A fast method for binary programming using first-order derivatives, with application to topology optimization with buckling constraints

2012 ◽  
Vol 92 (12) ◽  
pp. 1026-1043 ◽  
Author(s):  
P. A. Browne ◽  
C. Budd ◽  
N. I. M. Gould ◽  
H. A. Kim ◽  
J. A. Scott
Keyword(s):  
Topology Optimization ◽  
Fast Method ◽  
Binary Programming ◽  
First Order ◽  
Buckling Constraints

scholarly journals Topology optimization of elasto-plastic structures under reliability constraints: A first order approach

2021 ◽  
Vol 243 ◽  
pp. 106406
Author(s):  
Piotr Tauzowski ◽  
Bartlomiej Blachowski ◽  
János Lógó
Keyword(s):  
Topology Optimization ◽  
First Order

An Adaptive Continuation Method for Topology Optimization of Continuum Structures Considering Buckling Constraints

2017 ◽  
Vol 09 (07) ◽  
pp. 1750092 ◽  
Author(s):  
Xingjun Gao ◽  
Lijuan Li ◽  
Haitao Ma
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Continuation Method ◽  
Optimization Process ◽  
Continuum Structures ◽  
Design Evolution ◽  
Buckling Constraints ◽  
Load Factors ◽  
Structural Compliance ◽  
Parameter Values

This paper presents an adaptive continuation method for buckling topology optimization of continuum structures using the Solid Isotropic Material with Penalization (SIMP) model. For optimization problems of minimizing structural compliance subject to constraints on material volume and buckling load factors, it has been found that the conflict between the requirements for structural stiffness and stability may have an adverse impact on the performance of existing optimization algorithms. An automatic scheme for adjusting the penalization parameter is introduced to deal with this conflict and thus achieves better designs. Based on an investigation on the effect of the penalization parameter on design evolution during the optimization process, a rule is established to determine the appropriate penalization parameter values. Using this rule, an effective scheme is developed for determining the penalization parameter values such that the buckling constraints are appropriately considered throughout the optimization process. Numerical examples are presented to illustrate the effectiveness of the proposed method.

scholarly journals Conductomeric Evaluation of the Release Kinetics of Active Substances from Pharmaceutical Preparations Containing Iron Ions

Materials ◽  
2019 ◽  
Vol 12 (5) ◽  
pp. 730 ◽  
Author(s):  
Anna Lisik ◽  
Witold Musiał
Keyword(s):  
Release Kinetics ◽  
Pharmaceutical Preparations ◽  
Correlation Coefficients ◽  
Order Equation ◽  
Fast Method ◽  
Order Kinetic ◽  
Iron Ions ◽  
First Order ◽  
Kinetics Of ◽  
Active Substances

The aim of this study was to verify the effect of the formulation on the release kinetics of active substances from preparations containing iron ions using in-line conductivity measurements. A simple, fast method was developed and may be applied for detailed evaluation of some kinetics factors obtained from the release data. Four different equations were used: zero-order equation, first-order equation, models: Korsmeyer–Peppas and Hixson–Crowell. Values of the determined half-time release for zero and first-order kinetic models ranged from 11.56 to 89.97 min. In the case of analysis according to these typical models, the values of the square root of the correlation coefficients were included between 0.9916 and 0.9995. The results transformed for the Hixson–Crowell model as constant release Ks, ranged between 0.0160 and 0.0437. The values of the respective calculated squares of the correlation coefficient ranged from 0.9933 to 0.9959. The determined release rate constants according to the Korsmeyer–Peppas model were between 0.0023 and 0.1630. The coefficients ‘n’ of the Korsmeyer–Peppas equation did not exceed 1.2 with the corresponding r2 values 0.9408–0.9960. Obtained results confirmed that the method is applicable for evaluation of selected drug compositions containing iron ions.

scholarly journals Simultaneous Determination of Dapsone and Pyrimethamine by Derivative Spectrophotometry in Pharmaceutical Formulations

