بررسی تاریخچه دمایی جوش با روش المان‌مرزی دوگانه‌ای

(1)

رﺎﺗ ﻳ :ﻪﻟﺎﻘﻣ ﻪﭽﺨ

رد ﻳ ﺖﻓﺎ 6 / 9 / 89

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ﺎﺳ رد ﻪﺋارا ﻳ ﺖ 11 / 8 / 90

يا

ﻞﻴﺴﻧاﺮﻔﻳد تﻻدﺎﻌﻣ ﻞﺣ رد

ﻲﻣﻮﻤﻋ باﻮﺟ .ﺖﺳا نﻮﺳاﻮﭘ ﻪﻟدﺎﻌﻣ دراد دﺮﺑرﺎﻛ ﻲﺳﺪﻨﻬﻣ ﻞﺋﺎﺴﻣ زا يرﺎﻴﺴﺑ رد ﻪﻛ ﻢﻬﻣ ﻢﻛﺎﺣ تﻻدﺎﻌﻣ ﻦﻳا زا ﻲ ﺪﻳﺪﺟ رﺎﻜﻫا

ي ياﺮﺑ

شﻮﺟ ﻞﻴﻠﺤﺗ رد

ﻲﻳﺎﻣد ﻪﭽﺨﻳرﺎﺗ ياﺮﺑ ﻲﻘﻴﻗد ﻦﻴﻤﺨﺗ ﺪﻌﺑود شﻮﺟ

ي

ﺮﺣ لﺎﻘﺘﻧا ا ﻲﺳرﺮﺑ و تر

«Research Note

Study of welding temperature history by dual reciprocity

Abstract- Seve

is an important method for solving the partial differential equation in engineering problems. The Poison equation is an appli equation in variou

integrals on the domain boundaries, and one integral in the internal domain which is a drawback for this method. To remove th disadvantage, Dual R

transient zone where not homogeneous part is involved time dependent terms, is solved by this method. The calculation of the welding zone temperature hi

In this work, welding temperature history is obtained using the validation is carried out by commo

code. Because of the method simplicity and low time and error in computation process, the application of Keywords:

رﺎﺗ رد ﺬﭘ ﺎﺳ رد ﻪﺋارا

ود ﻪﻧﺎﮔ يا

ﺐﺳﺎﻨﻣ ﻞﻴﺴﻧاﺮﻔﻳد تﻻدﺎﻌﻣ ﻞﺣ رد

ﻲﻣﻮﻤﻋ باﻮﺟ .ﺖﺳا نﻮﺳاﻮﭘ ﻪﻟدﺎﻌﻣ دراد دﺮﺑرﺎﻛ ﻲﺳﺪﻨﻬﻣ ﻞﺋﺎﺴﻣ زا يرﺎﻴﺴﺑ رد ﻪﻛ ﻢﻬﻣ ﻢﻛﺎﺣ تﻻدﺎﻌﻣ ﻦﻳا زا ﻲ يزﺮﻣ

ﻪﻧﺎﮔود ر ﺪﻳﺪﺟ رﺎﻜﻫا

.دﻮﻤﻧ هدﺎﻔﺘﺳا شور ﻦﻳا زا ناﻮﺗ شﻮﺟ ﻞﻴﻠﺤﺗ رد

ﻢﻬﻣ ﺎﻫ ﻲﻣ ﺪﺷﺎﺑ .

ﻲﻳﺎﻣد ﻪﭽﺨﻳرﺎﺗ ياﺮﺑ ﻲﻘﻴﻗد ﻦﻴﻤﺨﺗ

رد هﺪﺷ ﻞﺣ ﻞﺋﺎﺴﻣ ﺎﺑ ﺪﻛ ﻲﻳﺎﻣزآ ﻲﺘﺳار ،ﻢﻛﺎﺣ ﻲﻜﻳﺰﻴﻓ تﺎﻴﺿﺮﻓ ، ﺮﺣ لﺎﻘﺘﻧا

ﻪﻴﺻﻮﺗ ﻲﻣ دﻮﺷ .

Research Note

Study of welding temperature history by dual reciprocity

Several numerical methods have been emerged to analyze the engineering problem

is an important method for solving the partial differential equation in engineering problems. The Poison equation is an appli equation in various engineering problems. General solution of this equation is obtained based on BEM

integrals on the domain boundaries, and one integral in the internal domain which is a drawback for this method. To remove th disadvantage, Dual Reciprocity Method

transient zone where not homogeneous part is involved time dependent terms, is solved by this method. The calculation of the welding zone temperature history is a significant step for the thermal loading and residual stress analysis of the process.

In this work, welding temperature history is obtained using the validation is carried out by commo

code. Because of the method simplicity and low time and error in computation process, the application of Keywords:Numerical Analyze

نﺎﻤﻟا يزﺮﻣ

ﻲﻟﺎﻬﻧ يﺪﻬﻣ

3

ناﺮﻬﺗ ناﺮﻬﺗ

ﺮﻴﺒﻛﺮﻴﻣا ﻲﺘﻌﻨﺻ هﺎﮕﺸﻧاد ،

، ناﺮﻬﺗ

gasemi@aut.ac.ir

يزﺮﻣ زا شور يﺎﻫ ﺐﺳﺎﻨﻣ

ﻲﻣﻮﻤﻋ باﻮﺟ .ﺖﺳا نﻮﺳاﻮﭘ ﻪﻟدﺎﻌﻣ دراد دﺮﺑرﺎﻛ ﻲﺳﺪﻨﻬﻣ ﻞﺋﺎﺴﻣ زا يرﺎﻴﺴﺑ رد ﻪﻛ ﻢﻬﻣ ﻢﻛﺎﺣ تﻻدﺎﻌﻣ ﻦﻳا زا ﻲ ﻲﻣ ﻒﻳﺮﻌﺗ ﻲﻧورد ﻪﻨﻣاد يور لاﺮﮕﺘﻧا ﻚﻳ و زﺮﻣ يور لاﺮﮕﺘﻧا ود ﻪﺑ دﻮﺷ

. شور نﺎﻤﻟا يزﺮﻣ

ﻲﻣ .دﻮﻤﻧ هدﺎﻔﺘﺳا شور ﻦﻳا زا ناﻮﺗ

جﺎﺟﻮﻋا و هﺪﻧﺎﻤﻴﻗﺎﺑ و ﺪﻧﺎﻤﺴﭘ ﻢﻬﻣ ﺎﻫ

ﻲﻳﺎﻣد ﻪﭽﺨﻳرﺎﺗ ياﺮﺑ ﻲﻘﻴﻗد ﻦﻴﻤﺨﺗ

رد هﺪﺷ ﻞﺣ ﻞﺋﺎﺴﻣ ﺎﺑ ﺪﻛ ﻲﻳﺎﻣزآ ﻲﺘﺳار ،ﻢﻛﺎﺣ ﻲﻜﻳﺰﻴﻓ تﺎﻴﺿﺮﻓ ، زا هدﺎﻔﺘﺳا

نآ ﻪﻴﺻﻮﺗ

Research Note»

Study of welding temperature history by dual reciprocity boundary e

M. Ghassabzadeh

1-Ph 2-Assoc.

