On the creep analysis of pressurized circular cylindrical shells

Creep analysis of cylindrical shell by a finite difference method

Nonlinear vibration of axially moving simply-supported circular cylindrical shell

Based on Reddy’s first-order shear deformation theory, the nonlinear dynamic response and vibration of imperfect functionally graded carbon nanotube-reinforced composite (FG CNTRC) circular cylindrical shells subjected to an external dynamic load uniformly distributed on the surface of the shell and axial compression in thermal environment are presented. The circular cylindrical shells are surrounded on elastic foundations and reinforced by single-walled carbon nanotubes which vary according to the linear functions of the shell thickness. The shell’s effective material properties are assumed to depend on temperature and estimated through the rule of mixture. By applying the stress function, Galerkin method and fourth-order Runge–Kutta method, nonlinear dynamic response and natural frequencies for imperfect FG CNTRC circular cylindrical shells are determined. In numerical results, the influences of geometrical parameters, elastic foundations, initial imperfection, temperature increment, dynamic loads and nanotube volume fraction on the nonlinear vibration of FG CNTRC circular cylindrical shells are investigated. The obtained results are validated by comparing with those of other authors.

A method for the simultaneous estimation of DPX Hydrochloride and TDX in a tablet dosage form using the simultaneous equation method was developed and validated. This method relies on the different maximum absorbance wavelengths of the two drugs: DPX Hydrochloride at 210 nm and TDX at 285 nm. Calibration curves were plotted for both drugs, and the concentrations in synthetic mixtures were determined using simultaneous equations derived from the absorbance measurements at these wavelengths. The method demonstrated high accuracy, precision, and specificity, adhering to ICH guidelines. In the linearity study at respective wavelengths, the linear regression equation for DPXHydrochloride, calibration curve at 285 nm was calculated by y = 0.088x +0.005 (r² = 0.999), where y is absorbance and x is the value of various concentrations of standard solutions and the linear regression equation for Dapoxtine Hydrochloride, calibration curve at 210.0 nm was calculated by y =0.073x + 0.002 (r² = 0.999) (Table – 3). Moreover, in the linearity study at of the other API at consecutive wavelengths, the linear regression equation for TDX, calibration curve at 285.0 nm was calculated by y = 0.022x+0.035 (r² = 0.996) and the linear regression equation for TDX, calibration curve at 210 m was calculated by y = 0.034x - 0.013 (r2=0.998). The simultaneous equation method provided a reliable and accurate means of quantifying DPXHydrochloride and TDX in tablet formulations. The calibration curves were linear, and the method complied with ICH guidelines for specificity, accuracy, and precision. This method is advantageous for quality control in pharmaceutical formulations, offering simplicity and efficiency.

Many materials exhibit the stress range dependent creep behavior. The power law creep observed for a certain stress range changes to the viscous type creep as the stress value decreases. Recently published experimental data for advanced heat resistant steels indicate that the high creep exponent (in the range 7–12) may decrease to the low value of approximately unity within the stress range relevant for engineering structures. The aim of this paper is to analyze the influence of the stress range dependent power-law-viscous creep transition on the behavior of structures at elevated temperature. A constitutive model for the minimum creep rate is introduced to describe both the linear and the power law creep depending upon the stress level. To demonstrate basic features of the stress range dependent creep modeling, several elementary examples from structural mechanics are presented. They include a stress relaxation problem, a beam subjected to pure bending and a pressurized thick-walled cylinder. Based on the uni-axial transition stress the transition value of the external load is estimated such that above this value the power law can be applied. For the loading levels below this value the character of the stress distribution as well as the stress values are essentially influenced by the viscous creep.

The extended Newton method combined with the method of finite-differences is shown to be a powerful means to the steady-state creep analysis of shells of revolution. The creep theory of von Mises type and the power creep law are assumed. As numerical examples, a simply-supported circular cylindrical shell with open ends and a clamped spherical shell, subjected to internal pressure respectively, are analysed. The results of calculation of the cylindrical shell, in particular, are compared with those of semi-infinite sandwich shell obtained by Rabotnov.

A multiple scale solution for circular cylindrical shells

The effect of transverse shear deformation on dynamic stability of simply supported, finite-length, circular cylindrical shells is investigated. The loading is cyclic axial compression and tension. The shell is orthotropic, which can be due to closely-spaced orthogonal stiffeners or due to many layers of composite material alternately oriented at angles of 0° and 90° or at + θ and −θ with respect to the shell axis. The theory used is a general shear deformable shell theory, which can be considered to be the thick-shell version of the Sanders-Koiter shell theory. Parametric studies are made to show the effects of shell geometry and different shell theories on stability boundaries.

