We explore T-splines, a generalization of NURBS enabling local refinement, as a basis for isogeometric analysis. We review T-splines as a surface design methodology and then develop it for engineering analysis applications. We test T-splines on some elementary two-dimensional and three-dimensional fluid and structural analysis problems and attain good results in all cases. We summarize the current status of T-splines, their limitations, and future possibilities.
SUMMARYWe present the Bézier extraction operator and isogeometric Bézier elements for non-uniform rational BSpline (NURBS)-based isogeometric analysis. The Bézier extraction operator allows numerical integration of smooth functions to be performed on C 0 Bézier elements. We show how the Bézier extraction operator is computed for NURBS. We then show that the extraction operator and Bézier elements provide an element structure for isogeometric analysis that can be easily incorporated into existing finite element codes, without any changes to element form and assembly algorithms, and standard data processing arrays. All significant changes may be implemented in a shape function subroutine.
SummaryBackgroundMore than half of patients with multiple sclerosis have progressive disease characterised by accumulating disability. The absence of treatments for progressive multiple sclerosis represents a major unmet clinical need. On the basis of evidence that mesenchymal stem cells have a beneficial effect in acute and chronic animal models of multiple sclerosis, we aimed to assess the safety and efficacy of these cells as a potential neuroprotective treatment for secondary progressive multiple sclerosis.MethodsPatients with secondary progressive multiple sclerosis involving the visual pathways (expanded disability status score 5·5–6·5) were recruited from the East Anglia and north London regions of the UK. Participants received intravenous infusion of autologous bone-marrow-derived mesenchymal stem cells in this open-label study. Our primary objective was to assess feasibility and safety; we compared adverse events from up to 20 months before treatment until up to 10 months after the infusion. As a secondary objective, we chose efficacy outcomes to assess the anterior visual pathway as a model of wider disease. Masked endpoint analyses was used for electrophysiological and selected imaging outcomes. We used piecewise linear mixed models to assess the change in gradients over time at the point of intervention. This trial is registered with ClinicalTrials.gov, number NCT00395200.FindingsWe isolated, expanded, characterised, and administered mesenchymal stem cells in ten patients. The mean dose was 1·6×106 cells per kg bodyweight (range 1·1–2·0). One patient developed a transient rash shortly after treatment; two patients had self-limiting bacterial infections 3–4 weeks after treatment. We did not identify any serious adverse events. We noted improvement after treatment in visual acuity (difference in monthly rates of change −0·02 logMAR units, 95% CI −0·03 to −0·01; p=0·003) and visual evoked response latency (−1·33 ms, −2·44 to −0·21; p=0·020), with an increase in optic nerve area (difference in monthly rates of change 0·13 mm2, 0·04 to 0·22; p=0·006). We did not identify any significant effects on colour vision, visual fields, macular volume, retinal nerve fibre layer thickness, or optic nerve magnetisation transfer ratio.InterpretationAutologous mesenchymal stem cells were safely given to patients with secondary progressive multiple sclerosis in our study. The evidence of structural, functional, and physiological improvement after treatment in some visual endpoints is suggestive of neuroprotection.FundingMedical Research Council, Multiple Sclerosis Society of Great Britain and Northern Ireland, Evelyn Trust, NHS National Institute for Health Research, Cambridge and UCLH Biomedical Research Centres, Wellcome Trust, Raymond and Beverly Sackler Foundation, and Sir David and Isobel Walker Trust.
We couple collocated isogeometric boundary element methods and unstructured analysissuitable T-spline surfaces for linear elastostatic problems. We extend the definition of analysis-suitable T-splines to encompass unstructured control grids (unstructured meshes) and develop basis functions which are smooth (rational) polynomials defined in terms of the Bézier extraction framework and which pass standard patch tests. We then develop a collocation procedure which correctly accounts for sharp edges and corners, extraordinary points, and T-junctions. This approach is applied to several three-dimensional problems, including a real-world T-spline model of a propeller. We believe this work clearly illustrates the power of combining new analysis-suitable computer aided design technologies with established analysis methodologies, in this case, the boundary element method.
Pulmonary fibrosis and interstitial lung disease are poorly understood in horses; the causes of such conditions are rarely identified. Equine herpesvirus 5 (EHV-5) is a gamma-herpesvirus of horses that has not been associated with disease in horses. Pathologic and virologic findings from 24 horses with progressive nodular fibrotic lung disease associated with EHV-5 infection are described and compared with 23 age-matched control animals. Gross lesions consisted of multiple nodules of fibrosis throughout the lungs. Histologically, there was marked interstitial fibrosis, often with preservation of an "alveolar-like" architecture, lined by cuboidal epithelial cells. The airways contained primarily neutrophils and macrophages. Rare macrophages contained large eosinophilic intranuclear viral inclusion bodies; similar inclusion bodies were also found cytologically. The inclusions were identified as herpesviral-like particles by transmission electron microscopy in a single horse. In situ hybridization was used to detect EHV-5 nucleic acids within occasional macrophage nuclei. With polymerase chain reaction (PCR), the herpesviral DNA polymerase gene was detected in 19/24 (79.2%) of affected horses and 2/23 (8.7%) of the control horses. Virus genera-specific PCR was used to detect EHV-5 in all of the affected horses and none of the control horses. EHV-2 was detected in 8/24 (33.3%) of affected horses and 1/9 (11.1%) of the control horses. This disease has not been reported before, and the authors propose that based upon the characteristic gross and histologic findings, the disease be known as equine multinodular pulmonary fibrosis. Further, we propose that this newly described disease develops in association with infection by the equine gamma-herpesvirus, EHV-5.
SUMMARYWe develop finite element data structures for T-splines based on Bézier extraction generalizing our previous work for NURBS. As in traditional finite element analysis, the extracted Bézier elements are defined in terms of a fixed set of polynomial basis functions, the so-called Bernstein basis. The Bézier elements may be processed in the same way as in a standard finite element computer program, utilizing exactly the same data processing arrays. In fact, only the shape function subroutine needs to be modified while all other aspects of a finite element program remain the same. A byproduct of the extraction process is the element extraction operator. This operator localizes the topological and global smoothness information to the element level, and represents a canonical treatment of T-junctions, referred to as 'hanging nodes' in finite element analysis and a fundamental feature of T-splines. A detailed example is presented to illustrate the ideas.
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