3-M.Sc., Marine Eng., Amirkabir Univ.

umerical methods have been emerged to analyze the engineering problem

is an important method for solving the partial differential equation in engineering problems. The Poison equation is an appli s engineering problems. General solution of this equation is obtained based on BEM

integrals on the domain boundaries, and one integral in the internal domain which is a drawback for this method. To remove th eciprocity Method (DRM)

transient zone where not homogeneous part is involved time dependent terms, is solved by this method. The calculation of the story is a significant step for the thermal loading and residual stress analysis of the process.

In this work, welding temperature history is obtained using the

validation is carried out by common heat transfer problems. The welding temperature history is studied for a specific case by the created code. Because of the method simplicity and low time and error in computation process, the application of

Numerical Analyzes,Welding

http://mechanics.journals.modares.ac.ir

95 - 103

شور ﺎﺑ شﻮﺟ نﺎﻤﻟا

ﻲﻤﺳﺎﻗ ﻦﺴﺣ

*2

، ﻲﻟﺎﻬﻧ يﺪﻬﻣ

ﺮﻴﺒﻛﺮﻴﻣا ﻲﺘﻌﻨﺻ هﺎﮕﺸﻧاد ،ﺎﻳرد ﻲﺳﺪﻨﻬﻣ ياﺮﺘﻛد يﻮﺠﺸﻧاد

،

ﺮﻴﺒﻛﺮﻴﻣا ﻲﺘﻌﻨﺻ هﺎﮕﺸﻧاد ،

، ناﺮﻬﺗ

ﺮﻴﺒﻛﺮﻴﻣا ﻲﺘﻌﻨﺻ هﺎﮕﺸﻧاد ، asemi@aut.ac.ir

شور .ﺖﺳا هﺪﻣآ دﻮﺟﻮﺑ يدﺪﻌﺘﻣ يدﺪﻋ نﺎﻤﻟا

يزﺮﻣ

ﻲﻣﻮﻤﻋ باﻮﺟ .ﺖﺳا نﻮﺳاﻮﭘ ﻪﻟدﺎﻌﻣ دراد دﺮﺑرﺎﻛ ﻲﺳﺪﻨﻬﻣ ﻞﺋﺎﺴﻣ زا يرﺎﻴﺴﺑ رد ﻪﻛ ﻢﻬﻣ ﻢﻛﺎﺣ تﻻدﺎﻌﻣ ﻦﻳا زا ﻲ ﻲﻣ ﻒﻳﺮﻌﺗ ﻲﻧورد ﻪﻨﻣاد يور لاﺮﮕﺘﻧا ﻚﻳ و زﺮﻣ يور لاﺮﮕﺘﻧا ود ﻪﺑ

ارﺬﮔ ﺶﺨﺑ رد شﻮﺟ تراﺮﺣ لﺎﻘﺘﻧا ﻪﻟﺄﺴﻣ ﻞﻴﻠﺤﺗ ياﺮﺑ لﺎﺜﻣ ﻲﻣ

يﺎﻫ جﺎﺟﻮﻋا و هﺪﻧﺎﻤﻴﻗﺎﺑ و ﺪﻧﺎﻤﺴﭘ

يزﺮﻣ ود ﻪﻧﺎﮔ يا ﻲﻳﺎﻣد ﻪﭽﺨﻳرﺎﺗ ياﺮﺑ ﻲﻘﻴﻗد ﻦﻴﻤﺨﺗ

رد هﺪﺷ ﻞﺣ ﻞﺋﺎﺴﻣ ﺎﺑ ﺪﻛ ﻲﻳﺎﻣزآ ﻲﺘﺳار ،ﻢﻛﺎﺣ ﻲﻜﻳﺰﻴﻓ تﺎﻴﺿﺮﻓ ، تﺎﺒﺳﺎﺤﻣ ﻢﺠﺣ و ﻲﻧﺎﻣز ﺮﻈﻧ زا زا هدﺎﻔﺘﺳا

Study of welding temperature history by dual reciprocity boundary e

Ghassabzadeh

Ph. D. Student, Marine Eng., Amirkabir Univ.

Assoc. Prof. of M

M.Sc., Marine Eng., Amirkabir Univ.

*P.O.B. 15875

integrals on the domain boundaries, and one integral in the internal domain which is a drawback for this method. To remove th (DRM) is suggested. For example, in analysis of the welding heat transfer problems in transient zone where not homogeneous part is involved time dependent terms, is solved by this method. The calculation of the

story is a significant step for the thermal loading and residual stress analysis of the process.

In this work, welding temperature history is obtained using the

n heat transfer problems. The welding temperature history is studied for a specific case by the created code. Because of the method simplicity and low time and error in computation process, the application of

elding Temperature

http://mechanics.journals.modares.ac.ir ﻤﻠﻋ ﻪﻠﺠﻣ

ﻲ ﺸﻫوﮋﭘ ﻲ

هرﺎﻤﺷ 3 ﺰﻴﻳﺎﭘ 1390 ص ص 95

شور ﺎﺑ شﻮﺟ

،1

ﻲﻤﺳﺎﻗ ﻦﺴﺣ

ﺮﻴﺒﻛﺮﻴﻣا ﻲﺘﻌﻨﺻ هﺎﮕﺸﻧاد ،ﺎﻳرد ﻲﺳﺪﻨﻬﻣ ياﺮﺘﻛد يﻮﺠﺸﻧاد ﺳﺪﻨﻬﻣ

ﻲ رد ﻳﺎ ﺮﻴﺒﻛﺮﻴﻣا ﻲﺘﻌﻨﺻ هﺎﮕﺸﻧاد ،

ﻲ ﻲﺘﺸﻛ يزﺎﺳ ﺮﻴﺒﻛﺮﻴﻣا ﻲﺘﻌﻨﺻ هﺎﮕﺸﻧاد ،

ﻲﺘﺴﭘ قوﺪﻨﺻ ، 4413

- 15875

،

شور .ﺖﺳا هﺪﻣآ دﻮﺟﻮﺑ يدﺪﻌﺘﻣ يدﺪﻋ ﻲﻣﻮﻤﻋ باﻮﺟ .ﺖﺳا نﻮﺳاﻮﭘ ﻪﻟدﺎﻌﻣ دراد دﺮﺑرﺎﻛ ﻲﺳﺪﻨﻬﻣ ﻞﺋﺎﺴﻣ زا يرﺎﻴﺴﺑ رد ﻪﻛ ﻢﻬﻣ ﻢﻛﺎﺣ تﻻدﺎﻌﻣ ﻦﻳا زا ﻲ

