We study the discretization behavior of classical finite element and NURBS approximations on problems of structural vibrations and wave propagation. We find that, on the basis of equal numbers of ...degrees-of-freedom and bandwidth, NURBS have superior approximation properties. In fact, we observe that the high mode behavior of classical finite elements is divergent with the order of approximation, a surprisingly negative result. On the other hand, NURBS offer almost spectral approximation properties, and all modes converge with increasing order of approximation.
We present a framework for geometric design and isogeometric analysis on unstructured quadrilateral meshes. Acknowledging the differing requirements posed by design (e.g., the convenience of an ...intuitive control net) and analysis (e.g., good approximation behavior), we propose the construction of a separate, smooth spline space for each while ensuring isogeometric compatibility – requiring the geometric models to be members of the analysis-suitable spaces. The methodology is simple and is presented for bi-cubic splines; extensions to higher degrees are possible, and are briefly discussed. The presentation has been structured to show compatibility with T-splines – a state-of-the-art CAD technology – but the approach should extend to other locally refinable spline technologies (based on local tensor-product structures). An instantiation of the framework is presented, and several numerical tests focused on geometric design and isogeometric analysis demonstrate the versatility of the developed framework, and show significantly higher convergence rates than attained previously in the considered setting.
•We present a framework for building smooth splines on meshes with extraordinary points.•The spline spaces possess several desirable properties for both CAD and IGA.•Vertex-based, smooth, linearly independent splines are used for modeling geometries.•Compatible design and analysis spaces imply exact satisfaction of all patch tests.•Optimal or almost-optimal convergence rates are achieved in typical analysis situations.
The Cahn–Hilliard equation involves fourth-order spatial derivatives. Finite element solutions are not common because primal variational formulations of fourth-order operators are only well defined ...and integrable if the finite element basis functions are piecewise smooth and globally
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-continuous. There are a very limited number of two-dimensional finite elements possessing
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-continuity applicable to complex geometries, but none in three-dimensions. We propose isogeometric analysis as a technology that possesses a unique combination of attributes for complex problems involving higher-order differential operators, namely, higher-order accuracy, robustness, two- and three-dimensional geometric flexibility, compact support, and, most importantly, the possibility of
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and higher-order continuity. A NURBS-based variational formulation for the Cahn–Hilliard equation was tested on two- and three-dimensional problems. We present steady state solutions in two-dimensions and, for the first time, in three-dimensions. To achieve these results an adaptive time-stepping method is introduced. We also present a technique for desensitizing calculations to dependence on mesh refinement. This enables the calculation of topologically correct solutions on coarse meshes, opening the way to practical engineering applications of phase-field methodology.
Globally, groupers (Epinephelidae) that form fish spawning aggregations (FSAs) are highly vulnerable to overfishing and often require site-specific approaches to management. Over 5-years (2009-2013), ...we conducted underwater visual censuses (UVC) at a well-known spawning site at Njari Island, Gizo, Western Province, Solomon Islands, that supports aggregations of squaretail coralgrouper (Plectropomus areolatus), camouflage grouper (Epinephelus polyphekadion) and brown-marbled grouper (E. fuscoguttatus). Findings show that while there were species-specific variations in the duration and timing of the spawning season, aggregation densities peaked from March to June, representing the main spawning season for all three species. For P. areolatus, gonad analysis from samples taken from 2008 to 2011 confirmed reproductive activity in support of density trends observed through UVC. Over the 5-year UVC monitoring period, FSA densities declined for P. areolatus and E. polyphekadion. Conversely, following the first year of monitoring, E. fuscoguttatus densities increased. These inter-specific differences may reflect variable responses to fishing as shown elsewhere, or for example, differences in recruitment success. In response to known declines in FSAs of these species, in 2018 the Solomon Islands government placed a nationwide ban on these species' harvest and sale between October and January. As this study shows, this ban does not encompass the peak aggregation period at Njari and will offer limited protection to other FSAs of these species that are known to vary in reproductive seasonality across the Solomon Islands. A more biologically meaningful and practical management strategy would be to implement a nationwide ban on the harvest and sale of these groupers each month between full and new moons when these FSAs form consistently throughout the country. Since effective management of FSAs typically requires a combined approach, spatial management that protects both spawning sites and reproductive migratory corridors is warranted.
