• No results found

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal , Volume 6, Issue 4, April 2016)

N/A
N/A
Protected

Academic year: 2020

Share "International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal , Volume 6, Issue 4, April 2016)"

Copied!
9
0
0

Loading.... (view fulltext now)

Full text

(1)

International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 6, Issue 4, April 2016)

1

The Numerical Experimental Verification of Evolutional

Theory of Identification of Mathematical Models of

Corrosive Destruction under Stress. Compressed Shell

George Filatov

Professor, Doctor of Techn. Sciences, Dnepropetrovsk State Agrarian-Economic University, Ukraine

Abstract — The results of numeral experimentation are

in-process expounded on COMPUTERS, related to the evolution of constructions in the process of their optimum planning and evolution of mathematical models of corrosive destruction, taking into account an influence of the stress-strained state on the rate of corrosion. The object of investigation is the axially compressed cylindrical shell.

Keywords — Corrosion destruction, Evolution Theory,

Identification, Mathematical Models, Optimal Design.

I. INTRODUCTION

The theoretical aspects of problem were considered in previous issue of journal IJETAE [1]. Information of the numeral experiment was there resulted on COMPUTER on the example of momentless shell, loaded with inside pressure at influence of aggressive environment. In this paper the results of experimental researches are brought on the example of the optimum planning of axially compressed cylindrical shell subjected to influence of aggressive environment. As well as in previous work {1] two mathematical models of corrosive destruction of constructions under stress are used:

I.G. Ovchinnikov’s model MMSS [2]:



i i thr

dt

d

; (1)

V.G. Karpunin’s model MMS [3]:



i

dt

d

.

(2)

The object of investigation is the factor

of the influence of stress-strained state of construction (SSS) on the corrosion rate. For identification of these mathematical models is used the random search method [4].

II.THE NUMERICAL EXPERIMENTS.

1. Axially compressed cylindrical shell. I.G.

Ovchinnikov’s Model

Fig.1. Estimated shell scheme

The cylindrical shell of the wall thickness

and the radius of the middle surface

R

is compressed by a longitudinal force

N

(Fig.1) and is subjected to corrosion of the inner wall surface. According to I.G. Ovchinnikov’s model the corrosion damage depth is determined by the expression (1). Taking the corrosion rate of unstressed metal

0

, transform the expression (1) to the form:

 

 

,

2

1

1

1 2

1

  

j

k

k k k

j

t

t

R

N

E

t

k

1

,

2

,...,

j

(3)

where the expression

 

2

2

1

R

N

E

f

is

(2)

International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 6, Issue 4, April 2016)

2

We form the functional:

 

,

2

1

2 1 1 2 1





   j k k k k e

j

t

t

R

N

E

J

j

1

,

2

,...,

n

;

k

1

,

2

,...,

j

(4)

W

ej  experimental depth of corrosion

damage.

[image:2.595.77.547.120.795.2]

Experimental data are presented in Table 1

Table 1 The experimental data

Observing Time (years)

0,1643 0,5753 1,0219 1,4410 2,0191 2,4602 2,957 3,2000

The depth of corrosion damage (sm))

0,0008 0,00016 0,00024 0,00032 0,0004 0,00048 0,00056 0,00064

The task of the determining of the coefficient

is solved by the identifying the model (3) by using an experimental data. Introducing a vector of govern

variables

X

 

x

1 and denoting

x

1

, we get the mathematical programming problem: find a minimum of the functional (4), when the restrictions are carry out:

g

1

 

X

x

1

x

1

0

;

g

2

 

X

x

1

x

1

0

;

(5) The solution of the problem of mathematical programming (4)−(5) is used by the random search method SGEF [4] with the following initial data:

1000

N

кН;

E

2

,

1

10

5МПа;

0

,

3

; n = 9,

 

1

,

0

,

1

 

0

,

0

1

x

x

.

At the first stage of research we choose a point in a permissible space of parameters with coordinates:

04

,

0

0

m;

R

0

2

m and carry out an identification of model for this point using the procedure described above. As a result we obtain the coefficient of SSS influence on the rate of corrosion process corresponding to this point

0

,

448707

.