ﻲﻣ ﻒﻳﺮﻌﺗ ﻲﻧورد ﻪﻨﻣاد يور لاﺮﮕﺘﻧا ﻚﻳ و زﺮﻣ يور لاﺮﮕﺘﻧا ود ﻪﺑ ارﺬﮔ ﺶﺨﺑ رد شﻮﺟ تراﺮﺣ لﺎﻘﺘﻧا ﻪﻟﺄﺴﻣ ﻞﻴﻠﺤﺗ ياﺮﺑ لﺎﺜﻣ

ﺶﻨﺗ ندﺮﻛ اﺪﻴﭘ و ﻲﺗراﺮﺣ يراﺬﮔرﺎﺑ ياﺮﺑ شﻮﺟ ﻪﻘﻄﻨﻣ ﻲﻳﺎﻣد ﻪﭽﺨﻳرﺎﺗ ندروآ يﺎﻫ

شور ﻚﻴﻨﻜﺗ نﺎﻤﻟا

يزﺮﻣ

رد هﺪﺷ ﻞﺣ ﻞﺋﺎﺴﻣ ﺎﺑ ﺪﻛ ﻲﻳﺎﻣزآ ﻲﺘﺳار ،ﻢﻛﺎﺣ ﻲﻜﻳﺰﻴﻓ تﺎﻴﺿﺮﻓ ، شور تﺎﺒﺳﺎﺤﻣ ﻢﺠﺣ و ﻲﻧﺎﻣز ﺮﻈﻧ زا

ﻪﻧﺎﮔود يا

Study of welding temperature history by dual reciprocity boundary element method

Ghassabzadeh¹, H. Ghassemi

Student, Marine Eng., Amirkabir Univ.

Prof. of Marine Eng., Amirkabir M.Sc., Marine Eng., Amirkabir Univ.

15875-4413, Tehran,

integrals on the domain boundaries, and one integral in the internal domain which is a drawback for this method. To remove th is suggested. For example, in analysis of the welding heat transfer problems in transient zone where not homogeneous part is involved time dependent terms, is solved by this method. The calculation of the

In this work, welding temperature history is obtained using the DRM

emperature History, Dual R

http://mechanics.journals.modares.ac.ir

هرود 11 هرﺎﻤﺷ

ﺎﻣد ﻪﭽﺨ ﻲﻳ

شور ﺎﺑ شﻮﺟ

هداﺰﺑﺎﺼﻗ ﻲﻀﺗﺮﻣ

1

ﺮﻴﺒﻛﺮﻴﻣا ﻲﺘﻌﻨﺻ هﺎﮕﺸﻧاد ،ﺎﻳرد ﻲﺳﺪﻨﻬﻣ ياﺮﺘﻛد يﻮﺠﺸﻧاد هﺪﻜﺸﻧاد رﺎﻴﺸﻧاد ﺳﺪﻨﻬﻣ

ﺪﺷرا سﺎﻨﺷرﺎﻛ ﻬﻣ

ﺳﺪﻨ ﻲ

ناﺮﻬﺗ ﻲﺘﺴﭘ قوﺪﻨﺻ ، شور .ﺖﺳا هﺪﻣآ دﻮﺟﻮﺑ يدﺪﻌﺘﻣ يدﺪﻋ ﻲﻣﻮﻤﻋ باﻮﺟ .ﺖﺳا نﻮﺳاﻮﭘ ﻪﻟدﺎﻌﻣ دراد دﺮﺑرﺎﻛ ﻲﺳﺪﻨﻬﻣ ﻞﺋﺎﺴﻣ زا يرﺎﻴﺴﺑ رد ﻪﻛ ﻢﻬﻣ ﻢﻛﺎﺣ تﻻدﺎﻌﻣ ﻦﻳا زا ﻲ

ﻲﻣ ﻒﻳﺮﻌﺗ ﻲﻧورد ﻪﻨﻣاد يور لاﺮﮕﺘﻧا ﻚﻳ و زﺮﻣ يور لاﺮﮕﺘﻧا ود ﻪﺑ ارﺬﮔ ﺶﺨﺑ رد شﻮﺟ تراﺮﺣ لﺎﻘﺘﻧا ﻪﻟﺄﺴﻣ ﻞﻴﻠﺤﺗ ياﺮﺑ لﺎﺜﻣ

ﺶﻨﺗ ندﺮﻛ اﺪﻴﭘ و ﻲﺗراﺮﺣ يراﺬﮔرﺎﺑ ياﺮﺑ شﻮﺟ ﻪﻘﻄﻨﻣ ﻲﻳﺎﻣد ﻪﭽﺨﻳرﺎﺗ ندروآ ﻚﻤﻛ ﻪﺑ ﻲﺒﺳﺎﻨﻣ ﺪﻛ

شور ﻚﻴﻨﻜﺗ

شور يرﻮﺌﺗ ﻪﻧﺎﮔود

يا رد هﺪﺷ ﻞﺣ ﻞﺋﺎﺴﻣ ﺎﺑ ﺪﻛ ﻲﻳﺎﻣزآ ﻲﺘﺳار ،ﻢﻛﺎﺣ ﻲﻜﻳﺰﻴﻓ تﺎﻴﺿﺮﻓ ،

ندﻮﺑ ﻪﻨﻳﺰﻫ ﻢﻛ و ﻲﮔدﺎﺳ ﻪﺑ ﻪﺟﻮﺗﺎﺑ . شور

شور ،شﻮﺟ ﻲﻳﺎﻣد ﻊﻳزﻮﺗ ،يدﺪﻋ ﻞﻴﻠﺤﺗ نﺎﻤﻟا

يزﺮﻣ ﻪﻧﺎﮔود

Study of welding temperature history by dual reciprocity lement method

Ghassemi^2*, M.Nahali

Amirkabir Univ.

M.Sc., Marine Eng., Amirkabir Univ.

