High-Dimensional Stochastic Design Optimization by Adaptive-Sparse Polynomial Dimensional Decomposition

This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic response for statistical moment and reliability analyses; a novel integration of the adaptive-sparse PDD approximation and score functions for estimating the first-order design sensitivities of the statistical moments and failure probability; and standard gradient-based optimization algorithms. New analytical formulae are presented for the design sensitivities that are simultaneously determined along with the moments or the failure probability. Numerical results stemming from mathematical functions indicate that the new method provides more computationally efficient design solutions than the existing methods. Finally, stochastic shape optimization of a jet engine bracket with 79 variables was performed, demonstrating the power of the new method to tackle practical engineering problems.Comment: 18 pages, 2 figures, to appear in Sparse Grids and Applications--Stuttgart 2014, Lecture Notes in Computational Science and Engineering 109, edited by J. Garcke and D. Pfl\"{u}ger, Springer International Publishing, 201

The subduction structure of the Northern Apennines: results from the RETREAT seismic deployment

The project Retreating-trench, extension, and accretion tectonics, RETREAT, is a multidisciplinary study of the Northern Apennines (earth.geology.yale.edu/RETREAT/), funded by the United States National Science Foundation (NSF) in collaboration with the Italian Istituto Nazionale di Geofisica e Vulcanologia (INGV) and the Grant Agency of the Czech Academy of Sciences (GAAV). The main goal of RETREAT is to develop a self-consistent dynamic model of syn-convergent extension, using the Northern Apennines as a natural laboratory. In the context of this project a passive seismological experiment was deployed in the fall of 2003 for a period of three years. RETREAT seismologists aim to develop a comprehensive understanding of the deep structure beneath the Northern Apennines, with particular attention on inferring likely patterns of mantle flow. Specific objectives of the project are the crustal and lithospheric thicknesses, the location and geometry of the Adriatic slab, and the distribution of seismic anisotropy laterally and vertically in the lithosphere and asthenosphere. The project is collecting teleseismic and regional earthquake data for 3 years. This contribution describes the RETREAT seismic deployment and reports on key results from the first year of the deployment. We confirm some prior findings regarding the seismic structure of Central Italy, but our observations also highlight the complexity of the Northern Apennines subduction system

A comparison of homogenization and standard mechanics analyses for periodic porous composites

Composite material elastic behavior has been studied using many approaches, all of which are based on the concept of a Representative Volume Element (RVE). Most methods accurately estimate effective elastic properties when the ratio of the RVE size to the global structural dimensions, denoted here as ν, goes to zero. However, many composites are locally periodic with finite ν. The purpose of this paper was to compare homogenization and standard mechanics RVE based analyses for periodic porous composites with finite ν. Both methods were implemented using a displacement based finite element formulation. For one-dimensional analyses of composite bars the two methods were equivalent. Howver, for two- and three-dimensional analyses the methods were quite different due to the fact that the local RVE stress and strain state was not determined uniquely by the applied boundary conditions. For two-dimensional analyses of porous periodic composites the effective material properties predicted by standard mechanics approaches using multiple cell RVEs converged to the homogenization predictions using one cell. In addition, homogenization estimates of local strain energy density were within 30% of direct analyses while standard mechanics approaches generally differed from direct analyses by more than 70%. These results suggest that homogenization theory is preferable over standard mechanics of materials approaches for periodic composites even when the material is only locally periodic and ν is finite.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47812/1/466_2004_Article_BF00369853.pd

Hf–Zr anomalies in clinopyroxene from mantle xenoliths from France and Poland: implications for Lu–Hf dating of spinel peridotite lithospheric mantle