Further, from the point with coordinates:

04

,

0

0

m;

R

0

2

m and with the coefficient

448707

,

0

perform the optimization of shell. For the considered shell as the target function takes the cross-sectional area of the cylindrical part:

A

2

R

. (6)

The restrictions are adduced:

N

E

2 2

1

3

2

; (7)

N

L

R

E

2 3 3

; (8)

N

R

T

2

; (9)

;

R

R

R

. (10)

The restriction (7) is a limitation to the critical buckling load for the ideal circular cylinder shell; the restriction (8) is a

load axis of the shell; restriction (9

restriction and, finally, restriction (10) limits the size and thickness of the shell wall.

Using the notation:



R

x

x

E

D

C

L

E

B

A

T 2 1 2 2 3

;

1

3

2

;

2

;

;

2



(11)

And substituting in equations (6)−(10), we obtain the following nonlinear programming problem: to find a non-negative values

x

1 and

x

2 minimizing the function:

 

Ax

1

x

2

F

X

(12)

(3)

International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 6, Issue 4, April 2016)

3

 

 

 

  

 

 

 



   

0

;

0

;

0

;

0

;

0

;

0

;

0

2 2 7 2 2 6 1 1 5 1 1 4 2 1 3 3 2 1 2 2 1 1

x

x

g

x

x

g

x

x

g

x

x

g

N

x

x

C

g

N

x

x

B

g

N

x

D

g

X

X

X

X

X

X

X

(13)

Let us formulate the problem of optimal design: we want to find parameters  and

R

which minimize the cross sectional area of the shell with the following initial

data:

E

8

,

16

10

4МPа;

y

162

МPа;

0

,

3

;

3

L

m. The load on the shell equals

N

1000

kN. Geometric restrictions are: 0,01

x

1

4,0 sm,

1

x

2

200 sm.

Solution of task (12)−(13) was performed using the method of random search SGEF [4]. On the search path was chosen 30 intermediate points in descending order of the objective function and the sampling results are listed in Table 2. Estimated time for which all calculations were carried out, was assumed to be

t

3,2 years.

Таble 2

The results of multiply identification and the optimal design of compressive cylindrical shell. Ovchinnicov’s model MMSS

Starting points Extreme designs

параметры оболочки и коэффициент влияния НДС, глубина коррозионного поражения

A

(sm2)

(sm)

R

(sm)

A

оpt (sm2)

(sm)

R

(sm)

(sm)

1 5026,56 4,000 200,00 0,448707000 117,93 3,753 5,001 1,7877 2 4256,36 3,605 187,93 0,321790600 107,88 3,433 5,001 1,4687 3 3548,49 3,228 174,96 0,223592500 98,459 3,132 5,003 1,1681 4 2899,10 2,833 162,87 0,149254300 89,726 2,854 5,004 0,8902 5 2307,91 2,396 153,31 0,094581950 81,851 2,605 5,000 0,6399 6 1769,55 1,947 144,67 0,055616080 75,020 2,385 5,006 0,4221 7 1279,59 1,484 137,24 0,029073960 69,405 2,203 5,015 0,2436 8 831,34 1,010 131,01 0,012267240 65,214 2,075 5,001 0,1109 9 416,43 0,525 126,34 0,003032155 62,642 1,991 5,006 0,0288 10 356,93 0,430 102,99 0,002262569 62,413 1,970 5,042 0,0215 11 324,01 0,501 135,55 0,001864774 62,307 1,948 5,091 0,0178 12 297,73 0,520 91,173 0,001548672 62,203 1,945 5,089 0,0148 13 291,92 0,554 83,887 0,001511989 62,197 1,936 5,113 0,0145 14 275,13 0,575 76,110 0,001345748 62,148 1,912 5,174 0,0129 15 269,54 0,703 61,057 0,001291586 62,149 1,838 5,383 0,0124 16 257,74 0,737 55,667 0,001159461 62,094 1,948 5,164 0,0111 17 239,10 0,790 48,146 0,001019473 62,056 1,914 5,214 0,0098 18 226,24 0,819 44,360 0,000921929 62,022 1,894 5,211 0,0089 19 213,70 1,279 26,598 0,000811018 61,994 1,909 5,169 0,0078 20 208,30 1,005 32,981 0,000776269 61,967 1,957 5,040 0,0075 21 193,70 1,174 26,260 0,000664819 61,938 1,921 5,132 0,0064 22 184,12 1,340 21,185 0,000500838 61,884 1,936 5,087 0,0048 23 177,77 1,425 19,849 0,000562107 61,904 1,905 5,171 0,0054 24 157,43 2,672 9,378 0,000440354 61,866 1,915 5,142 0,0042 25 132,07 2,170 10,14 0,000294763 61,821 1,925 5,110 0,0028 26 127,00 3,160 6,433 0,000284755 61,819 1,943 5,063 0,0028 27 120,49 3,606 5,318 0,000265616 61,810 1,936 5,080 0,0026 28 119,28 3,306 5,123 0,000253179 61,812 1,908 5,156 0,0024 29 118,15 3,752 5,071 0,000247884 61,812 1,861 5,287 0,0024 30 117,93 3,753 5,001 0,000253305 61,818 1,723 5,710 0,0024

