Martin Cohen

Reduced and selective integration techniques in the finite element analysis of plates

Efforts to develop effective plate bending finite elements by reduced integration techniques are described. The basis for the development is a ‘thick’ plate theory in which transverse shear strains are accounted for. The variables in the theory are all kinematic, namely, displacements and independent rotations. As only C0 continuity is required, isoparametric elements may be employed, which result in several advantages over thin plate elements. It is shown that the avoidance of shear ‘locking’ may be facilitated by reduced integration techniques. Both uniform and selective schemes are considered. Conditions under which selective schemes are invariant are identified, and they are found to have an advantage over uniform schemes in the present situation. It is pointed out that the present elements are not subject to the difficulties encountered by thin plate theory elements, concerning boundary conditions. For example, the polygonal approximation of curved, simply-supported edges is convergent. Other topics discussed are the equivalence with mixed methods, rank deficiency, convergence criteria and useful mass ‘lumping’ schemes for dynamics. Numerical results for several thin plate problems indicate the high degree of accuracy attainable by the present elements.

The “heterosis” finite element for plate bending

Abstract A new. high-accuracy, finite element for thick and thin plate bending is developed, based upon Mindlin plate theory. The element is a 9-node quadrilateral, which exhibits improved characteristics in comparison with the 8-node serendipity, or the 9-node Lagrange elements. In particular, the element stiffness possesses correct rank, and high accuracy is attainable for extremely thin plates. Due to the consistently good performance of the element, it is proposed as a candidate for inclusion in finite element programs available to the general user.

SPITZER PHOTOMETRY OF WISE-SELECTED BROWN DWARF AND HYPER-LUMINOUS INFRARED GALAXY CANDIDATES

We present Spitzer 3.6 and 4.5 μm photometry and positions for a sample of 1510 brown dwarf candidates identified by the Wide-field Infrared Survey Explorer (WISE) all-sky survey. Of these, 166 have been spectroscopically classified as objects with spectral types M(1), L(7), T(146), and Y(12). Sixteen other objects are non-(sub)stellar in nature. The remainder are most likely distant L and T dwarfs lacking spectroscopic verification, other Y dwarf candidates still awaiting follow-up, and assorted other objects whose Spitzer photometry reveals them to be background sources. We present a catalog of Spitzer photometry for all astrophysical sources identified in these fields and use this catalog to identify seven fainter (4.5 μm ~ 17.0 mag) brown dwarf candidates, which are possibly wide-field companions to the original WISE sources. To test this hypothesis, we use a sample of 919 Spitzer observations around WISE-selected high-redshift hyper-luminous infrared galaxy candidates. For this control sample, we find another six brown dwarf candidates, suggesting that the seven companion candidates are not physically associated. In fact, only one of these seven Spitzer brown dwarf candidates has a photometric distance estimate consistent with being a companion to the WISE brown dwarf candidate. Other than this, there is no evidence for any widely separated (>20 AU) ultra-cool binaries. As an adjunct to this paper, we make available a source catalog of ~7.33 × 10^5 objects detected in all of these Spitzer follow-up fields for use by the astronomical community. The complete catalog includes the Spitzer 3.6 and 4.5 μm photometry, along with positionally matched B and R photometry from USNO-B; J, H, and K_s photometry from Two Micron All-Sky Survey; and W1, W2, W3, and W4 photometry from the WISE all-sky catalog.