Clinopyroxenes in some fresh anhydrous spinel peridotite mantle xenoliths from the northern Massif Central (France) and Lower Silesia (Poland), analysed for a range of incompatible trace elements by laser ablation inductively coupled plasma mass spectrometry, show unusually strong negative anomalies in Hf and Zr relative to adjacent elements Sm and Nd, on primitive mantle-normalised diagrams. Similar Zr–Hf anomalies have only rarely been reported from clinopyroxene in spinel peridotite mantle xenoliths worldwide, and most are not as strong as the examples reported here. Low Hf contents give rise to a wide range of Lu/Hf ratios, which over geological time would result in highly radiogenic εHf values, decoupling them from εNd ratios. The high 176Lu/177Hf could in theory produce an isochronous relationship with 176Hf/177Hf over time; an errorchron is shown by clinopyroxene from mantle xenoliths from the northern Massif Central. However, in a review of the literature, we show that most mantle spinel peridotites do not show such high Lu/Hf ratios in their constituent clinopyroxenes, because they lack the distinctive Zr–Hf anomaly, and this limits the usefulness of the application of the Lu–Hf system of dating to garnet-free mantle rocks. Nevertheless, some mantle xenoliths from Poland or the Czech Republic may be amenable to Hf-isotope dating in the future

Inverse modeling of geochemical and mechanical compaction in sedimentary basins through Polynomial Chaos Expansion

We present an inverse modeling procedure for the estimation of model parameters of sedi- mentary basins subject to compaction driven by mechanical and geochemical processes. We consider a sandstone basin whose dynamics are governed by a set of unknown key quantities. These include geophys- ical and geochemical system attributes as well as pressure and temperature boundary conditions. We derive a reduced (or surrogate) model of the system behavior based on generalized Polynomial Chaos Expansion (gPCE) approximations, which are directly linked to the variance-based Sobol indices associated with the selected uncertain model parameters. Parameter estimation is then performed within a Maximum Likeli- hood (ML) framework. We then study the way the ML inversion procedure can benefit from the adoption of anisotropic polynomial approximations (a-gPCE) in which the surrogate model is refined only with respect to selected parameters according to an analysis of the nonlinearity of the input-output mapping, as quanti- fied through the Sobol sensitivity indices. Results are illustrated for a one-dimensional setting involving quartz cementation and mechanical compaction in sandstones. The reliability of gPCE and a-gPCE approxi- mations in the context of the inverse modeling framework is assessed. The effects of (a) the strategy employed to build the surrogate model, leading either to a gPCE or a-gPCE representation, and (b) the type and quality of calibration data on the goodness of the parameter estimates is then explored

La théorie variation des rayons complexes pour le calcul des vibrations moyennes fréquences

A new approach named the "Variational Theory of Complex Rays" is introduced for computing the vibrations of elastic structures weakly damped in the medium frequency range. Emphasis has been placed here on the most fundamental aspects. The effective quantities (elastic energy, vibration intensity ...) are evaluated after computing a small system of equations which does not derive from a finite element dicretization of the structure. Numerical examples related to plates show the interest and the possibilities ofthe VTRC

The cohesive band model: A cohesive surface formulation with stress triaxiality

In the cohesive surface model cohesive tractions are transmitted across a two-dimensional surface, which is embedded in a three-dimensional continuum. The relevant kinematic quantities are the local crack opening displacement and the crack sliding displacement, but there is no kinematic quantity that represents the stretching of the fracture plane. As a consequence, in-plane stresses are absent, and fracture phenomena as splitting cracks in concrete and masonry, or crazing in polymers, which are governed by stress triaxiality, cannot be represented properly. In this paper we extend the cohesive surface model to include in-plane kinematic quantities. Since the full strain tensor is now available, a three-dimensional stress state can be computed in a straightforward manner. The cohesive band model is regarded as a subgrid scale fracture model, which has a small, yet finite thickness at the subgrid scale, but can be considered as having a zero thickness in the discretisation method that is used at the macroscopic scale. The standard cohesive surface formulation is obtained when the cohesive band width goes to zero. In principle, any discretisation method that can capture a discontinuity can be used, but partition-of-unity based finite element methods and isogeometric finite element analysis seem to have an advantage since they can naturally incorporate the continuum mechanics. When using interface finite elements, traction oscillations that can occur prior to the opening of a cohesive crack, persist for the cohesive band model. Example calculations show that Poisson contraction influences the results, since there is a coupling between the crack opening and the in-plane normal strain in the cohesive band. This coupling holds promise for capturing a variety of fracture phenomena, such as delamination buckling and splitting cracks, that are difficult, if not impossible, to describe within a conventional cohesive surface model. © 2013 Springer Science+Business Media Dordrecht