Differential equation based method for accurate approximations in optimization

A method to efficiently and accurately approximate the effect of design changes on structural response is described. The key to this method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in most cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacements are used to approximate bending stresses

Senstitivty analysis and optimization of nodal point placement for vibration reduction

A method is developed for sensitivity analysis and optimization of nodal point locations in connection with vibration reduction. A straightforward derivation of the expression for the derivative of nodal locations is given, and the role of the derivative in assessing design trends is demonstrated. An optimization process is developed which uses added lumped masses on the structure as design variables to move the node to a preselected location - for example, where low response amplitude is required or to a point which makes the mode shape nearly orthogonal to the force distribution, thereby minimizing the generalized force. The optimization formulation leads to values for added masses that adjust a nodal location while minimizing the total amount of added mass required to do so. As an example, the node of the second mode of a cantilever box beam is relocated to coincide with the centroid of a prescribed force distribution, thereby reducing the generalized force substantially without adding excessive mass. A comparison with an optimization formulation that directly minimizes the generalized force indicates that nodal placement gives essentially a minimum generalized force when the node is appropriately placed

Sensitivity derivatives and optimization of nodal point locations for vibration reduction

A method is developed for sensitivity analysis and optimization of nodal point locations in connection with vibration reduction. A straightforward derivation of the expression for the derivative of nodal locations is given, and the role of the derivative in assessing design trends is demonstrated. An optimization process is developed which uses added lumped masses on the structure as design variables to move the node to a preselected location; for example, where low response amplitude is required or to a point which makes the mode shape nearly orthogonal to the force distribution, thereby minimizing the generalized force. The optimization formulation leads to values for added masses that adjust a nodal location while minimizing the total amount of added mass required to do so. As an example, the node of the second mode of a cantilever box beam is relocated to coincide with the centroid of a prescribed force distribution, thereby reducing the generalized force substantially without adding excessive mass. A comparison with an optimization formulation that directly minimizes the generalized force indicates that nodal placement gives essentially a minimum generalized force when the node is appropriately placed

Recent advances in multidisciplinary optimization of rotorcraft

A joint activity involving NASA and Army researchers at NASA LaRC to develop optimization procedures to improve the rotor blade design process by integrating appropriate disciplines and accounting for all of the important interactions among the disciplines is described. The disciplines involved include rotor aerodynamics, rotor dynamics, rotor structures, airframe dynamics, and acoustics. The work is focused on combining these five key disciplines in an optimization procedure capable of designing a rotor system to satisfy multidisciplinary design requirements. Fundamental to the plan is a three-phased approach. In phase 1, the disciplines of blade dynamics, blade aerodynamics, and blade structure are closely coupled while acoustics and airframe dynamics are decoupled and are accounted for as effective constraints on the design for the first three disciplines. In phase 2, acoustics is integrated with the first three disciplines. Finally, in phase 3, airframe dynamics is integrated with the other four disciplines. Representative results from work performed to date are described. These include optimal placement of tuning masses for reduction of blade vibratory shear forces, integrated aerodynamic/dynamic optimization, and integrated aerodynamic/dynamic/structural optimization. Examples of validating procedures are described

Rotor blade dynamic design

The rotor dynamic design considerations are essentially limitations on the vibratory response of the blades which in turn limit the dynamic excitation of the fuselage by forces and moments transmitted to the hub. Quantities which are associated with the blade response and which are subject to design constraints are discussed. These include blade frequencies, vertical and inplane hub shear, rolling and pitching moments, and aeroelastic stability margin

The minimal conditions for a financial crisis: a multiregional intertemporal CGE model of the Asian crisis

Cataloged from PDF version of article.The globalization of world capitalism constrains the ability of the developmental state to pursue an independent industrialization and foreign trade strategy. We use an intertemporal, multiregion CGE model, to study the fundamental reasons for a financial crisis. We find that we can create a realistic crisis in the Asia region when capital markets are open and there is an unexpected rise in the risk premium of the Asia region. When capital markets are closed and the state retains all its policy instruments, the Asia region not only avoids a crisis but increases its rate of growth. (C) 2000 Published by Elsevier Science Ltd. All rights reserved