Next for each of the intermediate points was carried out the identification of the mathematical model and found as a result of the identification the coefficient of SSS influence on the rate of corrosion process

(Table 2).

(4)

International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 6, Issue 4, April 2016)

4

Fig.2. The graph of stiffness dependences of the optimal shells on the ratio

for compressive shell. Ovchinnicov’s model MMSS

[image:4.595.71.264.138.303.2]

At the second stage from each of the intermediate points as from the starting points performed the search of the optimal solution with the corresponding to these points the values of the ratio of SSS influence on the rate of corrosion damage. Searching results are listed in Table 2.

Comparing the extreme values of the objective function obtained from the first starting point and last, note that the difference between these values is 2.6%. Fig. 3 shows a plot of extreme values of the objective function of SSS influence on the rate of corrosion process.

In the third stage we specify an extreme solution, given in the last row of the table 2. To do this, taking as a first the starting point with coordinates

1

,

732

sm

and

R

5

,

71

sm and carry out the identification of model (3).

The result that we obtain is the ratio of SSS influence on the rate of corrosion damage equal to

0000688764

,

0

. With this coefficient from

coordinates

1

,

732

sm и

R

5

,

71

sm how from the start, execute shell specifying optimization. We get the extreme value of the objective function

752

,

61

min

A

cm2 and coordinates of the point:

82

,

1

[image:4.595.321.534.148.471.2]

sm и

R

5

,

399

sm. Taking the point with these coordinates as the startsng, carry identification, etc. The results of specifying identifications and optimizations are given in Table 3.

Fig.3. Graph of dependence of extreme significant the objective function value on the of the function of SSS for compressed shell.

Ovchinnikov’s model MMSS

Таble 3

The results of specifying identifications and optimal parameters of the shell after the specify of SSS influence factor

Start point for specifying identification Optimal parameters of shell The depth of damage

A

(sm2)

(sm)

R

(sm)

min

A

(sm2)

(sm)

R

(sm)

(sm)

1 61,818 1,732 5,71 0,0000688764 61,752 1,820 5,399 0,00066 2 61,752 1,820 5,399 0,0000682867 61,752 1,820 5,399 0,00066

As you can see, to refine the resulting extreme value of the objective function it’s necessary only two iterations. The coefficient of influence of SSS, that is adduced in the last line of table 3, is considered as "the best", and the value of the objective function corresponding to the "optimal" coefficient will also be considered as optimal.

[image:4.595.347.519.287.469.2]
(5)

International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 6, Issue 4, April 2016)

[image:5.595.69.531.168.291.2]

5

Table 4

The results of the search of optimal solutions of various randomly selected starting points with "optimal" ratio of SSS influence on the rate of the corrosion process

The starting points Optimum shell parameters.

The depth of damage

A

(sm2)

h

(sm)

R

(sm) min

A

(sm2)

h

(sm)

R

(sm)

(sm)

1 12566,6 5,00 400,0 61,751 1,837 5,349 0,00067 2 4712,39 3,00 250,0 61,765 1,414 6,952 0,00067 3 3441,59 2,50 200,0 61,755 1,621 6,063 0,00067 4 1431,72 1,50 150,0 61,754 1,880 5,227 0,00067 5 1357,17 1,20 180,0 61,757 1,464 6,711 0,00067

In the fourth phase we will examine the dependence of the depth of corrosion damage on the function of SSS influence on the rate of corrosion. The values of the depth of corrosion damage calculated for the extreme design projects of the optimal shells, obtained from the intermediate points, are shown in the last column in table 2.

The graph of the dependence of the depth of corrosion damage on the SSS influence on the rate of corrosion destruction is shown in Fig. 4,a. In Fig. 4, b are shown the graphs of the dependence of the depth of corrosion damage on the corrosive time for different values of ratio

.

