Direct Determination of Stresses in Plane Elasticity Problems Based on the Properties of Isostatics

1959 ◽  
Vol 26 (2) ◽  
pp. 227-234
Author(s):  
Pericles S. Theocaris
Keyword(s):  
Boundary Conditions ◽  
Experimental Method ◽  
Complex Variable ◽  
Direct Determination ◽  
Plane Elasticity ◽  
First Order ◽  
Differential Parameter ◽  
Elasticity Problems ◽  
Comparison Of The Results

Abstract An experimental method is developed for the calculation of stresses in plane elasticity problems. The method consists substantially in determining a function of the complex variable representing the field of isostatics. This function has a convenient form so that the boundary conditions can be expressed by simple relations. From the isostatics, which are traced experimentally, the differential parameter of first order h can be calculated all over the field. The components of stresses are expressed by relations depending on boundary conditions and the parameter h. The method is applied to two particular problems of plane elasticity and a comparison of the results obtained by this method and by analytic methods is provided.

COMPLEX VARIABLE METHOD FOR THE PLANE ELASTICITY OF QUASICRYSTALS WITH POINT GROUP 10

2008 ◽  
Vol 22 (29) ◽  
pp. 5145-5153
Author(s):  
LIAN-HE LI ◽  
TIAN-YOU FAN
Keyword(s):  
Complex Variable ◽  
Point Group ◽  
Plane Elasticity ◽  
Complex Variable Method ◽  
Variable Method ◽  
Real Form ◽  
General Complex ◽  
Elasticity Problems ◽  
Group 10 ◽  
Special Case

General complex variable method for solving plane elasticity problems of quasicrystals with point group 10 has been proposed. The stress and displacement components of phonon and phason fields are expressed by four arbitrary analytic functions. Explicit real-form displacement expressions for the dislocation problem of the quasicrystal is obtained through the use of this method.The interaction between two parallel dislocations is also discussed in detail. All the present results can be reduced to the exact solutions for the quasicrystals with point group 10 mm in the special case.

Direkte Bestimmung der Geschwindigkeitskonstanten des Durchtritts vom kleinen zum großen Hohlraumsystem im Molekularsieb Typ 13 X für Sr-und Ba-Ionen / Direct Determination of the Rate Constants for the Sr- and Ba-exchange Between the Small and Large Channels in LMS 13 X

1975 ◽  
Vol 30 (8) ◽  
pp. 951-954 ◽  
Author(s):  
K. Frohnecke ◽  
H. Fischbach
Keyword(s):  
Ion Exchange ◽  
Rate Constants ◽  
Diffusion Coefficients ◽  
Large Diameter ◽  
Direct Determination ◽  
Order Reaction ◽  
First Order Reaction ◽  
First Order ◽  
Total Exchange

Abstract Direct Determination of the Rate Constants for the Sr-and Ba-exchange Between the Small and Large Channels in LMS 13X The rate constants for the intracristalline Sr-and Ba-exchange between the small and large diameter channels of LMS 13X were measured. For this matter the method of interrupting the ion exchange was modified. It is assumed, that a first order reaction takes place. Using the rate constants and the diffusion coefficients, which were measured by Hoinkis and Levi, the total exchange of Sr 2+ and Ba 2+ could be calculated.

Application of Numerical Mapping to the Muskhelishvili Method in Plane Elasticity

1963 ◽  
Vol 30 (3) ◽  
pp. 410-414 ◽  
Author(s):  
V. L. Pisacane ◽  
L. E. Malvern
Keyword(s):  
Exact Solution ◽  
Finite Difference ◽  
Complex Variable ◽  
Digital Computer ◽  
Plane Elasticity ◽  
Complex Variable Method ◽  
Variable Method ◽  
Elasticity Problems ◽  
Finite Difference Solution ◽  
Simply Connected

A procedure for treating plane-elasticity problems in simply connected regions, consisting of use of numerical mapping methods in order to apply the Muskhelishvili complex variable method, is demonstrated. This approach now makes the whole complex variable method susceptible to automatic solution on a digital computer. An example is considered for which the exact solution was known; a comparison to the finite-difference solution for this example is also made.

scholarly journals Pyrolysis of bromobenzene by the toluene carrier technique and determination of D(C6H5—Br)

1978 ◽  
Vol 56 (11) ◽  
pp. 1589-1592 ◽  
Author(s):  
R. John Kominar ◽  
Michael J. Krech ◽  
Stanley James W. Price
Keyword(s):  
Activation Energy ◽  
Experimental Method ◽  
Arrhenius Equation ◽  
First Order ◽  
Temperature Range

The pyrolysis of C6H5Br bas been studied by the toluene carrier technique over the temperature range 1018 to 1126 K using contact times of 1.18 to 2.85 s and total pressures of 3.8 to 4.4 kPa. Percent decomposition based on analyses of residual C6H5Br ranged from 4 to 89%. When HBr was trapped out and quantitatively determined it accounted for more than 95% of the bromine expected. Within the limits of the experimental method the decomposition was found to be homogeneous and first order.[Formula: see text]The Arrhenius equation for reaction [1] is[Formula: see text]Making an approximate correction of the activation energy to 298 K then gives D(C6H5—Br) = 313 ± 5.4 kJ mol−1.

scholarly journals Experimental Method for Determination of Boundary Conditions of Heat Exchange in Parts of External Combustion Engines

2017 ◽  
Vol 20 (4) ◽  
pp. 82
Author(s):  
V A Kulinkov ◽  
V N Syakterev ◽  
V V Syaktereva ◽  
I L Okhilkov
Keyword(s):  
Heat Exchange ◽  
Boundary Conditions ◽  
Experimental Method ◽  
Combustion Engines ◽  
External Combustion

Представлено обоснование экспериментального метода определения граничных условий теплообмена в камере сгорания двигателей внутреннего сгорания. Показано, что, несмотря на большие возможности современных численных методов определения теплового состояния деталей двигателей и имеющихся на их основе современных интегрированных пакетов, точность получаемых результатов определения теплового состояния деталей двигателя, образующих камеру сгорания, зависит от точности экспериментального определения граничных условий теплообмена. Граничными условиями теплообмена для дифференциального уравнения, описывающего процесс нестационарной теплоотдачи от рабочего тела к стенкам деталей, образующих камеру сгорания двигателя, являются значения мгновенного коэффициента теплоотдачи от газа к стенкам деталей камеры сгорания, температура газа в камере сгорания, мгновенная температура поверхности деталей камеры сгорания и температурный градиент по нормали к поверхности деталей. Для определения коэффициента теплоотдачи от газа к стенкам деталей, образующих камеру сгорания двигателя, разработан метод измерения температуры пламени в камере сгорания на основе пирометрии спектрального отношения со специальной оптической системой с интерференционными светофильтрами. Для измерения мгновенной температуры поверхности деталей камеры сгорания и температурного градиента по нормали к поверхности деталей разработана пленочная термопара и проведено исследование ее динамических характеристик. Для проведения экспериментальных исследований разработана усилительно-регистрирующая аппаратура и проведено экспериментальное измерение основных параметров теплообмена в камере сгорания двигателя. Полученные результаты подтверждают эффективность предложенных методов для экспериментального определения граничных условий теплообмена в двигателях внутреннего сгорания.

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