Fast modal extraction in NASTRAN via the FEER computer program

A new eigensolution routine, FEER (Fast Eigensolution Extraction Routine), used in conjunction with NASTRAN at Israel Aircraft Industries is described. The FEER program is based on an automatic matrix reduction scheme whereby the lower modes of structures with many degrees of freedom can be accurately extracted from a tridiagonal eigenvalue problem whose size is of the same order of magnitude as the number of required modes. The process is effected without arbitrary lumping of masses at selected node points or selection of nodes to be retained in the analysis set. The results of computational efficiency studies are presented, showing major arithmetic operation counts and actual computer run times of FEER as compared to other methods of eigenvalue extraction, including those available in the NASTRAN READ module. It is concluded that the tridiagonal reduction method used in FEER would serve as a valuable addition to NASTRAN for highly increased efficiency in obtaining structural vibration modes

Efficient reanalysis of structures by a direct modification method

A procedure for the local stiffness modifications of large structures is described. It enables structural modifications without an a priori definition of the changes in the original structure and without loss of efficiency due to multiple loading conditions. The solution procedure, implemented in NASTRAN, involved the decomposed stiffness matrix and the displacement vectors of the original structure. It solves the modified structure exactly, irrespective of the magnitude of the stiffness changes. In order to investigate the efficiency of the present procedure and to test its applicability within a design environment, several real and large structures were solved. The results of the efficiency studies indicate that the break-even point of the procedure varies between 8% and 60% stiffness modifications, depending upon the structure's characteristics and the options employed

Interactive computer graphics system for structural sizing and analysis of aircraft structures

A computerized system for preliminary sizing and analysis of aircraft wing and fuselage structures was described. The system is based upon repeated application of analytical program modules, which are interactively interfaced and sequence-controlled during the iterative design process with the aid of design-oriented graphics software modules. The entire process is initiated and controlled via low-cost interactive graphics terminals driven by a remote computer in a time-sharing mode

Modelling the transmission dynamics of Theileria annulata : model structure and validation for the Turkish context

A mathematical model that describes the transmission dynamics of Theileria annulata is proposed that consists of 2 host components: the Hyalomma tick population and a compartmental model of T. annulata infection in the cattle population. The model was parameterized using data describing tick infestation and the infection status of cattle in Turkey from 2006 to 2008. The tick attachment rates are highly seasonal and because of the temporal separation of infectious and susceptible ticks virtually all ticks are infected by carrier cattle, so that annual peaks of disease in cattle do not impact on infection in the Hyalomma tick population. The impact of intervention measures that target the tick population both on the host and in the environment and their impact on the transmission of T. annulata were investigated. Interventions that have a limited ‘one-off’ impact and interventions that have a more permanent impact were both considered. The results from the model show the importance of targeting ticks during the period when they have left their first host as nymphs but have yet to feed on their second host

THE π\pi-ELECTRON STATES OF BUTADIENE

Author Institution: Battlle Memorial InstituteUsing a Hartree-Fock representation for the $\sigma$-core (obtained from an all-electron calculation on the ground state), extensive configuration interaction calculations have been carried out on the $\pi$-electron states of trans-butadiene. The $\sigma$ basis set of contracted Gaussian functions is of double zeta quality, while the $\pi$ basis has been augmented with two diffuse functions on each carbon atom appropriate for the description of the first set of Rydberg states. It is found that the lowest two triplet states, of symetry $^{3}B_{u}$ and $^{3}A_{g}$, with calculated vertical transition energies of 3.45 e.v. and 5.04 e.v., respectively, are valence states, and that the effect of CI is in accordance with the Coulson-Rushbrooke theorem. The lowest two excited singlet states, on the other hand, are found to be Rydberg transitions from the highest occupied $\pi$-orbital of the ground state. The calculated vertical excitation energies for the four lowest singlet Rydberg states are 6.77 ev $(2^{1}A_{g}), 7.05 (1^{1}B_{u}), 7.83 (3^{1}A_{g})$ and $8.06 (2^{1}B_{u})$, with oscillator strengths of $\sim$0.2 and $\sim$0.45 for the allowed transitions ($1^{1}A_{g}\rightarrow 1^{1}B_{a}, 2^{1}B_{u}$). The Rydberg states are found to occur in sets of four with roughly the same spatial extent, e.g., for the Rydberg orbital in the four lowest singlet states, the expectation value $$ varies from $40 (a.u.)^{2}$, to $66 (a.u.)^{2}$, where Z is in the $\pi$-direction. These results are not in accord with the previous assignments of the spectrum of butadiene or with the basic formulation of $\pi$-electron theory as it has developed along semi-empirical lines