Fig 4. The graph of the dependence of depth of corrosion on the SSS influence on the rate of corrosion damage (a) and the graphs of the dependence of the depth of corrosion damage on the corrosive time for different values of the coefficients

(b).

The rate of corrosion can be considered as a tangent of the angle of slope of curve for

to abscise axis

t

. As for the membrane shell loaded internal pressure, the corrosion rate of the compressed cylindrical shell in an optimum state is the lowest.

2. Axially compressed cylindrical shell. Karpunin’s Model

Considered the same as in the previous section, the cylindrical shell, compressed by an axial force

N

. The thickness of the shell wall

, the radius of the middle surface

R

(Fig.1). Shell is subjected to corrosion on the inner wall surface.

Corrosive depth damage used the Karpunin’s model (MMS) we find the by the expression:

 



,

2

1

1 1

  

j

k

k k k

j

t

t

R

N

t

. (14)

k

1

,

2

,...,

j

The stress function in the equation (14) has the form:

 

R

N

f

[image:5.595.108.490.385.562.2]
(6)

International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 6, Issue 4, April 2016)

6

The coefficient of SSS influence on the rate of corrosion damage, we find by the identification of the model of corrosion destruction (14). For this aim let’s create such functional:



2

1

1 1

2





  

j

k

k k k e

j

t

t

R

N

J

(16)

j

1

,

2

,...,

n

;

k

1

,

2

,...,

j

Where

ej

damage. Experimental data are presented in Table 1. Taking as the govern variable the coefficient of SSS influence on the rate of corrosion process

and noting

it

x

1

get the following mathematical programming problem: find the functional minimum:

 



2

1

1 1

1

2





  

j

k

k k k э

j

t

t

R

N

x

J

X

j

1

,

2

,...,

n

;

k

1

,

2

,...,

j

(17) At the performance of restrictions:

g

1

 

X

x

1

x

1

0

;

, (18)

g

2

 

X

x

1

x

1

0

,

 

x

1

X

 the vector of govern variables. The problem (17)−(18) is solved by the method of random search SGEF with the following initial data:

1000

N

kN;

E

2

,

1

10

5МPа;

0

,

3

;

9

n

,

x

1

 

1

,

0

,

x

1

 

0

,

0

.

At the first stage of research we choose a point in a space of permissible parameters with coordinates:

04

,

0

0

m,

R

0

2

m and perform for this point identification of corrosive model (14) using the procedure described above. As a result, we obtain the coefficient of SSS influence on the rate of corrosion damage

0

,

0000109395

corresponding to this point. With this factor from the point with coordinates

04

,

0

0

(7)

International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 6, Issue 4, April 2016)

7

Таble 5

The results of multiple identification at the optimal design of compressed cylindrical shell. Karpunin’s Model MMS

Starting point The optimal parameters of shell

and the coefficient of the effect of SSS, the depth of corrosion damage

A(sm2)

(sm)

R

(sm)

оpt

A

(sm2)

(sm)

R

(sm)

(sm)