Analysis of circular cylindrical shells under harmonic forces

For the purpose of decreasing the lower critical speed of circular cylindrical shells which are used in centrifugal separators for uranium enrichment, and rotating at higher speeds, we consider circular cylindrical shells connected to bellows. Vibration analysis of circular cylindrical shells connected to bellows is carried out by the substructure synthesis method for various numbers and dispositions of bellows, and the optimum ones are examined. Moreover, the transfer matrix method, by which the critical speeds are simply obtained, is described, and the results are examined by the substructure synthesis method.

Free vibration analysis of skewed open circular cylindrical shells

A simple, accurate and precise spectroscopic method was developed for simultaneous estimation of Aripiprazole and Escitalopram Oxalate in synthetic mixture using simultaneous equation Method. In this spectroscopic method, 255.00 nm and 238.00 nm wavelengths were selected for measurement of absorptivity. Both the drugs show linearity in a concentration range of 5–30 μg/ml and 15–75 μg/ml at their respective λmax. Accuracy, precision and recovery studies were done by QC samples covering lower, medium and high concentrations of the linearity range. The relative standard deviation for accuracy, precision studies were found to be within the acceptance range (<2%). The limit of determination was 0.129 and 0.223μg/ml Aripiprazole and Escitalopram Oxalate, respectively. The limit of quantification was 0.392 and 0.677 for Aripiprazole and Escitalopram Oxalate, respectively. Recovery of Aripiprazole and Escitalopram Oxalate in were found to be 100.66% and 100.70% respectively confirming the accuracy of the proposed method. The proposed method is recommended for routine analysis since they are rapid, simple, accurate and also sensitive and specific by no heating and no organic solvent extraction.

For the simultaneous determination of linagliptin and metformin in pharmaceutical formulations, two spectrophotometric procedures were described that were direct, accurate, and precise. The first was based on the H-point standard addition method (HPSAM) in which a standard solution of linagliptin was added to a mixture of linagliptin and metformin to monitor the absorbance at the wavelength pair of 231.7 nm and 243.4 nm. Linearity, accuracy, and precision were accepted over the concentration range of 0-3.2 μg/mL and 0.8 - 2.8 μg/ mL for linagliptin and metformin, respectively. In the second method, the simultaneous equation method (Vierodt᾿s method) was developed and validated, where two wavelengths 226 and 238 nm of linagliptin and metformin, respectively, were chosen to form the simultaneous equation. The results of applying Vierodt's method showed that linagliptin and metformin could be quantified simultaneously in the concentration range of 0 - 25 μg/mL and 0 -20 μg/mL, respectively. These methods have been successfully applied to the simultaneous determination of linagliptin and metformin in various synthetic mixtures, and pharmaceutical products. Key words: Linagliptin ; Metformin ; H-Point Standard Addition Method ; Vierodt᾿S Method; Simultaneous Determination

Two simple, sensitive, accurate and precise spectrophotometric methods were developed and validated for quantitative determination of metoprolol succinate, atorvastatin calcium and ramipril in tablet dosage form. Method A is based on the simultaneous equation and method B is based on the multi-component analysis. The absorption maxima of the drugs were found to be 225 nm, 246 nm and 215 nm for metoprolol succinate, atorvastatin calcium and ramipril respectively in methanol. Beer’s law is obeyed in the concentration range of 5–25 μg/mL with correlation coefficient of 0.994, 0.994 and 0.997 for the above three drugs. The simultaneous equation method is based on the additivity of absorbances, and multi component analysis involves recording of absorbances of corresponding drugs at their respective absorbance maxima. These methods can be used for routine analysis of the above drugs in combined tablet formulation. Result of analysis for both methods were tested and validated for various parameters according to ICH guidelines.

Four new UV spectrophotometric methods namely simultaneous equation, absorbance ratio, area under curve and first derivative (zero crossing) spectroscopic methods were developed and validated for simultaneous estimation Empagliflozin and Metformin hydrochloride in bulk and tablet formulation. In simultaneous equation method, absorbance was measured at 224 and 232 nm for both the drugs. Empagliflozin and Metformin hydrochloride was estimated using 224 and 232 nm in absorbance ratio method. In Area under curve method both drugs were estimated at 224 and 232 nm respectively. First derivative (zero crossing) method was based on the transformation of UV spectra in to first derivative spectra followed by measurement of first derivative signal at 224 and 232 nm for Empagliflozin and Metformin hydrochloride, respectively using 2 nm as wavelength interval (Δλ) and 1 as scaling factor. Methods were found to be simple, fast, highly sensitive, cost effective and hence can be useful for simultaneous estimation of Empagliflozin and Metformin hydrochloride in commercial tablet formulation for routine quality control analysis.