Simultaneous optimisation of structural topology and material grading using level set method

Peer reviewed

On string topology of classifying spaces

Peer reviewed

On string topology of classifying spaces

Peer reviewed

Simultaneous material and structural optimization by multiscale topology optimization

Acknowledgments The authors acknowledge the support from Engineering and Physical Sciences Research Council, grant number EP/M002322/1. The authors would also like to thank Numerical Analysis Group at the Rutherford Appleton Laboratory for their FORTRAN HSL packages (HSL, a collection of Fortran codes for large-scale scientific computation. See http://www.hsl.rl.ac.uk/).

On string topology of classifying spaces

Peer reviewed

A completely kinematostatically decoupled XY compliant parallel manipulator through new topology structure

This paper deals with a completely kinematostaticaly decoupled XY compliant parallel manipulator (CPM) composed of exactly-constrained compliant modules. A new 4-PP XY translational parallel mechanism (TPM) with a new topology structure is firstly proposed where each two P (P: prismatic) joints on the base in two non-adjacent legs are rigidly connected. A novel 4-PP XY CPM is then obtained by replacing each traditional P join on the base in the 4-PP XY TPM with a compound basic parallelogram module (CBPM) and replacing each traditional P joint on the motion stage with a basic parallelogram module (BPM). Approximate analytical model is derived with comparison to the FEA (finite element analysis) model and experiment for a case study. The proposed novel XY CPM has a compact configuration with good dynamics, and is able to well constrain the parasitic rotation and the cross-axis coupling of the motion stage. The cross-axis motion of the input stage can be completely eliminated, and the lost motion between the input stage and the motion stage is significantly reduced.

Math 412 - Topology with Applications

Highlights of Data Expedition: • Students explored daily observations of local climate data spanning the past 35 years. • Topological Data Analysis, or TDA for short, provides cutting-edge tools for studying the geometry of data in arbitrarily high dimensions. • Using TDA tools, students discovered intrinsic dynamical features of the data and learned how to quantify periodic phenomenon in a time-series. • Since nature invariably produces noisy data which rarely has exact periodicity, students also considered the theoretical basis of almost-periodicity and even invented and tested new mathematical definitions of almost-periodic functions. Summary The dataset we used for this data expedition comes from the Global Historical Climatology Network. “GHCN (Global Historical Climatology Network)-Daily is an integrated database of daily climate summaries from land surface stations across the globe.” Source: https://www.ncdc.noaa.gov/oa/climate/ghcn-daily/ We focused on the daily maximum and minimum temperatures from January 1, 1980 to April 1, 2015 collected from RDU International Airport. Through a guided series of exercises designed to be performed in Matlab, students explore these time-series, initially by direct visualization and basic statistical techniques. Then students are guided through a special sliding-window construction which transforms a time-series into a high-dimensional geometric curve. These high-dimensional curves can be visualized by projecting down to lower dimensions as in the figure below (Figure 1), however, our focus here was to use persistent homology to directly study the high-dimensional embedding. The shape of these curves has meaningful information but how one describes the “shape” of data depends on which scale the data is being considered. However, choosing the appropriate scale is rarely an obvious choice. Persistent homology overcomes this obstacle by allowing us to quantitatively study geometric features of the data across multiple-scales. Through this data expedition, students are introduced to numerically computing persistent homology using the rips collapse algorithm and interpreting the results. In the specific context of sliding-window constructions, 1-dimensional persistent homology can reveal the nature of periodic structure in the original data. I created a special technique to study how these high-dimensional sliding-window curves form loops in order to quantify the periodicity. Students are guided through this construction and learn how to visualize and interpret this information. Climate data is extremely complex (as anyone who has suffered from a bad weather prediction can attest) and numerous variables play a role in determining our daily weather and temperatures. This complexity coupled with imperfections of measuring devices results in very noisy data. This causes the annual seasonal periodicity to be far from exact. To this end, I have students explore existing theoretical notions of almost-periodicity and test it on the data. They find that some existing definitions are also inadequate in this context. Hence I challenged them to invent new mathematics by proposing and testing their own definition. These students rose to the challenge and suggested a number of creative definitions. While autocorrelation and spectral methods based on Fourier analysis are often used to explore periodicity, the construction here provides an alternative paradigm to quantify periodic structure in almost-periodic signals using tools from topological data analysis.

