Dynamic Analysis Of Concrete Minaret Biology Essay

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The aim of this research is determination of maximum displacement of top of minaret under earthquake force using Gene Expression Programming. Gene expression programming, a genotype/phenotype genetic algorithm (linear and ramified), is presented here for the first time as a new technique for the creation of computer programs. Gene expression programing uses character linear chromosomes composed of genes structurally organized in a head and a tail. The chromosomes function as a genome and are subjected to modification by means of mutation, transposition, root transposition, gene transposition, gene recombination, and one- and two-point recombination. The chromosomes encode expression trees which are the object of selection. The creation of these separate entities) genome and expression tree) with distinct functions allows the algorithm to perform with high efficiency that greatly surpasses existing adaptive techniques [8]

In this paper, maximum displacement of top of minaret is calculated using SAP2000 software. 50 minarets with diameter of 2.5 meters and different thicknesses were analyzed. Then three parameters-length, diameter and thickness- and displacement in top of minaret (input and output, respectively), which are calculated by SAP2000 software, delivered to Gene Expression Programming for modeling and choosing the best model and delivering mathematical formulas and expression tree. Also, regard to maximum displacement in top of minaret, 50 extra samples using SAP2000 software created to test Gene Expression Programming. The models tested and the results are presented in tables and diagrams.

Gene Expression Programming (GEP) is, like genetic algorithm (GAS) and genetic programming (GP), a genetic algorithm as it uses populations of individuals, selects them according to fitness, and introduces genetic variation using one or more genetic operators. The fundamental difference between the three algorithms resides in the nature of the individuals are linear strings of fixed length (chromosomes); in GP the individuals are nonlinear entities of different sizes and shapes (parse trees) and in GEP the individuals are encoded as linear strings of fixed length (the genome or chromosomes) which are afterwards expressed as nonlinear entities of different sizes and shapes (i.e., simple diagram representations or expression trees). In this research, it has ben tried to study concrete minaret and this pendulum structure performance under earthquake using Gene Expression Programming (GEP) [7].

In lexicon, minaret means light and fire, but it is used for a tall and slender structure attached to mosques and holly shrine from which were used to call to prayers or guidance of passengers near the roads, mosques, inns (caravanserai) or schools. Because of lighting or firing up on it for guidance in night, it nominated minaret.

According some parameters such as diagonal, thickness and height of concrete minarets, the gene expression programming function were presented. Then after some genetic operators (reproduction, crossing, mutation and etc.) for each offspring, final population obtained which is maximum displacement in top of the minaret. Finally, the gene expression tree outputs were mathematical formula details for computing of maximum displacement in top of minarets. Also, to test of gene expression programming models, it is necessary to have secondary population by data. Then the results which are presented by SAP2000 software were compared by the best model of gene expression programming.

GENE EXPRESSION PROGRAMMING

The interplay of chromosomes (replicators) and expression trees (phenotype) in GEP implies an unequivocal translation system for translating the language of chromosomes into the language of expression trees (ETs). The structural or organization of GEP chromosomes presented in this work allows a truly functional genotype/phenotype relationship, as any modification made in genome always results in syntactically correct ETs or programs. [11] Indeed, the varied set of genetic operators developed to introduce genetic diversity in GEP populations always produces valid ETs. Thus, GEP is an artificial life system, well established beyond the replicator threshold, capable of adaptation and evolution. [9]

The advantages of a system like GEP are clear from nature, but the most important should be emphasized. First, the chromosomes are simple entitles: linear, compact, relatively small, easy to manipulate genetically (replicate, mutate, recombine, transpose, etc.). Second, the ETs are exclusively the expression of their respective chromosomes; they are the entities upon which selection acts and, according to fitness, they are selected to reproduce with modification .During reproduction it is the chromosomes of the individuals not the ETs, which are reproduced with modification and transmitted to the next generation. [12]

Indeed, in the most complex problem presented in this work, the evaluation of cellular automata rules for the density- classification task, GEP surpasses GP by more than four orders of magnitude. The presented work shows the structural organization of GEP chromosomes; how the language of the chromosomes is translated into language of ETs; how the chromosomes functions as genotype and the ETs as phenotype; and how an individual program is created, matured and reproduced, leaving offspring with new properties, thus capable of adaptation [14].

The flowchart of gene expression algorithm (GEA) begins with the random generation of the chromosomes of the initial population. Then the chromosomes are expressed and the fitness of each individual is evaluated. The individuals are then selected according to fitness to produce with modification, leaving progeny with new traits [13]. The individuals of this new generation are, in their return, subjected to the same developmental process expression of the genomes, confrontation of selection environment, and reproduction with modification. The process is repeated for a certain number of generation or until a solution has been found. [10]

Note that reproduction includes not only replication but also the action of genetic operators capable of erecting genetic diversity. During replication, the genome is copied and transmitted to the next generation. Obviously, replication alone cannot introduce variation: only with the action of the remaining operators is genetic variation introduced into the population. These operators randomly select the chromosomes to be modified. Thus, in GEP, a chromosome might be modified by one or several operators at a time or not be modified at all [15].

