Shape sensitivity analysis of flutter response of a laminated wing

A method is presented for calculating the shape sensitivity of a wing aeroelastic response with respect to changes in geometric shape. Yates' modified strip method is used in conjunction with Giles' equivalent plate analysis to predict the flutter speed, frequency, and reduced frequency of the wing. Three methods are used to calculate the sensitivity of the eigenvalue. The first method is purely a finite difference calculation of the eigenvalue derivative directly from the solution of the flutter problem corresponding to the two different values of the shape parameters. The second method uses an analytic expression for the eigenvalue sensitivities of a general complex matrix, where the derivatives of the aerodynamic, mass, and stiffness matrices are computed using a finite difference approximation. The third method also uses an analytic expression for the eigenvalue sensitivities, but the aerodynamic matrix is computed analytically. All three methods are found to be in good agreement with each other. The sensitivities of the eigenvalues were used to predict the flutter speed, frequency, and reduced frequency. These approximations were found to be in good agreement with those obtained using a complete reanalysis

Shape sensitivity analysis of wing static aeroelastic characteristics

A method is presented to calculate analytically the sensitivity derivatives of wing static aeroelastic characteristics with respect to wing shape parameters. The wing aerodynamic response under fixed total load is predicted with Weissinger's L-method; its structural response is obtained with Giles' equivalent plate method. The characteristics of interest include the spanwise distribution of lift, trim angle of attack, rolling and pitching moments, wind induced drag, as well as the divergence dynamic pressure. The shape parameters considered are the wing area, aspect ratio, taper ratio, sweep angle, and tip twist angle. Results of sensitivity studies indicate that: (1) approximations based on analytical sensitivity derivatives can be used over wide ranges of variations of the shape parameters considered, and (2) the analytical calculation of sensitivity derivatives is significantly less expensive than the conventional finite-difference alternative

Does clinical management improve outcomes following self-Harm? Results from the multicentre study of self-harm in England

Background Evidence to guide clinical management of self-harm is sparse, trials have recruited selected samples, and psychological treatments that are suggested in guidelines may not be available in routine practice. Aims To examine how the management that patients receive in hospital relates to subsequent outcome. Methods We identified episodes of self-harm presenting to three UK centres (Derby, Manchester, Oxford) over a 10 year period (2000 to 2009). We used established data collection systems to investigate the relationship between four aspects of management (psychosocial assessment, medical admission, psychiatric admission, referral for specialist mental health follow up) and repetition of self-harm within 12 months, adjusted for differences in baseline demographic and clinical characteristics. Results 35,938 individuals presented with self-harm during the study period. In two of the three centres, receiving a psychosocial assessment was associated with a 40% lower risk of repetition, Hazard Ratios (95% CIs): Centre A 0.99 (0.90–1.09); Centre B 0.59 (0.48–0.74); Centre C 0.59 (0.52–0.68). There was little indication that the apparent protective effects were mediated through referral and follow up arrangements. The association between psychosocial assessment and a reduced risk of repetition appeared to be least evident in those from the most deprived areas. Conclusion These findings add to the growing body of evidence that thorough assessment is central to the management of self-harm, but further work is needed to elucidate the possible mechanisms and explore the effects in different clinical subgroups

A method for dense packing discovery

The problem of packing a system of particles as densely as possible is foundational in the field of discrete geometry and is a powerful model in the material and biological sciences. As packing problems retreat from the reach of solution by analytic constructions, the importance of an efficient numerical method for conducting \textit{de novo} (from-scratch) searches for dense packings becomes crucial. In this paper, we use the \textit{divide and concur} framework to develop a general search method for the solution of periodic constraint problems, and we apply it to the discovery of dense periodic packings. An important feature of the method is the integration of the unit cell parameters with the other packing variables in the definition of the configuration space. The method we present led to improvements in the densest-known tetrahedron packing which are reported in [arXiv:0910.5226]. Here, we use the method to reproduce the densest known lattice sphere packings and the best known lattice kissing arrangements in up to 14 and 11 dimensions respectively (the first such numerical evidence for their optimality in some of these dimensions). For non-spherical particles, we report a new dense packing of regular four-dimensional simplices with density $\phi=128/219\approx0.5845$ and with a similar structure to the densest known tetrahedron packing.Comment: 15 pages, 5 figure