A Robust Approach to Topology Optimization Accounting for Geometric Imperfections (Een robuuste aanpak voor topologische optimalisatie rekening houdend met geometrische imperfecties)

Performance and cost efficiency are important demands in the design of civil structures such as bridges and high-rise buildings. This thesis investigates topology optimization as a tool for achieving these goals during the design process. In order to determine the best structural layout, topology optimization seeks the optimal material distribution in a predefined design domain using numerical optimization. Besides the efficiency and performance of the optimized structure, robustness with respect to uncertain variations in the system is another essential requirement for practical applicability. Variable boundary conditions, uncertain material properties and geometric imperfections are important examples of uncertainties in civil engineering. Topology optimization often leads to structures consisting of slender elements which are particularly sensitive to geometric imperfections. Moreover, imperfections affect the stability of a structure and induce large displacement phenomena such as P-Δ effects. The main goal of this thesis is therefore to develop a robust approach to topology optimization which takes into account geometric imperfections. Large displacements effects are incorporated in the optimization by means of a total Lagrangian formulation for geometric nonlinear mechanics. Robust optimization is considered in a probabilistic framework where uncertainties are modeled as random variables characterized by a probability distribution. A weighted sum of the mean and standard deviation of the performance is minimized in the robust optimization problem in order to obtain well-performing structures that are also insensitive to the uncertain variations in the system. During the optimization these stochastic moments of the performance are estimated by means of uncertainty quantification techniques such as Monte Carlo sampling and the stochastic perturbation method. It is shown that the robust designs obtained in this way achieve a good nominal performance and are also much less sensitive to imperfections.status: publishe

Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis

© 2014 Elsevier B.V. Topology optimization often leads to structures consisting of slender elements which are particularly sensitive to geometric imperfections. Such imperfections might affect the structural stability and induce large displacement effects in these slender structures. This paper therefore presents a robust approach to topology optimization which accounts for geometric imperfections and their potentially detrimental influence on the structural stability. Geometric nonlinear effects are incorporated in the optimization by means of a Total Lagrangian finite element formulation in the minimization of end-compliance. Geometric imperfections are modeled as a vector-valued random field in the design domain. The resulting uncertain performance of the design is taken into account by minimizing a weighted sum of the mean and standard deviation of the compliance in the robust optimization problem. These stochastic moments are typically estimated by means of sampling methods such as Monte Carlo simulation. However, these methods require multiple independent nonlinear finite element analyses in each design iteration of the optimization algorithm. An efficient solution algorithm which uses adjoint differentiation in a second-order perturbation method is therefore developed to estimate the stochastic moments during the optimization. Two applications with structures that exhibit different types of structural instabilities are examined. In both cases, it is demonstrated by means of an extensive Monte Carlo simulation that the deterministic design is very sensitive to imperfections, while the design obtained by means of the proposed method is much more robust.publisher: Elsevier articletitle: Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis journaltitle: Computer Methods in Applied Mechanics and Engineering articlelink: http://dx.doi.org/10.1016/j.cma.2014.11.028 content_type: article copyright: Copyright © 2014 Elsevier B.V. All rights reserved.status: publishe

A continuous tephrostratigraphic record from the Labrador Sea spanning the last 65 ka

Volcanic ash preserved in marine sediment sequences is key for independent synchronization of palaeoclimate records within and across different climate archives. Here we present a continuous tephrostratigraphic record from the Labrador Sea, spanning the last 65–5 ka, an area and time period that has not been investigated in detail within the established North Atlantic tephra framework. We investigated marine sediment core GS16‐204‐22CC for increased tephra occurrences and geochemically analysed the major element composition of tephra shards to identify their source volcano(es). In total we observed eight tephra zones, of which five concentration peaks show isochronous features that can be used as independent tie‐points in future studies. The main transport mechanism of tephra shards to the site was near‐instantaneous deposition by drifting of sea ice along the East Greenland Current. Our results show that the Icelandic Veidivötn volcanic system was the dominant source of tephra material, especially between late Marine Isotope Stage (MIS) 4 and early MIS 3. The Veidivötn system generated volcanic eruptions in cycles of ca. 3–5 ka. We speculate that the quantity of tephra delivered to the Labrador Sea was a result of variable Icelandic ice volume and/or changes in the transportation pathway towards the Labrador Sea

Insolation and Glacial Meltwater Influence on Sea‐Ice and Circulation Variability in the Northeastern Labrador Sea During the Last Glacial Period

