In this paper, a generalized FE formulation for buckling analysis of nonprismatic columns with various cross-sections is established by using the Chebyshev polynomial approach to the governing differential equation. The proposed formulation includes the effects of shear deformation and is therefore applicable to solid or built-up columns. The change of the sectional properties along the length direction, such as the area and inertia moment, need not be fitted with approximate expressions and can be defined exactly and freely with user-defined functions in programming. Buckling of the three structures, respectively for a tapered mast column with a circular hollow section, a web-tapered I-sectional column and a tapered lattice column, is studied numerically and compared with the results of previous studies. The effects of shear deformation on the buckling loads of those tapered columns are specified.
To gain a better understanding of differentially expressed sequence tags (ESTs) for aluminum (Al) tolerance and to investigate the molecular mechanisms of Al toxicity, cDNA subtraction libraries were generated from Al-stressed roots of alfalfa (Medicago sativa L.) compared with no Al-stressed ones, employing suppression subtractive hybridization. Using differential screening technique in which the probes were labeled with DIG, we identified 45 non-redundant ESTs in Al-stressed alfalfa root tips with significantly altered expression. Among the up-regulated ESTs, we have found genes encoding identified proteins, including malate dehydrogenase, 6-phosphogluconate dehydrogenase, peroxidase, and an ABC transporter, while the down-regulate genes included ATPase, secretory carrier membrane protein 2, pectinesterase inhibitor. In addition, two novel ESTs, EW678752 and EY976957, up- and down-regulated by Al stress were sequenced. Analyzed by real-time PCR, the expressions of EST EW678718, EW678739, EY976969 and EW678728, which encode for ABC transporter, malate dehydrogenase, peroxidase and 6-phosphogluconate dehydrogenase correspondingly, increased 1.64-, 2.75-, 3.27- and 6.54-folds, respectively, and the expression of EY976957 encoding for ATPase decreased 3.27 folds. The expression of EST EW678752 increased 34.54-fold, while that of EY976957 decreased 16.68 folds. It suggested that the two novel ESTs maybe play a significant role in the aluminum tolerance of alfalfa.
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