An ether-functionalised cyclic sulfonium based ionic liquid as an electrolyte for electrochemical double layer capacitors

A novel cyclic sulfonium cation-based ionic liquid (IL) with an ether-group appendage and the bis{(trifluoromethyl)sulfonyl}imide anion was synthesised and developed for electrochemical double layer capacitor (EDLC) testing. The synthesis and chemical-physical characterisation of the ether-group containing IL is reported in parallel with a similarly sized alkyl-functionalised sulfonium IL. Results of the chemical-physical measurements demonstrate how important transport properties, i.e. viscosity and conductivity, can be promoted through the introduction of the ether-functionality without impeding thermal, chemical or electrochemical stability of the IL. Although the apparent transport properties are improved relative to the alkyl-functionalised analogue, the ether-functionalised sulfonium cation-based IL exhibits moderately high viscosity, and poorer conductivity, when compared to traditional EDLC electrolytes based on organic solvents (propylene carbonate and acetonitrile). Electrochemical testing of the ether-functionalised sulfonium IL was conducted using activated carbon composite electrodes to inspect the performance of the IL as a solvent-free electrolyte for EDLC application. Good cycling stability was achieved over the studied range and the performance was comparable to other solvent free,
IL-based EDLC systems. Nevertheless, limitations of the attainable performance are primarily the result of sluggish transport properties and a restricted operative voltage of the IL, thus highlighting key aspects of this field which require further attention.

Implementing a structural continuity constraint and a halting method for the topology optimization of energy absorbers

This study investigates topology optimization of energy absorbing structures in which material damage is accounted for in the optimization process. The optimization objective is to design the lightest structures that are able to absorb the required mechanical energy. A structural continuity constraint check is introduced that is able to detect when no feasible load path remains in the finite element model, usually as a result of large scale fracture. This assures that designs do not fail when loaded under the conditions prescribed in the design requirements. This continuity constraint check is automated and requires no intervention from the analyst once the optimization process is initiated. Consequently, the optimization algorithm proceeds towards evolving an energy absorbing structure with the minimum structural mass that is not susceptible to global structural failure. A method is also introduced to determine when the optimization process should halt. The method identifies when the optimization method has plateaued and is no longer likely to provide improved designs if continued for further iterations. This provides the designer with a rational method to determine the necessary time to run the optimization and avoid wasting computational resources on unnecessary iterations. A case study is presented to demonstrate the use of this method.

Using virtual topology operations to generate analysis topology

Virtual topology operations have been utilized to generate an analysis topology definition suitable for downstream mesh generation. Detailed descriptions are provided for virtual topology merge and split operations for all topological entities. Current virtual topology technology is extended to allow the virtual partitioning of volume cells and the topological queries required to carry out each operation are provided. Virtual representations are robustly linked to the underlying geometric definition through an analysis topology. The analysis topology and all associated virtual and topological dependencies are automatically updated after each virtual operation, providing the link to the underlying CAD geometry. Therefore, a valid description of the analysis topology, including relative orientations, is maintained. This enables downstream operations, such as the merging or partitioning of virtual entities, and interrogations, such as determining if a specific meshing strategy can be applied to the virtual volume cells, to be performed on the analysis topology description. As the virtual representation is a non-manifold description of the sub-divided domain the interfaces between cells are recorded automatically. This enables the advantages of non-manifold modelling to be exploited within the manifold modelling environment of a major commercial CAD system, without any adaptation of the underlying CAD model. A hierarchical virtual structure is maintained where virtual entities are merged or partitioned. This has a major benefit over existing solutions as the virtual dependencies are stored in an open and accessible manner, providing the analyst with the freedom to create, modify and edit the analysis topology in any preferred sequence, whilst the original CAD geometry is not disturbed. Robust definitions of the topological and virtual dependencies enable the same virtual topology definitions to be accessed, interrogated and manipulated within multiple different CAD packages and linked to the underlying geometry.

Exchange protein directly activated by cyclic AMP (EPAC) activation reverses neutrophil dysfunction induced by β2-agonists, corticosteroids, and critical illness

Background Neutrophils play a role in the pathogenesis of asthma, chronic obstructive pulmonary disease, and pulmonary infection. Impaired neutrophil phagocytosis predicts hospital-acquired infection. Despite this, remarkably few neutrophil-specific treatments exist. 

Objectives We sought to identify novel pathways for the restoration of effective neutrophil phagocytosis and to activate such pathways effectively in neutrophils from patients with impaired neutrophil phagocytosis. 