Tehran, Iran, gasemi@aut.ac.ir umerical methods have been emerged to analyze the engineering problem

DRM. The Method and its

Reciprocity Boundary

ﻲﺗﺎﻘﻴﻘﺤﺗ ﺖﺷاددﺎﻳ

«

ﻳ ﺎﻣد ﻪﭽﺨ

هداﺰﺑﺎﺼﻗ ﻲﻀﺗﺮﻣ

1 - ﺮﻴﺒﻛﺮﻴﻣا ﻲﺘﻌﻨﺻ هﺎﮕﺸﻧاد ،ﺎﻳرد ﻲﺳﺪﻨﻬﻣ ياﺮﺘﻛد يﻮﺠﺸﻧاد

2 - هﺪﻜﺸﻧاد رﺎﻴﺸﻧاد

3 - ﺪﺷرا سﺎﻨﺷرﺎﻛ

ناﺮﻬﺗ*

ﻲﺳﺪﻨﻬﻣ ﻞﺋﺎﺴﻣ ﻞﻴﻠﺤﺗ ياﺮﺑ شور

يﺎﻫ شور .ﺖﺳا هﺪﻣآ دﻮﺟﻮﺑ يدﺪﻌﺘﻣ يدﺪﻋ

ﻜﻳ .ﺖﺳا ﻲﺳﺪﻨﻬﻣ ﻞﺋﺎﺴﻣ رد ﻢﻛﺎﺣ ﻲﻣﻮﻤﻋ باﻮﺟ .ﺖﺳا نﻮﺳاﻮﭘ ﻪﻟدﺎﻌﻣ دراد دﺮﺑرﺎﻛ ﻲﺳﺪﻨﻬﻣ ﻞﺋﺎﺴﻣ زا يرﺎﻴﺴﺑ رد ﻪﻛ ﻢﻬﻣ ﻢﻛﺎﺣ تﻻدﺎﻌﻣ ﻦﻳا زا ﻲ

يزﺮﻣ ﻲﻣ ﻒﻳﺮﻌﺗ ﻲﻧورد ﻪﻨﻣاد يور لاﺮﮕﺘﻧا ﻚﻳ و زﺮﻣ يور لاﺮﮕﺘﻧا ود ﻪﺑ

.ﺖﺳا ﻪﺑ رﻮﻃ ارﺬﮔ ﺶﺨﺑ رد شﻮﺟ تراﺮﺣ لﺎﻘﺘﻧا ﻪﻟﺄﺴﻣ ﻞﻴﻠﺤﺗ ياﺮﺑ لﺎﺜﻣ

ﺶﻨﺗ ندﺮﻛ اﺪﻴﭘ و ﻲﺗراﺮﺣ يراﺬﮔرﺎﺑ ياﺮﺑ شﻮﺟ ﻪﻘﻄﻨﻣ ﻲﻳﺎﻣد ﻪﭽﺨﻳرﺎﺗ ندروآ ﺎﺑ ﺖﺳا هﺪﺷ

ﻬﺗ ﻴ ﻪ ﻚﻤﻛ ﻪﺑ ﻲﺒﺳﺎﻨﻣ ﺪﻛ

اﺪﺘﺑا ،ﺐﻴﺗﺮﺗ ﻪﺑ ﻪﻣادا رد .ﺪﻳآ ﻪﺑ

شور يرﻮﺌﺗ

ندﻮﺑ ﻪﻨﻳﺰﻫ ﻢﻛ و ﻲﮔدﺎﺳ ﻪﺑ ﻪﺟﻮﺗﺎﺑ .

شور ،شﻮﺟ ﻲﻳﺎﻣد ﻊﻳزﻮﺗ ،يدﺪﻋ ﻞﻴﻠﺤﺗ

Study of welding temperature history by dual reciprocity lement method

M.Nahali³

Univ.

asemi@aut.ac.ir

umerical methods have been emerged to analyze the engineering problems. Boundary Element Method is an important method for solving the partial differential equation in engineering problems. The Poison equation is an appli

s engineering problems. General solution of this equation is obtained based on BEM

. The Method and its theory are explained. Then, the code n heat transfer problems. The welding temperature history is studied for a specific case by the created code. Because of the method simplicity and low time and error in computation process, the application of DRM

oundary Element

ﻲﺗﺎﻘﻴﻘﺤﺗ ﺖﺷاددﺎﻳ

ﺳرﺮﺑ ﻲ رﺎﺗ ﻳ ﺎﻣد ﻪﭽﺨ

ﻲﺳﺪﻨﻬﻣ ﻞﺋﺎﺴﻣ ﻞﻴﻠﺤﺗ ياﺮﺑ ﻜﻳ .ﺖﺳا ﻲﺳﺪﻨﻬﻣ ﻞﺋﺎﺴﻣ رد ﻢﻛﺎﺣ

شور سﺎﺳا ﺮﺑ ﻪﻟدﺎﻌﻣ ﻦﻳا نﺎﻤﻟا

يزﺮﻣ

ﻪﻨﻣاد يور لاﺮﮕﺘﻧا ﻲﻧورد

.ﺖﺳا

ﺶﻨﺗ ندﺮﻛ اﺪﻴﭘ و ﻲﺗراﺮﺣ يراﺬﮔرﺎﺑ ياﺮﺑ شﻮﺟ ﻪﻘﻄﻨﻣ ﻲﻳﺎﻣد ﻪﭽﺨﻳرﺎﺗ ندروآ شﻼﺗ ﻪﻟﺎﻘﻣ ﻦﻳا رد ﺎﺑ ﺖﺳا هﺪﺷ

اﺪﺘﺑا ،ﺐﻴﺗﺮﺗ ﻪﺑ ﻪﻣادا رد .ﺪﻳآ ﻪﺘﺧا ﻲﻣ دﻮﺷ ندﻮﺑ ﻪﻨﻳﺰﻫ ﻢﻛ و ﻲﮔدﺎﺳ ﻪﺑ ﻪﺟﻮﺗﺎﺑ .

