Analytical and numerical solutions for a class of optimization problems in elasticity

The subject of topology optimization methods in structural de- sign has increased rapidly since the publication of [?], where some ideas from homogenization theory were put into practice. Since then, several engineering applications have been developed successfully. However, in the literature, there is a lack of analytical solutions, even for simple cases, which might help in the validation of the numerical results. In this work, we develop analytical solu- tions for simple minimum compliance problems, in the framework of elasticity theory. We compare these analytical solutions with numerical results obtained via an algorithm proposed in [?]

An open ocean record of the Toarcian oceanic anoxic event

Oceanic anoxic events were time intervals in the Mesozoic characterized by widespread distribution of marine organic matter-rich sediments (black shales) and significant perturbations in the global carbon cycle. These perturbations are globally recorded in sediments as carbon isotope excursions irrespective of lithology and depositional environment. During the early Toarcian, black shales were deposited on the epi- and pericontinental shelves of Pangaea, and these sedimentary rocks are associated with a pronounced (ca. 7 ‰) negative (organic) carbon isotope excursion (CIE) which is thought to be the result of a major perturbation in the global carbon cycle. For this reason, the lower Toarcian is thought to represent an oceanic anoxic event (the T-OAE). If the T-OAE was indeed a global event, an isotopic expression of this event should be found beyond the epi- and pericontinental Pangaean localities. To address this issue, the carbon isotope composition of organic matter (δ13Corg of lower Toarcian organic matter-rich cherts from Japan, deposited in the open Panthalassa Ocean, was analysed. The results show the presence of a major (>6 ‰) negative excursion in δ13Corg that, based on radiolarian biostratigraphy, is a correlative of the lower Toarcian negative CIE known from Pangaean epi- and pericontinental strata. A smaller negative excursion in δ13Corg (ca. 2 ‰) is recognized lower in the studied succession. This excursion may, within the current biostratigraphic resolution, represent the excursion recorded in European epicontinental successions close to the Pliensbachian/Toarcian boundary. These results from the open ocean realm suggest, in conjunction with other previously published datasets, that these Early Jurassic carbon cycle perturbations affected the active global reservoirs of the exchangeable carbon cycle (deep marine, shallow marine, atmospheric)

A new subsurface record of the Pliensbachian-Toarcian, Lower Jurassic, of Yorkshire

Here, we describe the upper Pliensbachian to middle Toarcian stratigraphy of the Dove's Nest borehole, which was drilled near Whitby, North Yorkshire, in 2013. The core represents a single, continuous vertical section through unweathered, immature Lower Jurassic sedimentary rocks. The thickness of the Lias Group formations in the Dove's Nest core is approximately the same as that exposed along the North Yorkshire coast between Hawsker Bottoms and Whitby. The studied succession consists of epeiric-neritic sediments and comprises cross-laminated very fine sandstones, (oolitic) ironstones, and argillaceous mudstones. Dark argillaceous mudstone is the dominant lithology. These sediments were deposited in the Cleveland Basin, a more subsident area of an epeiric sea, the Laurasian Sea. We present a set of geochemical data that includes organic carbon isotope ratios (δ13Corg) and total organic carbon (TOC). The δ13Corg record contains a negative excursion across the Pliensbachian–Toarcian boundary and another in the lower Toarcian that corresponds to the Toarcian Oceanic Anoxic Event (T-OAE). Below the T-OAE negative excursion, δ13Corg values are less 13C-depleted than above it. We find no evidence of a long-term δ13Corg positive excursion. TOC values below the T-OAE negative excursion are lower than above it. Sedimentary evidence suggests that, during much of the Pliensbachian–Toarcian interval, the seafloor of the Cleveland Basin was above storm wave-base and that storm-driven bottom currents were responsible for much sediment erosion, transport, and redeposition during the interval of oceanic anoxia. The abrupt shifts observed in the δ13Corg record (lower Toarcian) are likely to reflect the impact of erosion by storms on the morphology of the δ13C record of the T-OAE

Organic geochemistry of the early Toarcian oceanic anoxic event in Hawsker Bottoms, Yorkshire, England