2003 ◽  
Vol 86 (2) ◽  
pp. 241-245 ◽  
Author(s):  
M Inés Toral ◽  
Andrés Tassara ◽  
César Soto ◽  
Pablo Richter
Keyword(s):  
Simultaneous Determination ◽  
Signal To Noise Ratio ◽  
Pharmaceutical Formulations ◽  
Derivative Spectrophotometry ◽  
Fast Method ◽  
Signal To Noise ◽  
Zero Crossing ◽  
First Order ◽  
First Derivative

Abstract A simple and fast method was developed for the simultaneous determination of dapsone and pyrimethamine by first-order digital derivative spectrophotometry. Acetonitrile was used as a solvent to extract the drugs from the pharmaceutical formulations, and the samples were subsequently evaluated directly by digital derivative spectrophotometry. The simultaneous determination of both drugs was performed by the zero-crossing method at 249.4 and 231.4 nm for dapsone and pyrimethamine, respectively. The best signal-to-noise ratio was obtained when the first derivative of the spectrum was used. The linear range of determination for the drugs was from 6.6 × 10−7 to 2.0 × 10−4 and from 2.5 × 10−6 to 2.0 × 10−4 mol/L for dapsone and pyrimethamine, respectively. The excipients of commercial pharmaceutical formulations did not interfere in the analysis. Chemical and spectral variables were optimized for determination of both analytes. A good level of repeatability, 0.6 and 1.7% for dapsone and pyrimethamine, respectively, was observed. The proposed method was applied for the simultaneous determination of both drugs in pharmaceutical formulations.

A Fast Method for the Determination of Emergent Intensities in Radiative Transfer Theory

1971 ◽  
Vol 2 (1) ◽  
pp. 42-43 ◽  
Author(s):  
C. J. Cannon
Keyword(s):  
Differential Equation ◽  
Radiative Transfer ◽  
Source Function ◽  
Order Differential Equation ◽  
Fast Method ◽  
First Order ◽  
Integration Schemes ◽  
Emergent Intensity ◽  
Difficult Part

One of the quantities usually required when solving the equation of radiative transfer is the intensity of radiation emerging from the surface of the medium under consideration. For multi-dimensional situations however, the methods presented to date have been numerical, and these first calculate the so-called source function Sv (r, Ω) as a function of position r, angle Ω and frequency v. This is generally the most difficult part of the exercise since an integro-difierential equation must be solved. The emergent intensity is then determined by solving a relatively simple first order differential equation by any of the well known numerical integration schemes. However, if the emergent intensity is required at a large number of angles, frequencies, and positions on the surface of the medium, and this is usually the case, the amount of computing needed may be considerable.

scholarly journals Level-set topology optimization with many linear buckling constraints using an efficient and robust eigensolver

2016 ◽  
Vol 107 (12) ◽  
pp. 1029-1053 ◽  
Author(s):  
Peter D. Dunning ◽  
Evgueni Ovtchinnikov ◽  
Jennifer Scott ◽  
H. Alicia Kim
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Buckling Constraints ◽  
Linear Buckling

Scanning Mirror Topology Optimization of the Imaging Spectrometer

2014 ◽  
Vol 599-601 ◽  
pp. 1205-1210
Author(s):  
Hai Fang Cong
Keyword(s):  
Topology Optimization ◽  
Working Condition ◽  
Dynamic Deformation ◽  
Optimization Method ◽  
Imaging Spectrometer ◽  
Scanning Mirror ◽  
First Order ◽  
High Dynamic ◽  
Topology Optimization Method

In order to obtain high dynamic RMS performance of the scanning mirror in the working condition, the topology optimization method based on the constrain of dynamic deformation was carried out. Effective simplifications are implemented to reduce the complexity of the calculation. With the topology method, a lightweight form of the scanning mirror was generated on the dynamic working condition. The result shows that the lightweight ratio of the optimized structure is 47.4%, the PV value is 19.36nm and the RMS value is 5.65nm, which is improved by 18.46% and 17.41%, respectively. Besides, the first order frequency has increased by 113.8Hz. The results illustrate that the proposed method for the optimization of the scanning mirror is reasonable and practically.

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