MINARETS

Minarets include three distinct parts: base, body and cape. Because the minaret with high height and low area tolerates high pressures on its base area, weakness of bases leads to collapse of the structure. So, for more firmness and confidence, the ground will be dig deeply, and then it will be filling by foundation paste and stone. Then the platform or the main bases of minaret will lay the foundation by stone and brick. Usually, the bases are in shape of square or multisided and the minaret is located in the center of it.[2]

There are different body forms of minaret in Islamic countries which are determined by innovation and talents of architects in these countries. For examples, in Palestine, Syria and Spain, the minarets are made with square bases. In Abbasi government period were made conical with outer turret steps. In bottleneck, minaret body will be polyhedral or circular with increasing cross section. This section makes Moazen place. The minaret walls will be slender as a regular column and its height is 2-3 meters above minaret cape. The minaret will be exposed to static and dynamic loads. The static loads include dead loads, live loads and pressure of changing temperatures loads. The dead and live loads are calculated by masonry density. Dynamic loads include inertia loads which are originated from structure vibration. In figure 1 shows a reinforced concrete minaret. [1]

Fig.1.Concrete minaret

ANALYSIS METHOD

One of difficulties in structural designing is that after linear analysis, they are uninformed of their structure capacity. They should know about the capacity and performance level of their structure or are structures which are designed by previous regulations, are resistant or not. They can find weakness and sensitive points in their designed structure to refine it. So, the necessity of using nonlinear analysis is obvious. Nonlinear analysis performed in two methods: [4]

1-Dynamic nonlinear analysis with time history method

2-Static nonlinear analysis or pushover

Time history nonlinear analysis evaluates a structure in special earthquake for related values of acceleration-time. It means that other earthquake will happen which in view point of acceleration density, vibration frequency, earthquake duration and etc., is differ with earthquake which was under dynamic analysis [3]. Time dynamic analysis (or time history) is used to determine structure momentary response and include two different methods: elastic- linear and inelastic- nonlinear. It is recommended that damping ratio in elastic- linear is 5%, in nonlinear calculations; it is determined by specialized recommendations and nonlinear behavior of structure. In this paper, using time dynamic analysis method (time history) and acceleration-time components in El Centro earthquake in 1940, dynamic analysis of concrete minaret performed. [6]

DYNAMIC ANALYSIS IN SAP2000

In this paper, point of support in minaret base is fixed. Meshbandi minaret member (fig.2)is calculated in the best calcification ( meshbandi is divided to smaller parts and is stopped so that the results don’t change). To study of dynamic behavior of concrete minaret, three parameters- height, diameter and thickness- are used. The height, diameter and thickness are 21 to 66, 2.5 to 7 and 0.2 to 0.46m, respectively. Also, modeling is presented on a cylindered minaret with height of 30 m, diameter of 2 m and thickness of 20 cm. Approximate dimensions of this minaret is shown in figure 3 [5].

Figure2. Meshing of minaret Figure 3. Minaret modeling

DATA MODELING USING GENE EXPRESSION PROGRAMMING (GEP)

Concrete specification

Concrete compressive strength ()

Kg/cm2

Density kg/m3

Youngʾs modulus (E)

kg/cm2

Poissonʾs ratio ()

Concrete minaret

210

2400

2188197889

0.2

Table 1: General characteristics of used concrete minaret [32]

THE ANALYSED RESULTSS OF SAP2000 SOFTEWARE IN CALCULATION OF TOP DISPLACEMENT OF MINARET

The results of analysis of 50 samples of concrete minaret and displacement in top of minaret as output are presented in table 2.

Raw

Average diameter of minaret (m)

Length of minaret (m)

Thickness of minaret (m)

Weight of minaret (kg)

Top displacement of minaret by SAP2000(m)