The variable amounts of ice rafted debris (IRD) and foraminifers in North Atlantic sediments are related to the abrupt, millennial‐scale alteration from Greenland stadials to interstadials during the last glacial period and indicate past ice sheet instabilities, changes in sea‐ice cover and productivity. In the Norwegian Sea, Greenland stadials were likely characterized by an extensive, near‐perennial sea‐ice cover whereas Greenland interstadials were seasonally ice‐free. The variability in other areas, such as the Labrador Sea, remains, however, obscure. We therefore investigated deep‐sea sediment core GS16‐204‐22CC retrieved south of Greenland. Using a multiproxy approach, we distinguish two sediment regimes and hence different environmental conditions between ca. 65 and 25 ka b2k. Regime 1 (~65‐49 ka b2k) is characterized by the dominance of planktic foraminifers in the sediments. During late MIS4 and early MIS3, the site was covered by near‐perennial sea‐ice with occasional periods of iceberg discharge. During the younger part of regime 1 the northeastern Labrador Sea was seasonally ice‐free with hardly any icebergs melting near the site and long‐term environmental conditions were less variable. Regime 2 (~49‐25 ka b2k) is characterized by pronounced stadial‐interstadial variability of foraminifer and IRD fluxes, suggesting an extensive sea‐ice cover during most Greenland stadials and seasonally ice‐free conditions during most Greenland interstadials. During MIS2 environmental conditions were very similar to those of the younger part of regime 1. While all Heinrich (H) related Greenland stadials are marked by depleted oxygen isotope values at our core site, only H4 and H3 are associated with pronounced IRD peaks

Tephra horizons identified in the western North Atlantic and Nordic Seas during the Last Glacial Period: Extending the marine tephra framework

Geochemically distinct volcanic ash (tephra) deposits are increasingly acknowledged as a key geochronological tool to synchronize independent paleoclimate archives. Recent advances in the detection of invisible (crypto) tephra have led to the ongoing establishment, development and integration of regional tephra lattices. These frameworks offer an overview of the spatial extent of geochemically characterized tephra from dated eruptions – a valuable tool for precise correlation of paleorecords within these areas. Here, we harness cryptotephra analysis to investigate the occurrence of two well-known tephra markers from the Last Glacial Period (i.e. FMAZ II-1 (26.7 ka b2k) and NAAZ II (II-RHY-1) (55.3 ka b2k)), in marine sediment cores from the Nordic, Irminger and Labrador Seas. In addition, we assess the imprint of bioturbation on two of these tephra deposits using Computed Tomography (CT) imagery. We have successfully identified FMAZ II-1 in the Nordic and Irminger Seas. The tephra deposit is a visible deposit in the Nordic Seas, whereas it appears as a single high concentration peak within the fine-grained shard size fraction (i.e. 25-80 μm) in the Irminger Sea. Both horizons are primary airfall deposits, and this study is the first to identify a FMAZ II-1 deposit of isochronous nature in the Irminger Sea region. In addition, we have identified a new tephra horizon in the Irminger Sea, which is stratigraphically associated with FMAZ II-1, and geochemically similar to the known 2-JPC-192-1 population. We discuss its potential to serve as a new reference tie-point for correlations in the region. Lastly, we have successfully identified NAAZ II (II-RHY-1) of isochronous nature in both the Irminger and Labrador Sea. The layers are interpreted to be deposited by either direct airfall or by sea-ice drifting past the sites. Compared to the existing frameworks, which previously mainly focused on sites east of Iceland, our findings expand the knowledge and utility of the FMAZ II-1 and NAAZ II (II-RHY-1) horizons

Topology optimization of fail-safe structures using a simplified local damage model

Topology optimization of mechanical structures often leads to efficient designs which resemble statically determinate structures. These economical structures are especially vulnerable to local loss of stiffness due to material failure. This paper therefore addresses local failure of continuum structures in topology optimization in order to design fail-safe structures which remain operable in a damaged state. A simplified model for local failure in continuum structures is adopted in the robust approach. The complex phenomenon of local failure is modeled by removal of material stiffness in patches with a fixed shape. The damage scenarios are taken into account by means of a minimax formulation of the optimization problem which minimizes the worst case performance. The detrimental influence of local failure on the nominal design is demonstrated in two representative examples: a cantilever beam optimized for minimum compliance and a compliant mechanism. The robust approach is applied successfully in the design of fail-safe alternatives for the structures in these examples. © 2013 Springer-Verlag Berlin Heidelberg.status: publishe