1 5026,56 4,000 200,00 0,0000109395 63,387 2,014 5,009 0,0523 2 4459,35 3,841 184,76 0,0000097039 63,199 2,004 5,019 0,0465 3 3929,61 3,670 170,43 0,0000085535 63,023 2,006 5,095 0,0410 4 3414,92 3,550 153,12 0,0000074328 62,889 1,966 5,090 0,0357 5 2928,78 3,464 134,57 0,0000063742 62,701 1,987 5,021 0,0307 6 2468,48 3,405 115,37 0,0000053718 62,560 1,953 5,096 0,0259 7 2022,47 3,347 96,16 0,0000044011 62,401 1,976 5,026 0,0213 8 1589,95 3,283 77,09 0,0000034609 62,258 1,973 5,023 0,0167 9 1172,75 3,222 57,93 0,0000025524 62,135 1,942 5,092 0,0123 10 780,76 3,247 38,27 0,0000016924 61,995 1,960 5,095 0,0082 11 384,71 3,179 19,26 0,0000008372 61,859 1,926 5,110 0,0041 12 237,898 3,156 12,00 0,0000005177 61,816 1,828 5,381 0,0025 13 218,97 3,107 11,22 0,0000004766 61,802 1,955 5,095 0,0023 14 159,652 3,238 7,857 0,0000003461 61,787 1,915 5,134 0,0017 15 118,81 3,281 5,764 0,0000002586 61,776 1,645 5,976 0,0013 16 107,53 3,330 5,140 0,0000002431 61,775 1,524 5,095 0,0011 17 98,413 2,914 5,375 0,0000002142 61,763 1,900 5,171 0,0010 18 93,199 2,920 5,079 0,0000002028 61,767 1,708 5,753 0,00098 19 90,059 2,621 5,468 0,0000001960 61,766 1,846 5,324 0,00095 20 88,985 2,337 6,061 0,0000001937 61,766 1,647 5,967 0,00094 21 86,365 2,555 5,380 0,0000001879 61,764 1,705 5,764 0,00091 22 80,593 2,513 5,105 0,0000001754 61,760 1,675 5,866 0,00085 23 75,629 2,190 5,496 0,0000001646 61,757 1,722 5,705 0,00079 24 72,366 1,904 6,049 0,0000001575 61,757 1,913 5,137 0,00076 25 69,629 0,950 11,60 0,0000001507 61,754 1,868 5,261 0,00073 26 67,239 1,486 7,201 0,0000001463 61,756 1,762 5,577 0,00071 27 66,984 0,629 15,46 0,0000001456 61,756 1,793 5,479 0,00071 28 64,144 1,580 6,463 0,0000001396 61,754 1,789 5,491 0,00068 29 63,485 1,977 5,106 0,0000001380 61,751 1,895 5,186 0,00068 30 63,383 2,014 5,010 0,0000001379 61,751 1,938 5,071 0,00067

In the second phase from each intermediate point as from the starting point, we perform the optimization of shell with the corresponding ratio

.

Results of optimization (objective function value, the wall thickness and the radius of the middle surface of the shell) enter in the table 5 and construct a graph of the dependence of objective function on the effect of the SSS on the rate of the corrosion process (Fig.5, a) and on the contrary (Fig. 5,b).

(8)

International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 6, Issue 4, April 2016)

8

Таble 6

The results of the search an optimal decision from the various randomly selected starting points with "optimal" ratio of SSS effect on the rate of the corrosion process

Starting points Optimal parameters of shell

The depth of damage

A

(sm2)

(sm)

R

(sm) min

A

(sm2)

(sm)

R

(sm)

(sm)

1 12566,6 5,00 400,0 61,751 1,837 5,349 0,00067 2 4712,39 3,00 250,0 61,765 1,414 6,952 0,00067 3 3441,59 2,50 200,0 61,755 1,621 6,063 0,00067 4 1431,72 1,50 150,0 61,754 1,880 5,227 0,00067 5 1357,17 1,20 180,0 61,757 1,464 6,711 0,00067

As shown in Table 6, the optimal values of the objective function is almost the same. A slight variation of these values is explained by the stochastic nature of the search algorithm.

In the fourth stage we investigated the dependence of the depth of corrosion damage on the effect of SSS on the rate of the corrosion process. The depth data of corrosion damage, corresponding to the extreme values of the objective function, is given in the last column of Table 5. A plot of the dependence of parameter of damage

on the effect of the SSS function on the corrosion rate is shown in Fig. 6,a.

The graph clearly shows the direct relationship between the depth of the damage and the influence of

SSS function

 

A

: the decreasing of the value of function of SSS influence on the rate of corrosion decreases the depth of corrosion damage. If the value of

[image:8.595.62.540.496.612.2]

coefficient

 

A

is close to "optimal" the depth of corrosion damage is stabilized and no longer growing or growing very slowly. Table 7 shows the calculation of the depth of corrosion damage during corrosion time for different size ratios of SSS effect on the rate of corrosion, and Fig.6,b shows a corresponding graph of the dependence of parameter of shell damage on corrosive time.

Table 7

The dependence of the depth of corrosion damage on time of corrosion at different values of the influence function SSS

Time

t

(years)

The depth of corrosion damage (m)

7 10 37 , 8   

5,18107 3,46107 2,59107 1,75107 1,58107 1,38107

(9)

International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 6, Issue 4, April 2016)

9

Fig.6. The dependence of corrosion damage depth (year) on the SSS influence function (a) and the dependence of the depth of corrosion damage on corrosion time for different values of the influence functions SSS (b)

The graph shows that the smaller the value of influence function of SSS on the corrosion rate, the lower the slope of the curve depending on the depth of corrosion damage during corrosion time. From this it follows that, the closer to the value of objective function

to optimum, the lower the rate of corrosion process. The lowest values of corrosion rate reaches at "optimal" coefficient of SSS influence, i.e, when the objective function is in the optimal state.

