposed age of basement at the site and thus provides the first robust radiometric age for these samples. The initial 187Os/188Os of 0.1298+/-0.0069 is consistent with global MORB, and precludes significant metasomatic enrichment of Os by radiogenic slab fluids. Re-Os data for Sites 446A (two suites, Daito Basin) and 450 (Parece-Vela Basin) indicate ages of 73, 68 and 43 Ma, which are respectively, 30, 17 and >12 Ma older than previously proposed ages. The alkalic and tholeiitic suites from Site 446A define regression lines with different 187Os/188Osinitial (0.170+/-0.033 and 0.112+/-0.024, respectively) which could perhaps be explained by preferential sampling of interstitial, metasomatic sulphides (with higher time-integrated Re/Os ratios) by smaller percentage alkalic melts. One sample, with lithophile elements indistinguishable from MORB, is Os-rich (146 pg/g) and has an initial 187Os/188Os of 0.1594, which is at the upper limit of the accepted OIB range. Given the Os-rich nature of this sample and the lack of evidence for subduction or recycled crust inputs, this osmium isotope ratio likely reflects heterogeneity in the DMM. The dataset as a whole is a striking indication of the possible PGE and Os isotope variability within a region of mantle that has experienced a complex tectonic history.

Improved Integration Methods for P-Adaptive Boundary Element Techniques

Non linear transformations are a good alternative for the numerical evaluation of singular and quasisingular integrals appearing in Boundary Element Method specially in the p-adaptive version. Some aspects of its numerical implementation in 2-D Potential codes is discussed and some examples are shown.

Finite element simulation of dispersion in the Bay of Santander

Two mathematical models are used to simulate pollution in the Bay of Santander. The first is the hydrodynamic model that provides the velocity field and height of the water. The second gives the pollutant concentration field as a resultant. Both models are formulated in two-dimensional equations. Linear triangular finite elements are used in the Galerkin procedure for spatial discretization. A finite difference scheme is used for the time integration. At each time step the calculated results of the first model are input to the second model as field data. The efficiency and accuracy of the models are tested by their application to a simple illustrative example. Finally a case study in simulation of pollution evolution in the Bay of Santander is presented