A comprehensive organic geochemical investigation of the Hawsker Bottoms outcrop section in Yorkshire, England has provided new insights about environmental conditions leading into and during the Toarcian oceanic anoxic event (T-OAE; ~183 Ma). Rock-Eval and molecular analyses demonstrate that the section is uniformly within the early oil window. Hydrogen index (HI), organic petrography, polycyclic aromatic hydrocarbon (PAH) distributions, and tricyclic terpane ratios mark a shift to a lower relative abundance of terrigenous organic matter supplied to the sampling locality during the onset of the T-OAE and across a lithological transition. Unlike other ancient intervals of anoxia and extinction, biomarker indices of planktonic community structure do not display major changes or anomalous values. Depositional environment and redox indicators support a shift towards more reducing conditions in the sediment porewaters and the development of a seasonally stratified water column during the T-OAE. In addition to carotenoid biomarkers for green sulfur bacteria (GSB), we report the first occurrence of okenane, a marker of purple sulfur bacteria (PSB), in marine samples younger than ~1.64 Ga. Based on modern observations, a planktonic source of okenane's precursor, okenone, would require extremely shallow photic zone euxinia (PZE) and a highly restricted depositional environment. However, due to coastal vertical mixing, the lack of planktonic okenone production in modern marine sulfidic environments, and building evidence of okenone production in mat-dwelling Chromatiaceae, we propose a sedimentary source of okenone as an alternative. Lastly, we report the first parallel compound-specific δ[superscript 13]C record in marine- and terrestrial-derived biomarkers across the T-OAE. The δ[superscript 13]C records of short-chain n-alkanes, acyclic isoprenoids, and long-chain n -alkanes all encode negative carbon isotope excursions (CIEs), and together, they support an injection of isotopically light carbon that impacted both the atmospheric and marine carbon reservoirs. To date, molecular δ[superscript 13]C records of the T-OAE display a negative CIE that is smaller in magnitude compared to the bulk organic δ[superscript 13]C excursion. Although multiple mechanisms could explain this observation, our molecular, petrographic, and Rock-Eval data suggest that variable mixing of terrigenous and marine organic matter is an important factor affecting the bulk organic δ[superscript 13]C records of the T-OAE.NASA Astrobiology InstituteExobiology Program (U.S.)National Science Foundation (U.S.). Graduate Research Fellowshi

Some results in topology optimization applied to biomechanics

This paper presents the application of a topology optimization algorithm based in homogenization theory. Three examples in structural design will be solved numerically. The first two are formulated such that analytical solutions can also be developed. To obtain this goal, the microscopic structure that we considered is formed of laminates because for this type of composite materials there is an explicit dependence of the homogenized coefficients on the design variables. The last example regards bone remodelling. Here, where it is impossible to obtain the analytical solution, the applied algorithm produces numerical results which are in good agreement with Wolffs Law.info:eu-repo/semantics/publishedVersio

Laboratory Observation of the Buffering Effect of Aragonite Dissolution at the Seafloor

Carbon dioxide entering and acidifying the ocean can be neutralized by the dissolution of calcium carbonate, which is mainly found in two mineral forms. Calcite is the more stable form and is often found in deep-sea sediments, whilst aragonite is more soluble and therefore rarely preserved. Recent research shows aragonite may account for a much larger portion of marine calcium carbonate export to the ocean interior via the biological pump than previously thought, and that aragonite does reach the deep sea and seafloor despite rarely being buried. If aragonite is present and dissolving at the seafloor it will raise local pH and calcium and carbonate concentrations, potentially enough to inhibit calcite dissolution, representing a deep-sea, carbonate version of galvanization. Here, we test this hypothesis by simulating aragonite dissolution at the sediment-water interface in the laboratory and measuring its effects on pH using microsensors. We show that the addition of aragonite to calcite sediment, overlain by seawater undersaturated with respect to both minerals, results in an unchanged alkalinity flux out of the dissolving sediment, suggesting a decrease the net dissolution rate of calcite. In combination with a diagenetic model, we show that aragonite dissolution can suppress calcite dissolution in the top millimeters of the seabed, locally leading to calcite precipitation within 1 day. Future research efforts should quantify this galvanization effect in situ, as this process may represent an important component of the marine carbon cycle, assigning a key role to aragonite producers in controlling ocean alkalinity and preserving climatic archives

Asymptotic analysis of an elastic rod with rounded ends

We derive a one-dimensional model for an elastic shuttle, that is, a thin rod with rounded ends and small fixed terminals, by means of an asymptotic procedure of dimension reduction. In the model, deformation of the shuttle is described by a system of ordinary differential equations with variable degenerating coefficients, and the number of the required boundary conditions at the end points of the one-dimensional image of the rod depends on the roundness exponent m is an element of(0,1). Error estimates are obtained in the case m is an element of(0,1/4) by using an anisotropic weighted Korn inequality, which was derived in an earlier paper by the authors. We also briefly discuss boundary layer effects, which can be neglected in the case m is an element of(0,1/4) but play a crucial role in the formulation of the limit problem for m >= 1/4.Peer reviewe

Analysis of Optimality Conditions for Some Topology Optimization Problems in Elasticity

The subject of topology optimization has undergone an enormous practical development since the appearance of the paper by Bends\o e and Kikuchi (1988), where some ideas from homogenization theory were put into practice. Since then, several engineering applications as well as different approaches have been developed successfully. However, it is difficult to find in the literature some analytical examples that might be used as a test in order to assess the validity of the solutions obtained with different algorithms. As a matter of fact, one is often faced with numerical instabilities requiring a fine tuning of the algorithm for each specific case. In this work, we develop a family of analytical solutions for very simple topology optimization problems, in the framework of elasticity theory, including bending and extension of rods, torsion problems as well as plane stress and plane strain elasticity problems. All of these problems are formulated in a simplified theoretical framework. A key issue in this type of problems is to be able to evaluate the sensitivity of the homogenized elastic coefficients with respect to the microstructure parameter(s). Since we are looking for analytical solutions, we use laminates for which an explicit dependence of the homogenized coefficients on the microstructure is known