We review the treatment of trimmed geometries in the context of design, data exchange, and computational simulation. Such models are omnipresent in current engineering modeling and play a key role ...for the integration of design and analysis. The problems induced by trimming are often underestimated due to the conceptional simplicity of the procedure. In this work, several challenges and pitfalls are described.
We study NURBS-based isogeometric analysis of contact problems and compare with standard
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-continuous Lagrange finite elements. A knot-to-surface (KTS) algorithm is developed to treat the contact ...constraints with NURBS contact surface discretizations. Qualitative studies deliver satisfactory results for various finite deformation frictionless thermoelastic contact problems. Quantitative studies based on the Hertz problem suggest the need for a relaxation of the mechanical contact constraints that appear in the standard KTS approach. The improved mortar-based KTS algorithm delivers robust and accurate results for NURBS discretizations. Based on numerical examples, we conclude that NURBS-based isogeometric analysis is a viable technology for contact problems and offers potential accuracy as well as convergence improvements over
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-continuous finite elements.
•We study the performance of IsoGeometric Analysis for large strain incompressible plasticity.•High order standard NURBS elements exhibit spurious stresses and F-bar NURBS elements produce good ...results.•Displacements and reaction forces are misleading measures of element performance.•Mesh locking is not a relevant issue for higher order NURBS.
We study the behavior of NURBS-based Isogeometric Analysis on problems of large-deformation plasticity. We evaluate the performance of standard NURBS elements and elements based on the F¯ formulation of Elguedj et al. (2008) 1. Our experience shows that standard measures of evaluation employed in the literature, namely, displacements at selected locations and graphs of reaction forces versus displacements, are often misleading metrics in problems of plasticity. On the other hand, stress distributions, in the form of contour plots, are, in our experience,revealing measure of element performance. We also determine that the concept of “mesh locking”, which has dominated investigations of low-order elements, is not a relevant issue for higher-order NURBS elements for problems of large-deformation plasticity. However, standard higher-order NURBS elements of type Qk, of continuity class Ck-1,k⩾2, typically exhibit spurious stress oscillations, whereas the F¯ elements of type Qk/Qk-1 produce good results in all cases.
Weakly enforced Dirichlet boundary conditions are compared with strongly enforced conditions for boundary layer solutions of the advection–diffusion equation and incompressible Navier–Stokes ...equations. It is found that weakly enforced conditions are effective and superior to strongly enforced conditions. The numerical tests involve low-order finite elements and a quadratic NURBS basis utilized in the Isogeometric Analysis approach. The convergence of the mean velocity profile for a turbulent channel flow suggests that weak no-slip conditions behave very much like a wall function model, although the design of the boundary condition is based purely on numerical, rather than physical or empirical, conditions.
•Innate immune activation is evident in the periphery of individuals with autism spectrum disorders and correlates with increased behavioral impairment.•Activation of microglia and increased innate ...immune cytokines underlie neuroinflammation in autism brain specimens.•Brain transcriptome studies suggest increased innate immune activation in autism.•Animal models with relevance to autism exhibit macrophage activation and M1 skewing as well as microglia activation.
Autism spectrum disorder (ASD) is a highly heterogeneous neurodevelopmental disorder characterized by communication and social behavior deficits. The presence of restricted and repetitive behaviors often accompanies these deficits, and these characteristics can range from mild to severe. The past several decades have seen a significant rise in the prevalence of ASD. The etiology of ASD remains unknown; however, genetic and environmental risk factors play a role. Multiple hypotheses converge to suggest that neuroinflammation, or at least the interaction between immune and neural systems, may be involved in the etiology of some ASD cases or groups. Repeated evidence of innate immune dysfunction has been seen in ASD, often associated with worsening behaviors. This evidence includes data from circulating myeloid cells and brain resident macrophages/microglia in both human and animal models. This comprehensive review presents recent findings of innate immune dysfunction in ASD, including aberrant innate cellular function, evidence of neuroinflammation, and microglia activation.
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