Study of welding temperature history by dual reciprocity

. Boundary Element Method is an important method for solving the partial differential equation in engineering problems. The Poison equation is an appli

s engineering problems. General solution of this equation is obtained based on BEM by definition of the two integrals on the domain boundaries, and one integral in the internal domain which is a drawback for this method. To remove th

is suggested. For example, in analysis of the welding heat transfer problems in transient zone where not homogeneous part is involved time dependent terms, is solved by this method. The calculation of the

theory are explained. Then, the code n heat transfer problems. The welding temperature history is studied for a specific case by the created

DRM is recommended.

lement Method

» ﻲﺗﺎﻘﻴﻘﺤﺗ ﺖﺷاددﺎﻳ

ﺳرﺮﺑ

ﻜﭼ ﻴ -هﺪ ﻲﺳﺪﻨﻬﻣ ﻞﺋﺎﺴﻣ ﻞﻴﻠﺤﺗ ياﺮﺑ

رﺎﭘ يﺎﻫ ﻜﻳ .ﺖﺳا ﻲﺳﺪﻨﻬﻣ ﻞﺋﺎﺴﻣ رد ﻢﻛﺎﺣ

شور سﺎﺳا ﺮﺑ ﻪﻟدﺎﻌﻣ ﻦﻳا ﻞﺣ ﻪﻨﻣاد يور لاﺮﮕﺘﻧا

ﻪﺑ ﺖﺳد ﺶﻨﺗ ندﺮﻛ اﺪﻴﭘ و ﻲﺗراﺮﺣ يراﺬﮔرﺎﺑ ياﺮﺑ شﻮﺟ ﻪﻘﻄﻨﻣ ﻲﻳﺎﻣد ﻪﭽﺨﻳرﺎﺗ ندروآ

شﻼﺗ ﻪﻟﺎﻘﻣ ﻦﻳا رد ﻪﺑ ﺖﺳد اﺪﺘﺑا ،ﺐﻴﺗﺮﺗ ﻪﺑ ﻪﻣادا رد .ﺪﻳآ

ﻪﭽﺨﻳرﺎﺗ دﺮﭘ ﻪﺘﺧا

ﻠﻛ ﻴ ﺪ نﺎﮔژاو :

Study of welding temperature history by dual reciprocity

. Boundary Element Method (BEM) is an important method for solving the partial differential equation in engineering problems. The Poison equation is an applicable

by definition of the two integrals on the domain boundaries, and one integral in the internal domain which is a drawback for this method. To remove this is suggested. For example, in analysis of the welding heat transfer problems in transient zone where not homogeneous part is involved time dependent terms, is solved by this method. The calculation of the

theory are explained. Then, the code n heat transfer problems. The welding temperature history is studied for a specific case by the created

is recommended.

»

ﻜﭼ رﺎﭘ شور سﺎﺳا ﺮﺑ ﻪﻟدﺎﻌﻣ ﻦﻳا ﻞﺣ ﻪﺑ ﻪﺑ ﻪﭽﺨﻳرﺎﺗ ﻠﻛ

(BEM) cable by definition of the two is is suggested. For example, in analysis of the welding heat transfer problems in transient zone where not homogeneous part is involved time dependent terms, is solved by this method. The calculation of the theory are explained. Then, the code n heat transfer problems. The welding temperature history is studied for a specific case by the created

[ Downloaded from mme.modares.ac.ir on 2022-10-31 ]

(2)

يزﺮﻣ نﺎﻤﻟا شور ﺎﺑ شﻮﺟ ﻲﻳﺎﻣد ﻪﭽﺨﻳرﺎﺗ ﻲﺳرﺮﺑ ...

هداﺰﺑﺎﺼﻗ ﻲﻀﺗﺮﻣ رﺎﻜﻤﻫ و

نا

1 - ﻪﻣﺪﻘﻣ

يرﻮﺌﺗ ﺪﻴﺋﺎﺗ ياﺮﺑ شور ﻦﻳﺮﺘﻬﺑ ،ﺶﻴﭘ ﺎﻬﻟﺎﺳ يﺎﻫ

و نﺎﻘﻘﺤﻣ

ﺶﻳﺎﻣزآ مﺎﺠﻧا ،ناﺪﻨﻤﺸﻧاد يﺎﻫ

يرادﺮﺑ ﻪﻧﻮﻤﻧ و ﻲﺑﺮﺠﺗ

يﺎﻫ

هﺪﻳﺪﭘ زا ﻢﻴﻘﺘﺴﻣ .دﻮﺑ ﺎﻬﻧآ نداد خر ﻦﻴﺣ رد ﺎﻫ

ﺲﭙﺳ ﺎﺑ اﻳ دﺎﺠ

ﻳﺰﻴﻓ ناﺪﻴﻣ ﻦﻴﺑ تﻻﺎﺼﺗا و طﺎﻘﻧ ﻪﻋﻮﻤﺠﻣ ﻚﻳ زا هدﺎﻔﺘﺳا ﺎﺑ ﻲﻜ

آ دﻮﺟﻮﺑ ار ﻲﺗﺎﺒﺳﺎﺤﻣ ﻪﻜﺒﺷ ﺎﻬﻧآ ﻲﻜﻳﺰﻴﻓ يﺎﻀﻓ و ﺪﻣ

يﺎﻀﻓ ﻪﺑ

ﻞﻳﺪﺒﺗ ﻲﺗﺎﺒﺳﺎﺤﻣ ﺪﺷ

. ﭙﻣﺎﻛ عاﺮﺘﺧا ﺎﺑ ﻴ

ﺮﺗﻮ تﺎﺒﺳﺎﺤﻣ ﻧ گرﺰﺑ

ﻴ ﺰ

ﺪﺷ مﺎﺠﻧا ﻞﺑﺎﻗ ﻲﺗﺎﺒﺳﺎﺤﻣ ﻪﻜﺒﺷ ﻦﻳا ﻞﺣ ياﺮﺑ .

شور يﺎﻫ يدﺪﻋ

،ﻦﻴﺑ ﻦﻳا رد .ﺪﺷ عاﺪﺑا و دﺎﺠﻳا يدﺎﻳز شور

يﺎﻫ ﻋ يدﺪﻌﺘﻣ يدﺪ

شور ،يراﻮﻧ يرﻮﺌﺗ ،دوﺪﺤﻣ نﺎﻤﻟا ،دوﺪﺤﻣ ﻞﺿﺎﻔﺗ ﺮﻴﻈﻧ ﻪﺤﻔﺻ يا و نﺎﻤﻟا يزﺮﻣ ﻦﻳا زا ﻚﻳ ﺮﻫ .ﺪﻣآ دﻮﺟﻮﺑ شور

ﺎﻫ ياراد

ﻲﺗﺎﻴﻠﻤﻋ ﻪﻨﻣاد ﻚﻳ نﺪﻣآ دﻮﺟﻮﺑ ﺐﺒﺳ ﻪﻛ هدﻮﺑ ﻲﺒﻳﺎﻌﻣ و ﺎﻳاﺰﻣ ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ و هﺪﺷ ﺮﺸﺑ تﻼﻜﺸﻣ ﻊﻓر رد ﺎﻬﻧآ ياﺮﺑ ﺺﺨﺸﻣ ﻲﻳﺎﻧاﻮﺗ و تﻼﻜﺸﻣ و ﺎﻫزﺎﻴﻧ يﺎﻫ

