Soil collapse computations with finite elements

Summary The elastic-plastic finite element method is reviewed with a view to predict collapse loads of geotechnical constructions. The basic technique of using an incremental-iterative approach with a constant stiffness matrix is well-known, but we fill a gap by proving that the procedure converges not only for small steps but also for large load increments. Here restriction is made to associated plasticity, as uniqueness of solution is not ensured for non-associated plasticity problems. Differences between associated and nonassociated problems are illustrated by showing results of numerical analyses. Finally, a number of practical aspects associated with the method are discussed.

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Finite-Element-Berechnungen des Versagens von Böden

Übersicht Im Hinblick auf die Vorhersage der Versagenlasten von Erdbauten wird ein Überblick über die elastisch-plastische Finite-Element-Methode gegeben. Das grundlegende Verfahren mit inkrementelliterativem Vorgehen mit einer konstanten Steifigkeitsmatrix ist wohlbekannt. Durch den Beweis, daß das Verfahren nicht nur bei kleinen Schrittweiten, sondern auch bei großen Laststufen konvergiert, werden jedoch neuartige Erkenntnisse vorgestellt. Hierbei muß einschränkend assoziierte Plastizität gelten, da bei nicht-assoziierter Plastizität die Eindeutigkeit von Lösungen nicht gewährleistet ist. Anhand von numerischen Ergebnissen werden Unterschiede zwischen Aufgabenstellungen mit assoziierter und nichtassoziierter Plastizität aufgezeigt. Schließlich werden auch noch praktische Gesichtspunkte des Verfahrens erörtert.

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Presented at the workshop on Limit Analysis and Bifurcation Theory, held at the University of Karlsruhe (FRG), February 22–25, 1988     

Influence of Pore Structure and Metal-Node Geometry on the Polymerization of Ethylene over Cr-Based Metal–Organic Frameworks

Metal–organic frameworks (MOFs) have received increasing interest as solid single-site catalysts, owing to their tunable pore architecture and metal node geometry. The ability to exploit these modulators makes them prominent candidates for producing polyethylene (PE) materials with narrow dispersity index (Ð) values. Here a study is presented in which the ethylene polymerization properties, with Et₂AlCl as activator, of three renowned Cr-based MOFs, MIL-101(Cr)-NDC (NDC=2,6-dicarboxynapthalene), MIL-53(Cr) and HKUST-1(Cr), are systematically investigated. Ethylene polymerization reactions revealed varying catalytic activities, with MIL-101(Cr)-NDC and MIL-53(Cr) being significantly more active than HKUST-1(Cr). Analysis of the PE products revealed large Ð values, demonstrating that polymerization occurs over a multitude of active Cr centers rather than a singular type of Cr site. Spectroscopic experiments, in the form of powder X-ray diffraction (pXRD), UV/Vis-NIR diffuse reflectance spectroscopy (DRS) and CO probe molecule Fourier transform infrared (FTIR) spectroscopy corroborated these findings, indicating that indeed for each MOF unique active sites are generated, however without alteration of the original oxidation state. Furthermore, the pXRD experiments indicated that one major prerequisite for catalytic activity was the degree of MOF activation by the Et₂AlCl co-catalyst, with the more active materials portraying a larger degree of activation.     

Dynamic Ligand Reactivity in a Rhodium Pincer Complex

Ligand cooperativity provides (transition) metal complexes with new reactivities in substrate activation and catalytic reactions, but usually the ligand acts as an internal (Brønsted) base, while the metal acts as a (Lewis) acid. We describe the synthesis and stepwise activation of a new phosphane‐pyridine‐amide ligand PNN^H2 in combination with Rh^I. The ligand is susceptible to stepwise proton and hydride loss from the nitrogen arm (imine formation) and deprotonation at the pyridylphosphine arm (dearomatization), giving rise to amine complex 1 , amido species 2 , imine complex 3 and dearomatized compound 4 . Complex 4 bears a dual‐mode cooperative PNN′ ligand containing both a (nucleophilic) basic methine fragment and a reactive (electrophilic) imine moiety. The basic ligand arm enables substrate deprotonation while the imine ligand arm enables reversible “storage” of the activated (nucleophilic) form of a sulfonamide substrate at the ligand. In combination with metal‐based reactivity, this allows for the mono‐alkylation of o‐toluenesulfonamide with iodomethane. Compounds 1 , 3 and 4 are structurally characterized. We also report the first structurally characterized example of an aminal in the coordination sphere of rhodium, complex 5 , [Rh(CO)( PNN′′ )], formed by sequential N?H activation of sulfonamide by the dearomatized ligand PNN′ and follow‐up nucleophilic attack of anionic sulfonamide onto the imine fragment.     