1

2.5

21

0.21

86602.66479

0.007924757

2

2.5

21

0.26

106539.0481

0.007799649

3

2.5

21

0.31

126478.0703

0.007700439

4

2.5

21

0.36

146419.7314

0.007614157

5

2.5

21

0.41

166364.0315

0.007534257

6

2.5

26

0.21

106394.6982

0.018418875

7

2.5

26

0.26

131043.4703

0.018157624

8

2.5

26

0.31

155694.8815

0.017946723

9

2.5

26

0.36

180348.9315

0.017760082

10

2.5

26

0.41

205005.6205

0.017584565

11

2.5

31

0.21

126186.7316

0.036910664

12

2.5

31

0.26

155547.8926

0.036433329

13

2.5

31

0.31

184911.6926

0.036041493

14

2.5

31

0.36

214278.1316

0.035689217

15

2.5

31

0.41

243647.2095

0.035353431

16

2.5

36

0.21

145978.7649

0.066684417

17

2.5

36

0.26

180052.3149

0.065888382

18

2.5

36

0.31

214128.5038

0.0652247

19

2.5

36

0.36

248207.3317

0.064619486

20

2.5

36

0.41

282288.7985

0.064035734

21

2.5

41

0.21

165770.7983

0.111589017

22

2.5

41

0.26

204556.7372

0.110346894

23

2.5

41

0.31

243345.315

0.109296264

24

2.5

41

0.36

282136.5318

0.108325844

25

2.5

41

0.41

320930.3874

0.107380039

26

2.5

46

0.21

185562.8317

0.176037943

27

2.5

46

0.26

229061.1595

0.174195471

28

2.5

46

0.31

272562.1262

0.172616073

29

2.5

46

0.36

316065.7318

0.171140269

30

2.5

46

0.41

359571.9764

0.169688598

31

2.5

51

0.21

205354.8651

0.265009269

32

2.5

51

0.26

253565.5817

0.26238321

33

2.5

51

0.31

301778.9374

0.26010398

34

2.5

51

0.36

349994.9319

0.257951769

35

2.5

51

0.41

398213.5654

0.255817348

36

2.5

56

0.21

225146.8985

0.384045659

37

2.5

56

0.26

278070.004

0.380421705

38

2.5

56

0.31

330995.7485

0.377239807

39

2.5

56

0.36

383924.132

0.374206376

40

2.5

56

0.41

436855.1544

0.371175911

41

2.5

61

0.21

244938.9318

0.539254375

42

2.5

61

0.26

302574.4263

0.53438504

43

2.5

61

0.31

360212.5597

0.530063343

44

2.5

61

0.36

417853.3321

0.525907151

45

2.5

61

0.41

475496.7434

0.521727594

46

2.5

66

0.21

264730.9652

0.737307268

47

2.5

66

0.26

327078.8486

0.730909794

48

2.5

66

0.31

389429.3709

0.725174346

49

2.5

66

0.36

451782.5322

0.719614182

50

2.5

66

0.41

514138.3323

0.713989391

Table 2: The results of analysis of concrete minaret with diameter of 2.5 m and output of displacement in top of minaret using SAP2000 software

MODELING USING GEP FOR CALCULATION OF TOP DISPLACEMENT OF MINARET

Using the results in table 2 as primary population in gene expression programming, some models were provided. Then the best model was chose, which its tree diagram and formula details are presented in figure 4 figure 5, respectively.

Figure 3: Expression tree of the best gene expression programming model in calculation of top displacement of concrete minaret with diagonal of 2.5m

Figure 5: Mathematic formula details of the best gene expression programming model in calculation of displacement of top of concrete minaret with diagonal of 2.5m

TEST OF MODELS USING GENE EXPRESSION PROGRAMMING (GEP)

To test of provided gene expression programming models, 50 other model samples were provided for each concrete minaret with determined diameter and according minaret period, displacement of top of minaret and base shearing of minaret. Then the models were tested and the results presented in tables and diagrams.

To test of gene expression programming models, the secondary population is needed. This population is unique and may not found in primary population. Then the results of minaret period, displacement of top of the minaret and base shearing of minaret, using SAP200 software are compared with the best model of gene expression modeling.

COMPARING GENE EXPRESSION PROGRAMMING AND SAP2000 SOFTEWARE FOR TOP DISPLACEMENT OF MINARET

Using SAP2000 software, the displacement of 50 samples of concrete minaret were calculated and compared with the best model of gene expression programming. The results are presented in table 3. The diagram of comparing displacement in top of minaret using SAP2000 software and gene expression programming model is presented in figure 6. Also, the diagram of comparing sample errors percent is presented in figure 7. In this model, the average of error percent is 13.21%.

