Structural optimization with parameter-transfer finite element

A mathematical method to solve structural problems, using parameter-transfer finite elements (P-TFE) was recently proposed by the authors [1] [2] [3]. The proposed transfer finite element approach is able to create a mathematical model of a structure, taking into account directly the whole behaviour of the structure under dynamic, aerodynamic, and thermal actions, and not by assembling, in a separate fashion, the stiffness and the mass matrix on one side and the external load vector as performed by the classical finite element procedure.The purpose of this paper is to apply the above methodology to optimization problems, in particular to obtain the minimum structural weight for a beam, under primary constraints on buckling load or natural frequencies.The use of P-TFE in the field of structural optimization overcomes most difficulties of the usual techniques of solution and the element is particularly useful in the evaluation of the sensitivity matrix.The formulation of the optimization problem based on P-TFE is presented and some applications are studied. The numerical results obtained are compared with other existing methodologies and briefly discussed.

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Sommario Gli autori hanno già proposto un metodo per studiare problemi strutturali [1] [2] [3], introducendo una nuova metodologia di discretizzazione, basata sull'impiego di elementi finiti di trasferimento, funzioni esplicite di un parametro, indicati come P-TFE. Tali elementi sono in grado di rappresentare, in similitudine alla funzione di trasferimento, il comportamento completo dell'elemento strutturale in esame, soggetto ad azioni dinamiche, aerodinamiche e termiche; sono parimenti in grado di produrre, in similitudine al metodo degli elementi finiti, un modello matematico discreto di un continuo.Scopo del presente lavoro è di applicare detta metodologia a problemi di ottimizzazione, in particolare alla ricerca del minimo peso per una trave che mantenga inalterate le sue caratteristiche di carico critico o le frequenze naturali di vibrazione.Vengono quindi presentati alcuni risultati numerici dei casi esaminati e confrontati con quelli ottenuti da altri autori con l'impiego di altre metodologie.

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List of Symbols {B} _m vector of the generalized state variables - {C} _m vector of integration constants - [I] unit matrix - EI bending stiffness - A cross-sectional area - u adimensional thickness - l beam length - M,M bending moment - [N] _m shape function ofm-th order - [N*] shape function atx ₀ - P axial load - [R] _i transfer matrix of thei-th element - T,T shear force - w transverse displacement - x adimensional independent variable - x ₀ value ofx at the left of the element - {Y} vector of state variables - {Y*} imposed condition atx ₀ - _0m Kronecker delta with the first pedix always set equal to zero - normalized eigenfrequency - normalized buckling load - mass density     

Austauscher mit cyclischen Polyethern als Ankergruppen—II: Anwendungen

Exchangers with cyclic polyethers as anchor groups have a large range of applications such as separations of cations with a common anion, of anions with a common cation, and of neutral organic compounds, and the determination of water by elution chromatography. Some crown ether monomers, especially 4- and 4,4′-alkyl-substituted benzo-derivatives are suitable for extractions and their adducts with heteropoly acids are used as liquid ion-exchangers. The exchangers are also applied in thin-layer chromatography and thin-layer electrophoresis. Furthermore the exchangers are successfully used in preparative chemistry, e.g., in salt conversions in order to isolate salts which are difficult to prepare by other means, in isolation and purification of organic compounds, and for anion activation in organic reactions.     

Automated determination of verapamil and norverapamil in human plasma with on-line coupling of dialysis to high-performance liquid chromatography and fluorometric detection

A fully automated method for the simultaneous determination of verapamil and its main metabolite norverapamil in human plasma is described. This method is based on on-line sample preparation using dialysis followed by clean-up and enrichment of the dialysate on a precolumn and subsequent HPLC analysis with fluorometric detection. All sample handling operations were performed automatically by a sample processor equipped with a robotic arm (ASTED system). The plasma samples were dialysed on a cellulose acetate membrane (cut-off: 15 kD) and the dialysate was purified and enriched on a short pre-column filled with cyanopropyl silica. Before starting dialysis, this trace enrichment column (TEC) was first conditioned with the HPLC mobile phase and then with pH 3.0 acetate buffer. 370 μl of plasma sample spiked with the internal standard (gallopamil) were dialysed in the static-pulsed mode. The solution at the donor side was pH 3.0 acetate buffer containing Triton X-100 while the acceptor solution was made of the same acetate buffer. When dialysis was discontinued, the analytes were desorbed from the TEC by the HPLC mobile phase and transferred to the C₁₈ analytical column by means of a switching valve. This mobile phase consisted of a mixture of acetonitrile, pH 3.0 acetate buffer and 2-aminoheptane. The influence of different parameters of the dialysis process on the recovery of verapamil and norverapamil has been studied. The effect of the volume, the aspirating and dispensing flow-rates of the dialysis solution has been investigated. The recoveries of verapamil and norverapamil in plasma were close to 75% and the limits of quantification were 5 ng/ml for both analytes. The method was found to be linear in the concentration range from 5 to 500 ng/ml (r²: 0.9996 for both analytes). The intra-day and inter-day reproducibilities at a concentration of 100 ng/ml were 2.3% and 5.6% for verapamil and 1.7% and 5.1% for norverapamil, respectively.