ﺮﻫ ﻦﻳا زا ماﺪﻛ شور

ﺎﻫ ،

ﺐﺳﺎﻨﻣ .ﺖﺳا هﺪﺷ بﺎﺨﺘﻧا شور ﻦﻳﺮﺗ

شور نﺎﻤﻟا يزﺮﻣ زا ﻲﻜﻳ شور يﺎﻫ تﻻدﺎﻌﻣ ﻞﺣ رد ﺐﺳﺎﻨﻣ

يﺎﺟ ﻢﻛ ﻢﻛ ﻪﻛ ﺖﺳا ﻲﺳﺪﻨﻬﻣ ﻞﺋﺎﺴﻣ رد ﻢﻛﺎﺣ ﻞﻴﺴﻧاﺮﻔﻳد ﻦﻴﺑ رد ار دﻮﺧ شور

يﺎﻫ ﻲﻤﻳﺪﻗ شور ﻦﻳا رد .ﺖﺳا هدﺮﻛ زﺎﺑ ﺮﺗ

ﻪﺘﺴﺴﮔ زا ﻲﻟاﺮﮕﺘﻧا تﻻدﺎﻌﻣ ندﺮﻛ ﻞﺣ ياﺮﺑ زﺮﻣ يزﺎﺳ

يزﺮﻣ

هدﺎﻔﺘﺳا ﻲﻣ دﻮﺷ ﻪﻫد ﻞﻳاوا رد . 60

ﻪﻨﻴﻣز رد يﺎﻫ

ﻒﻠﺘﺨﻣ

ﺪﺷ ﻪﺘﻓﺮﮔ ﻚﻤﻛ عﻮﺿﻮﻣ ﻦﻳا زا ﻲﺳﺪﻨﻬﻣ 1]

- 2 رد لﻮﺤﺗ ﻪﻄﻘﻧ .[

ﻪﻟﺎﻘﻣ رﺎﺸﺘﻧا ،شور ﻦﻳا ﺖﻓﺮﺸﻴﭘ نﺎﻤﻟا نآ رد ﻪﻛ دﻮﺑ يا

يﺎﻫ

زا هدﺎﻔﺘﺳا ﺚﻋﺎﺑ و ﺪﺷ هدﺎﻔﺘﺳا رﺎﺑ ﻦﻴﻟوا ياﺮﺑ ﻚﻳﺮﺘﻣارﺎﭘوﺰﻳا ﻢﺘﻳرﻮﮕﻟا يﺎﻫ دوﺪﺤﻣ نﺎﻤﻟا شور يﻮﻗ ﺪﺷ شور ﻦﻳا رد

3] رد .[

لﺎﺳ 1978 شور يزوﺮﻣا رﺎﺘﺧﺎﺳ نﺎﻤﻟا

يزﺮﻣ رﺎﺑ ﻦﻴﻟوا ياﺮﺑ

ﺪﺷ ﻲﻓﺮﻌﻣ 4]

ﻪﻋﻮﻤﺠﻣ نﻮﻳﺪﻣ شور ﻦﻳا ﺖﻓﺮﺸﻴﭘ زا ﻲﺸﺨﺑ .[

ﻲﻠﻠﻤﻟا ﻦﻴﺑ ﺲﻧاﺮﻔﻨﻛ ﻦﻴﺘﺴﺨﻧ تﻻﺎﻘﻣ نﺎﻤﻟا

يزﺮﻣ 5] ﺶﺨﺑ و [

بﺎﺘﻛ ﻦﻴﻟوا رﺎﺸﺘﻧا نﻮﻳﺪﻣ ﺮﮕﻳد 6]

هوﺮﮔ ﻂﺳﻮﺗ ﻪﻨﻴﻣز ﻦﻳا رد [

ﻲﻜﻴﻧﺎﻜﻣ تﺎﺒﺳﺎﺤﻣ ﻖﻴﻘﺤﺗ ﻲﻣ

ﺪﺷﺎﺑ ناﻮﻨﻋ ﺖﺤﺗ بﺎﺘﻛ ﻦﻴﻟوا .

شور يﺎﻫ راﺪﻘﻣ ﻞﻳﺎﺴﻣ يدﺪﻋ ﻞﺣ ياﺮﺑ ﻲﻟاﺮﮕﺘﻧا تﻻدﺎﻌﻣ

ﻞﻴﺴﻧﺎﺘﭘ يرﻮﺌﺗ و ﻪﺘﻴﺴﺘﻴﺘﺳﻻا يزﺮﻣ 7]

لﺎﺳ رد[ 1977 ﻂﺳﻮﺗ

.ﺪﺷ ﺮﺸﺘﻨﻣ ﻢﻴﺳ و نﻮﺳﺎﺟ

شور ﺐﻴﺗﺮﺗ ﻦﻳﺪﺑ نﺎﻤﻟا

يزﺮﻣ ﻞﻴﻠﺤﺗ هزﻮﺣ دراو يﺎﻫ

رﺎﻨﻛ رد ﺐﺳﺎﻨﻣ ﻲﺷور ناﻮﻨﻌﺑ ﻢﻜﻤﻛ و ﺪﺷ ﻲﺳﺪﻨﻬﻣ شور

يﺎﻫ ﻳد

ﺪﻨﻧﺎﻤﻫ شور ﻦﻳا .ﺪﺷ ﻲﻓﺮﻌﻣ دوﺪﺤﻣ نﺎﻤﻟا ﺮﻴﻈﻧ ﺮﮕ شور يﺎﻫ ﻪﻄﻘﻧ ﻚﻳ .ﺖﺴﻴﻧ ﺺﻘﻧ و ﻞﻜﺸﻣ نوﺪﺑ يدﺪﻋ ﺮﮕﻳد

ﻲﻄﺧﺮﻴﻏ ﻞﺋﺎﺴﻣ ﻞﻴﻠﺤﺗ شور ﻦﻳا ﻢﻬﻣ ﻒﻌﺿ ﻲﻣ

ﺪﺷﺎﺑ هزوﺮﻣا .

شور يﺎﻫ ﻳا ﻞﺣ ياﺮﺑ ﻲﻔﻠﺘﺨﻣ ﻦ

ﻞﺋﺎﺴﻣ ﺑ دﻮﺟﻮ ﺖﺳا هﺪﻣآ .