Raw

Average diameter of minaret (m)

Length of minaret (m)

Thickness of minaret (m)

Weight of minaret (kg)

Top displacement of minaret by SAP2000(m)

Top displacement of minaret by gene programming (m)

Error percent

1

3

20

0.2

95482.41146

0.004643916

0.004669319

0.547018779

2

3

20

0.25

118272.0897

0.004554674

0.004944103

8.550103952

3

3

20

0.3

141064.4068

0.004489401

0.004730109

5.361704785

4

3

20

0.35

163859.3629

0.004436891

0.004824855

8.744038981

5

3

20

0.4

186656.9579

0.00439157

0.004691865

6.837996925

6

3

25

0.2

118101.8782

0.011177557

0.010292875

7.91480323

7

3

25

0.25

146546.4231

0.010987678

0.011491206

4.582652566

8

3

25

0.3

174993.6069

0.010847009

0.010513026

3.079026659

9

3

25

0.35

203443.4297

0.010732184

0.011311947

5.402094534

10

3

25

0.4

231895.8914

0.010631591

0.011017948

3.634048237

11

3

30

0.2

140721.3449

0.022924402

0.024005135

4.714333879

12

3

30

0.25

174820.7565

0.022574972

0.021616397

4.246184463

13

3

30

0.3

208922.807

0.02231285

0.025181688

12.85733369

14

3

30

0.35

243027.4964

0.022095911

0.024253409

9.764240292

15

3

30

0.4

277134.8248

0.021903231

0.02455096

12.0883012

16

3

35

0.2

163340.8116

0.042104474

0.039342098

6.560766003

17

3

35

0.25

203095.0899

0.041521072

0.039866147

3.985748893

18

3

35

0.3

242852.0071

0.041078152

0.043425942

5.715424652

19

3

35

0.35

282611.5632

0.040706795

0.040381043

0.800240651

20

3

35

0.4

322373.7582

0.040372802

0.044334771

9.813461016

21

3

40

0.2

185960.2783

0.071330894

0.075253423

5.499060533

22

3

40

0.25

231369.4233

0.070422619

0.066673884

5.323196219

23

3

40

0.3

276781.2071

0.069725075

0.064795634

7.06982548

24

3

40

0.35

322195.6299

0.069133103

0.076482481

10.63076487

25

3

40

0.4

367612.6917

0.068594563

0.074376429

8.429043352

26

3

45

0.2

208579.7451

0.113609882

0.115231068

1.426976927

27

3

45

0.25

259643.7567

0.112268373

0.108052426

3.755240246

28

3

45

0.3

310710.4072

0.111226717

0.113496749

2.040904917

29

3

45

0.35

361779.6967

0.110332645

0.102043878

7.512525033

30

3

45

0.4

412851.6251

0.109510724

0.108144515

1.247557047

31

3

50

0.2

231199.2118

0.172340755

0.177107358

2.76580114

32

3

50

0.25

287918.0901

0.170439219

0.17578411

3.135951312

33

3

50

0.3

344639.6073

0.168947114

0.174717716

3.415626418

34

3

50

0.35

401363.7635

0.167652774

0.190955454

13.89936985

35

3

50

0.4

458090.5586

0.16645144

0.167692515

0.745607581

36

3

55

0.2

253818.6785

0.25131593

0.235326081

6.362449408

37

3

55

0.25

316192.4235

0.248708165

0.248736933

0.011567042

38

3

55

0.3

378568.8074

0.246641233

0.259604505

5.255922345

39

3

55

0.35

440947.8302

0.244830387

0.232681328

4.962235032

40

3

55

0.4

503329.492

0.243134819

0.265914957

9.369344176

41

3

60

0.2

276438.1452

0.354720922

0.338059328

4.697099209

42

3

60

0.25

344466.7569

0.351240339

0.386977445

10.17454499

43

3

60

0.3

412498.0075

0.348454983

0.359812217

3.259311783

44

3

60

0.35

480531.897

0.345991924

0.353625247

2.206214192

45

3

60

0.4

548568.4254

0.343666914

0.349950454

1.828380944

46

3

65

0.2

299057.6119

0.487134343

0.467778037

3.973504652

47

3

65

0.25

372741.0903

0.482592992

0.528766999

9.567898419

48

3

65

0.3

446427.2075

0.478925204

0.484749564

1.216131329

49

3

65

0.35

520115.9637

0.475653368

0.512047585

7.651415866

50

3

65

0.4

593807.3589

0.472541728

0.472994157

0.095743883

Table 3: The results of comparing the best model of gene expression programming and SAP2000 software in displacement of top of concrete minaret with diameter of 3 m

Figure 6: Comparing the best model of gene expression programming and SAP2000 software in displacement of top of concrete minaret with diameter of 3 m

Figure 7: Comparing error percent of the best the best model of gene expression programming and SAP2000 software in calculation of displacement of top of concrete minaret with diameter of 3m

CONCLUSION

According fig.8, the results show that because the results of comparing error percent in gene expression programming (GEP) models are acceptable as compared with SAS2000 software, so using mentioned parameters, we can use gene expression models in determination of displacement of top of concrete minaret.

Figure 8: diagram of comparing error percent of gene expression programming models in concrete minaret

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