Methods Blood neutrophils were isolated from healthy volunteers and patients with impaired neutrophil function. In healthy neutrophils phagocytic impairment was induced experimentally by using β₂-agonists. Inhibitors and activators of cyclic AMP (cAMP)-dependent pathways were used to assess the influence on neutrophil phagocytosis in vitro. 

Results β₂-Agonists and corticosteroids inhibited neutrophil phagocytosis. Impairment of neutrophil phagocytosis by β₂-agonists was associated with significantly reduced RhoA activity. Inhibition of protein kinase A (PKA) restored phagocytosis and RhoA activity, suggesting that cAMP signals through PKA to drive phagocytic impairment. However, cAMP can signal through effectors other than PKA, such as exchange protein directly activated by cyclic AMP (EPAC). An EPAC-activating analog of cAMP (8CPT-2Me-cAMP) reversed neutrophil dysfunction induced by β₂-agonists or corticosteroids but did not increase RhoA activity. 8CPT-2Me-cAMP reversed phagocytic impairment induced by Rho kinase inhibition but was ineffective in the presence of Rap-1 GTPase inhibitors. 8CPT-2Me-cAMP restored function to neutrophils from patients with known acquired impairment of neutrophil phagocytosis. 

Conclusions EPAC activation consistently reverses clinical and experimental impairment of neutrophil phagocytosis. EPAC signals through Rap-1 and bypasses RhoA. EPAC activation represents a novel potential means by which to reverse impaired neutrophil phagocytosis.

Mannich-Type reactions in the Gas-Phase: the addition of Enol Silanes to cyclic N-Acyliminium Ions

The intrinsic gas-phase reactivity of cyclic N-acyliminium ions in Mannich-type reactions with the parent enol silane, vinyloxytrimethylsilane, has been investigated by double- and triple-stage pentaquadrupole mass spectrometric experiments. Remarkably distinct reactivities are observed for cyclic N-acyliminium ions bearing either endocyclic or exocyclic carbonyl groups. NH-Acyliminium ions with endocyclic carbonyl groups locked in s-trans forms participate in a novel tandem N-acyliminium ion reaction:  the nascent adduct formed by simple addition is unstable and rearranges by intramolecular trimethylsilyl cation shift to the ring nitrogen, and an acetaldehyde enol molecule is eliminated. An NSi(CH3)3-acyliminium ion is formed, and this intermediate ion reacts with a second molecule of vinyloxytrimethylsilane by simple addition to form a stable acyclic adduct. N-Acyl and N,N-diacyliminium ions with endocyclic carbonyl groups, for which the s-cis conformation is favored, react distinctively by mono polar [4+ + 2] cycloaddition yielding stable, ressonance-stabilized cycloadducts. Product ions were isolated via mass-selection and structurally characterized by triple-stage mass spectrometric experiments. B3LYP/6-311G(d,p) calculations corroborate the proposed reaction mechanisms.

The Addition of Allyltrimethylsilane to Cyclic N-Acyliminium Ions Derived from (S)-(+)-Mandelic Acid and Cyclohexyl-Based Chiral Auxiliaries

A adição de aliltrimetilsilano, promovida por TiCl4, a íons N-aciliminios cíclicos de 5- e 6-membros derivados do ácido (S)-(+)-mandélico, (1R,2S)-trans-2-fenil-1-cicloexanol e (1R,2S,5R)-8-fenilmentol ocorreu com baixas a moderadas razões diastereoisoméricas (1:1-6:1) e forneceu as respectivas amidas e carbamatos em bons rendimentos. A melhor diastereosseleção facial foi observada com o uso de (1R,2S,5R)-8-fenilmentol como auxiliar quiral. As amidas e carbamatos 2-substituídos foram convertidos nos alcalóides (S)- e (R)-propil pirrolidina e coniina com eficiente recuperação dos auxiliares quirais.

Topology Optimization of continuum structures with epsilon-relaxed stress constraints

Topology optimization of linear elastic continuum structures is a challenging problem when considering local stress constraints. The reasons are the singular behavior of the constraint with the density design variables, combined with the large number of constraints even for small finite element meshes. This work presents an alternative formulation for the s-relaxation technique, which provides an workaround for the singularity of the stress constraint. It also presents a new global stress constraint formulation. Derivation of the sensitivities for the constraint by the adjoint method is shown. Results for single and multiple load cases show the potential of the new formulation.