Dynamic Interplay between Defective UiO-66 and Protic Solvents in Activated Processes

UiO-66, composed by Zr-oxide inorganic bricks [Zr₆(μ₃-O)₄(μ₃-OH)₄] and organic terephthalate linkers, is one of the most studied metal–organic frameworks (MOFs) due to its exceptional thermal, chemical, and mechanical stability. Thanks to its high connectivity, the material can withstand structural deformations during activation processes such as linker exchange, dehydration, and defect formation. These processes do alter the zirconium coordination number in a dynamic way, creating open metal sites for catalysis and thus are able to tune the catalytic properties. In this work, it is shown, by means of first-principle molecular-dynamics simulations at operating conditions, how protic solvents may facilitate such changes in the metal coordination. Solvent can induce structural rearrangements in the material that can lead to undercoordinated but also overcoordinated metal sites. This is demonstrated by simulating activation processes along well-chosen collective variables. Such enhanced MD simulations are able to track the intrinsic dynamics of the framework at realistic conditions.     

Complexation of Phenol and Thiophenol by Amine N‐Oxides: Isothermal Titration Calorimetry and ab Initio Calculations

To develop a new solvent‐impregnated resin (SIR) system for removal of phenols from water, the complex formation of dimethyldodecylamine N‐oxide (DMDAO), trioctylamine N‐oxide (TOAO), and tris(2‐ethylhexyl)amine N‐oxide (TEHAO) with phenol (PhOH) and thiophenol (PhSH) is studied. To this end we use isothermal titration calorimetry (ITC) and quantum chemical modeling (on B3LYP/6‐311G(d,p)‐optimized geometries: B3LYP/6‐311+G(d,p), B3LYP/6‐311++G(2d,2p), MP2/6‐311+G(d,p), and spin component scaled (SCS) MP2/6‐311+G(d,p); M06‐2X/6‐311+G(d,p)//M06‐2X/6‐311G(d,p), MP2 with an extrapolation to the complete basis set limit (MP2/CBS), as well as CBS‐Q). The complexes are analyzed in terms of structural (e.g., bond lengths) and electronic elements (e.g., charges). Furthermore, complexation and solvent effects (in benzene, toluene, and mesitylene) are investigated by ITC measurements, yielding binding constants K, enthalpies ΔH⁰, Gibbs fre energies ΔG⁰, and entropies ΔS⁰ of complex formation, and stoichiometry N. The ITC measurements revealed strong 1:1 complex formation between both DMDAO–PhOH and TOAO–PhOH. The binding constant (K=1.7–5.7×10⁴ M ^?1) drops markedly when water‐saturated toluene was used (K=5.8×10³ M ^?1), and π–π interaction with the solvent is shown to be relevant. Quantum mechanical modeling confirms formation of stable 1:1 complexes with linear hydrogen bonds that weaken on attachment of electron‐withdrawing groups to the amine N‐oxide moiety. Modeling also showed that complexes with PhSH are much weaker than those with PhOH, and in fact too weak for ITC determination. CBS‐Q incorrectly predicts equal or even higher binding enthalpies for PhSH than for PhOH, which invalidates it as a benchmark for other calculations. Data from the straightforward SCS‐MP2 method without counterpoise correction show very good agreement with the MP2/CBS values.     

Phase recovery,MaxCut and complex semidefinite programming

Mathematical Programming - Phase retrieval seeks to recover a signal $$x \in {\mathbb {C}}^p$$ from the amplitude $$|A x|$$ of linear measurements $$Ax \in {\mathbb {C}}^n$$ . We cast the phase...     

A survey on the linear ordering problem for weighted or unweighted tournaments

In this paper, we survey some results, conjectures and open problems dealing with the combinatorial and algorithmic aspects of the linear ordering problem. This problem consists in finding a linear order which is at minimum distance from a (weighted or not) tournament. We show how it can be used to model an aggregation problem consisting of going from individual preferences defined on a set of candidates to a collective ranking of these candidates.      

Engineering Crystals Using sp3-C Centred Tetrel Bonding Interactions

1,1,2,2-Tetracyanocyclopropane derivatives 1 and 2 were designed and synthesized to probe the utility of sp³-C centred tetrel bonding interactions in crystal engineering. The crystal packing of 1 and 2 and their 1,4-dioxane cocrystals is dominated by sp³-C(CN)₂⋅⋅⋅O interactions, has significant C⋅⋅⋅O van der Waals overlap (≤0.266 Å) and DFT calculations indicate interaction energies of up to −11.0 kcal mol⁻¹. A cocrystal of 2 with 1,4-thioxane reveals that the cyclopropane synthon prefers interacting with O over S. Computational analyses revealed that the electropositive C₂(CN)₄ pocket in 1 and 2 can be seen as a strongly directional ‘tetrel-bond donor’, similar to halogen bond or hydrogen bond donors. This disclosure is expected to have implications for the utility of such ‘tetrel bond donors’ in molecular disciplines such as crystal engineering, supramolecular chemistry, molecular recognition and medicinal chemistry.