ﻦﻳا ﻦﻳﺮﺘﻤﻬﻣ شور

ﺎﻫ ﻲﺻﻮﺼﺧ ﻞﺣ شور : زا ﺪﻨﺗرﺎﺒﻋ شور ،1

يﺮﻴﮕﻟاﺮﮕﺘﻧا زﺮﻣ نورد

زﺮﻣ ﻪﺑ لاﺮﮕﺘﻧا لﺎﻘﺘﻧا ،2

يزﺎﺳ ﻲﻄﺧ ،3

و4

شور ﻪﻧﺎﮔ ود

5يا .

ﻲﻠﻛ رد شور ﻦﻳﺮﺗ نﺎﻤﻟا

يزﺮﻣ ﻪﻧﻮﮕﻨﻳا ﻪﺒﺳﺎﺤﻣ ياﺮﺑ

ﺎﻬﻟاﺮﮕﺘﻧا يا ﻪﺒﻧﺎﺟ ود شور ﺮﮕﻳد .ﺖﺳا

شور ﺎﻫ ﺖﻟﺎﺣ رد يﺎﻫ

.ﺪﻨﺘﺴﻫ هدﺎﻔﺘﺳا ﻞﺑﺎﻗ صﺎﺧ ﻂﺳﻮﺗ رﺎﺑ ﻦﻴﻟوا ياﺮﺑ شور ﻦﻳا

ﺎﻴﺑﺮﺑ و ﻲﻨﻳدرﺎﻧ 8]

ﻻا ﻞﺋﺎﺴﻣ ﻞﺣ ياﺮﺑ [ ﺲﭙﺳ و ﻚﻴﻣﺎﻨﻳدﻮﺘﺳ

ﺎﻴﺑﺮﺑ و ﻞﺑار ﻂﺳﻮﺗ 9]

نژﻮﻴﻔﻳد ﻞﺋﺎﺴﻣ ياﺮﺑ[ ﻪﺑ

رﺎﻛ .ﺖﻓر

ﻦﻳﺮﺗدﺮﺑرﺎﻛﺮﭘ زا ﻲﻜﻳ يدوﺮﺘﻜﻟا شﻮﺟ شور

يﺎﻫ ﺖﺧﺎﺳ

ﺖﻤﺴﻗ و تﺎﻌﻄﻗ لﺎﺼﺗا ياﺮﺑ يﺎﻫ

هزﺎﺳ ﻒﻠﺘﺨﻣ ﻲﻣ

ﺪﺷﺎﺑ ﺮﻃﺎﺨﺑ .

ﺮﻴﺛﺄﺗ و شﻮﺟ ﺪﻨﻳآﺮﻓ زا ﺪﻌﺑ و ﻦﻴﺣرد شﻮﺟ ﻪﻘﻄﻨﻣ يﻻﺎﺑ يﺎﻣد ﺶﻨﺗ ﻊﻳزﻮﺗ ﺮﺑ نآ يﺎﻫ

و ﺪﻧﺎﻤﺴﭘ ﻞﻜﺷﺮﻴﻴﻐﺗ

يﺎﻫ ،ﻪﺘﺳاﻮﺧﺎﻧ

ﻪﺑ ﺖﺳد نآ زا ﻲﺷﺎﻧ تاﺮﺛا ﺶﻫﺎﻛ ﺲﭙﺳ و ﻲﻳﺎﻣد ﻊﻳزﻮﺗ ندروآ

سﺎﭘ ﻲﻟاﻮﺗ بﺎﺨﺘﻧا رد هﮋﻳﻮﺑ يﺎﻫ

.دراد ﻲﺻﺎﺧ ﺖﻴﻤﻫا يرﺎﻜﺷﻮﺟ

ترﻮﺻ يدﺎﻳز تﺎﻘﻴﻘﺤﺗ ﻪﻨﻴﻣز ﻦﻳا رد نﻮﻨﻛ ﺎﺗ ﻪﻜﻨﻳا ﻢﻏﺮﻴﻠﻋ ﻦﻳا ﺪﻧاﻮﺘﺑ ﻪﻛ ﻲﺒﺳﺎﻨﻣ ﻪﻣﺎﻧﺮﺑ ﻪﺑ نﺪﻴﺳر ياﺮﺑ شﻼﺗ ،ﺖﺳا ﻪﺘﻓﺮﮔ

ﻳﺎﻣد ﻪﭽﺨﻳرﺎﺗ ﻊﻳزﻮﺗ ﺮﺑ نآ ﺮﻴﺛﺄﺗ ﻲﺳرﺮﺑ و ﺪﻨﻛ جاﺮﺨﺘﺳا ار ﻲ

ﺶﻨﺗ يﺎﻫ ﻞﻜﺷﺮﻴﻴﻐﺗ و ﺪﻧﺎﻤﺴﭘ يﺎﻫ

،ﺪﻳﺎﻤﻧ هدﺎﺳ ار ﻪﺘﺳاﻮﺧﺎﻧ

ﻲﻣ ﻢﻬﻣ زﻮﻨﻫ ﻦﻳا ﻪﺑ نﺪﺷ ﻚﻳدﺰﻧ ياﺮﺑ ﻲﺷﻼﺗ ﻪﻟﺎﻘﻣ ﻦﻳا .ﺪﻳﺎﻤﻧ

زا ﻦﺘﻓﺮﮔ ﻚﻤﻛ ﺎﺑ يﺪﻌﺑ ود شﻮﺟ ﻲﻳﺎﻣد ﻊﻳزﻮﺗ ﻪﺋارا و ﻪﻣﺎﻧﺮﺑ ﻪﺒﻧﺎﺟ ود شور ﻚﻴﻨﻜﺗ شور رد يا

نﺎﻤﻟا يزﺮﻣ ﻲﻣ ﺪﺷﺎﺑ .