III. INTERMEDIATE CONCLUSIONS

1.As well as in previous paper [1], for both mathematical models of corrosive destruction (2) and (3) dependence of the coefficient of influence of SSS on the rate of corrosive destruction on SSS of construction (Fig.2 and Fig. 5) is observed. 2.There is dependence of extreme values of objective

function on the values of coefficient of influence of SSS on the rate of corrosive process (Fig.3) and (Fig. 6). Dependence is straight proportional: the value of objective function diminishes with the diminishing of coefficient of influence of SSS. At the «optimum» value of coefficient of influence of SSS

on the rate of corrosion the economy of

mass at comparison of extreme values of objective functions is 48,2% for the Ovchinnikov’s model of and 2,6% for the Karpunin’s model. Such difference can be explained that the model MMSS is more exact, because takes into account not only influence of stresses on the rate of corrosive destruction but also influence of deformations.

The similar difference of economy on mass at comparison of extreme values of objective functions was observed and for the thin-walled momentless shell, the results of research of which are published in the paper [1] − for model MMSS the economy was 20,18%, for the model MMS the economy was 20,18%, for the model MMS was 8,57%.

3. The dependence of the depth of corrosive damage on the influence of SSS function on the rate of corrosion process is observed (Fig.4,a) and (Fig. 7,а). Dependence is straight proportional: the depth of corrosive destruction of shell wall diminishes with the diminishing of coefficient of influence of SSS..

4. It is observed, that the rate of corrosion depends on the value of the coefficient of influence of SSS. The least rate of corrosion damage arises up in an optimum state of shell.

In the next issue of journal IJETAE the results of numerical researches will be resulted on the examples of the optimum planning of beams. After this it will be possible to do the final conclusions and formulate the recommendation on determination of optimum values of the ratio of influence of SSS

on the rate of corrosive destruction.

REFERENCES

[1] Filatov G.V. The Foundations of the Evolution Theory of Identification of Mathematical Models of Corrosion Destruction at the Optimal Planning of Constructions [Text] // G.V. Filatov/ −

International Journal of Emerging Technology & Advanced Engg., Volume 6, Issue 3, March 2016, p.p.166-180.

[2] Petrov, V.V Calculation of Structural Elements, Interacting with Aggressive Media [Text]: Monograph / I.G.Ovchinnikov, Yu.M.Shihov. − Saratov: Saratov State University. 1987. − 288 p. [3] Karpunin, V.G. Study Bending and Stability of Plates and Shells

Based on a Solid Corrosion [Text]: Author. Dis .... Cand. Tehn. Science / V.G Karpunin. − Sverdlovsk. 1977 − 24 p.

Figure

Table 1 The experimental data
Fig. 3 shows a plot of extreme values of the objective function of SSS influence on the rate of corrosion process
Table 4 The results of the search of optimal solutions of various randomly selected starting points with "optimal" ratio of SSS influence on the rate of the
Table 7

References

Related documents

The pure Krishna River Water has Good Water Quality, but due to amalgamation of Godavari water its nature changed from Good Quality Region to Poor. water

Special Relativity, Varying Speed of Light, Hardy’s Quantum Entanglement, Dark Energy, Measure Concentration in Banach Space, ‘tHooft Fractal Spacetime, Witten Fractal

In addition to PUMA induction, TNF inhibition, an impor- tant means for treatment of IBD (1), suppressed DSS-induced colitis (Figure 7C), colonic damage (Figure 7D and

The identification of surrogates of conservation, the formulation of conservation goals, the prioritization of key ar- eas and the formulation of conservation strategies based on

Spontaneous and progressive inflammation in the gastric mucosa of the Tff1-knockout mice

In the ti- tanic sweepstake, extraneous actors such as party leaders, presidency, inspector general of the police, Afenifere (a yorubal socio-cultural group) and

Interactions between fetal trophoblast and mater- nal uterine NK (uNK) cells — specifically interactions between HLA-C molecules expressed by the fetal tro- phoblast cells and

This study aimed to clarify the relationship between muscle activity and pain by focusing on muscle activity during positioning for craniocaudal (CC) imaging complementing MLO