High resolution spectroscopic study of red clump stars in the Galaxy: iron group elements

The main atmospheric parameters and abundances of the iron group elements (vanadium, chromium, iron, cobalt and nickel) are determined for 62 red giant "clump" stars revealed in the Galactic field by the Hipparcos orbiting observatory. The stars form a homogeneous sample with the mean value of temperature T=4750 +- 160K, of surface gravity log g = 2.41 +- 0.26 and the mean value of metallicity [Fe/H] = -0.04 +- 0.15 dex. A Gaussian fit to the [Fe/H] distribution produces the mean [Fe/H] = -0.01 dex and dispersion of [Fe/H] = 0.08 dex. The near-solar metallicity and small dispersion of [Fe/H] of clump stars of the Galaxy obtained in this work confirm the theoretical model of the Hipparcos clump by Girardi & Salaris (2001). This suggests that nearby clump stars are (in the mean) relatively young objects, reflecting mainly the near-solar metallicities developed in the local disk during the last few Gyrs of its history. We find iron group element to iron abundance ratios in clump giants to be close to solar.Comment: 9 pages, 7 figures, accepted for publication in MNRA

Optimal placement of tuning masses for vibration reduction in helicopter rotor blades

Described are methods for reducing vibration in helicopter rotor blades by determining optimum sizes and locations of tuning masses through formal mathematical optimization techniques. An optimization procedure is developed which employs the tuning masses and corresponding locations as design variables which are systematically changed to achieve low values of shear without a large mass penalty. The finite-element structural analysis of the blade and the optimization formulation require development of discretized expressions for two performance parameters: modal shaping parameter and modal shear amplitude. Matrix expressions for both quantities and their sensitivity derivatives are developed. Three optimization strategies are developed and tested. The first is based on minimizing the modal shaping parameter which indirectly reduces the modal shear amplitudes corresponding to each harmonic of airload. The second strategy reduces these amplitudes directly, and the third strategy reduces the shear as a function of time during a revolution of the blade. The first strategy works well for reducing the shear for one mode responding to a single harmonic of the airload, but has been found in some cases to be ineffective for more than one mode. The second and third strategies give similar results and show excellent reduction of the shear with a low mass penalty

Extremely metal-poor stars from the SDSS

We give a progress report about the activities within the CIFIST Team related to the search for extremely metal-poor stars in the Sloan Digital Sky Survey's spectroscopic catalog. So far the search has provided 25 candidates with metallicities around or smaller -3. For 15 candidates high resolution spectroscopy with UVES at the VLT has confirmed their extremely metal-poor status. Work is under way to extend the search to the SDSS's photometric catalog by augmenting the SDSS photometry, and by gauging the capabilities of X-shooter when going to significantly fainter targets.Comment: 6 pages, 6 figures, Proceedings paper of the conference "A stellar journey: A symposium in celebration of Bengt Gustafsson's 65th birthday

Vertical distribution of chromium in the atmospheres of HgMn stars

We use multiplet 30 Cr II lines in the wings of H_beta to test the hypothesis of an anomalous concentration of Cr in the upper layers of the atmospheres of a sample of 10 HgMn stars. These lines are at different distances from the H_beta line center and are therefore formed at different depths in the stellar atmosphere. Except for HD49606, all HgMn stars show an increase of Cr abundance with height in the stellar atmosphere. A similar vertical distribution of Cr, but less pronounced, has been previously found in Am stars. In contrast, no variation of Cr abundance with the depth has been found for the normal late B-type star HD196426 and the weak magnetic late B-type star HD168733. It is possible that in HgMn stars the vertical stratification parameter, a, depends on T_eff, with the strongest vertical gradient being found in the hotter stars. No correlation was found between $a$ and the average stellar abundance log epsilon(Cr/H).Comment: 7 pages, 3 figures, accepted for publication in A&