2 - و نﻮﺳاﻮﭘ ﻪﻟدﺎﻌﻣ شور

يا ﻪﻧﺎﮔ ود 10]

[

شور رد ﻪﻧﺎﮔود

يا ﻒﻠﺘﺨﻣ تﻻﺎﺣ رد نﻮﺳاﻮﭘ ﻪﻟدﺎﻌﻣ ﻞﺣ ﻪﺑ

ﻪﺘﺧادﺮﭘ ﻲﻣ دﻮﺷ نﻮﺳاﻮﭘ ﻪﻟدﺎﻌﻣ ﻲﻠﻛ ﻞﻜﺷ . ﻪﺑ

ترﻮﺻ : ﺖﺳا ﺮﻳز

) 1

∇T = (

1. Particular Solution Method 2. Domain integration Method 3. Transfer of Domain to Boundary 4. Quasi linearization

(3)

ﻲﺳﺪﻨﻬﻣ ﻧﺎﻜﻣ ﻴ ﻚ سرﺪﻣ رود

ة

،ﻢﻫدزﺎﻳ ةرﺎﻤﺷ 3 / ﺰﻴﻳﺎﭘ 1390

97

ﺎﺠﻨﻳا رد نﺎﺸﻧT

.ﺖﺳا ﻲﺗراﺮﺣ ﻞﺋﺎﺴﻣ رد ﺎﻣد هﺪﻨﻫد

ﻲﻣ نﻮﺳاﻮﭘ ﻞﺋﺎﺴﻣ ﻊﺑﺎﺗ ﺖﻴﻫﺎﻣ ﻪﺑ ﻪﺘﺴﺑ ﺪﻨﻧاﻮﺗ

b

ﻣ ﻪﺑ ﻞﺋﺎﺴ

ﻪﺘﺳد ﻲﻄﺧ ﺮﻴﻏ ﺎﻳ ﻲﻄﺧ .ﺪﻧﻮﺷ يﺪﻨﺑ

ﻪﻧﻮﻤﻧ ﻳﺎﻫ : زا ﺪﻨﺗرﺎﺒﻋ نﻮﺳاﻮﭘ ﻲﻄﺧ ﻞﺋﺎﺴﻣ زا ﻲ

•

=b

ﺖﺑﺎﺛ

= , • نآ رد ﻪﻛ

وa .ﺪﻨﺘﺴﻫ ﺖﺑﺎﺛb

b = ax, y + cx, yT • ﻲﻄﺧ ﺖﻟﺎﺣ ﻦﻳﺮﺗ ﻲﻠﻛ ﻪﻛ

ﺖﺳا نﻮﺳاﻮﭘ .

ﻲﻠﻛ ﺖﻟﺎﺣ ﻦﻳﺮﺗ ﻲﻄﺧﺮﻴﻏ

ار يﺪﻌﺑ ود ﻞﺋﺎﺴﻣ ياﺮﺑ ﻲﻣ

ناﻮﺗ

ﻪﺑ ترﻮﺻ : دﻮﻤﻧ نﺎﻴﺑ ﺮﻳز

) 2

b = b x, y, T,, (

شور ﻪﻛ ﻲﻣﺎﮕﻨﻫ نﺎﻤﻟا

يزﺮﻣ ،دﻮﺷ لﺎﻤﻋا نﻮﺳاﻮﭘ ﻪﻟدﺎﻌﻣ ﺮﺑ

مﺮﺗ ﺮﺑ هوﻼﻋ زﺮﻣ نورد ﻲﻟاﺮﮕﺘﻧا مﺮﺗ ﻚﻳ يﺎﻫ

طﻮﺑﺮﻣ ﻲﻟاﺮﮕﺘﻧا

دﺎﺠﻳا ﺎﻫزﺮﻣ ﻪﺑ ﻲﻣ

دﻮﺷ .

شور رد ﻪﻧﺎﮔود

يا ﻊﺑﺎﺗ ، رد نآ ﺮﻳدﺎﻘﻣ ﺐﺴﺣﺮﺑ b

هﺮﮔ ﺎﻫ ي

هداد ﻂﺴﺑ زﺮﻣ نورد ﻲﻣ

دﻮﺷ ورد ﻊﺑﺎﺗ يداﺪﻌﺗ . بﺎﻴﻧ

φ ياﺮﺑ

راﺮﻗ هدﺎﻔﺘﺳا درﻮﻣ رﻮﻈﻨﻣ ﻦﻳا ﻲﻣ

دﺮﻴﮔ ﺪﻨﻧﺎﻣ ﻲﻌﺑﺎﺗ ﺮﮔا لﺎﺣ . f_k

ﺮﺑاﺮﺑ نآ سﻼﭘﻻ ﻪﻛ دﻮﺷ ﺖﻓﺎﻳ φ

،دﻮﺷ ﻲﻣ ناﻮﺗ نورد لاﺮﮕﺘﻧا

.دﻮﻤﻧ ﻞﻘﺘﻨﻣ زﺮﻣ يور ﻪﺑ ار زﺮﻣ

ﻊﺑﺎﺗ ﻖﻴﻗد ﺖﺷﺎﮕﻧ ياﺮﺑ ،زﺮﻣ يور ﻪﺑb

هﺮﮔ ﺎﻫ ي ﻧ ﺪﻳﺎﺑ بﺎﻴﻧورد ﻪ

نآ نورد زا ﻪﻜﻠﺑ زﺮﻣ يور زا ﺎﻬﻨﺗ .ﺪﻨﺷﺎﺑ ﺰﻴﻧ

هﺮﮔ ﺎﻫ ي ار زﺮﻣ يور

هﺮﮔ و يزﺮﻣ هﺮﮔ ﺎﻫ ي ار نآ نورد ود هﺮﮔ

ﺒﻧﺎﺟ ﻪ يا ﻲﻣ .ﻢﻴﻣﺎﻧ

ضﺮﻓ ﺎﺑ هﺮﮔ N

يزﺮﻣ و هﺮﮔ L ود ﻪﻧﺎﮔ يا ﻊﺑﺎﺗ ﻪﺑ b ترﻮﺻ

ﻲﻣ هدز ﺐﻳﺮﻘﺗ ﺮﻳز .دﻮﺷ

) 3

bx, y = ∑φx, yα (

نآ رد ﻪﻛ

φ

و بﺎﻴﻧورد ﻊﺑاﻮﺗ

α

.ﺪﻨﺘﺴﻫ ﻲﺑﺎﻴﻧورد ﺐﻳاﺮﺿ

رد ﻪﻛ ﻲﺗرﻮﺻ دﻮﺧ زا ﻲﻌﺑﺎﺗb

ﻞﻜﺷ ﻦﻴﻤﻫ ﻪﺑ ﻪﻟﺎﺴﻣ ،ﺪﺷﺎﺑ ﻢﻫT

ار ﻪﻟﺎﺴﻣ ﺪﻳﺎﺑ ترﻮﺻ نآ رد ﻪﻛ توﺎﻔﺗ ﻦﻳا ﺎﺑ ﺖﺳا ﻞﺣ ﻞﺑﺎﻗ ﻪﺑ ترﻮﺻ راﺮﻜﺗ .ﻢﻴﻳﺎﻤﻧ ﻞﺣ يا

بﺎﻴﻧورد ﻊﺑاﻮﺗ ﻲﻣ

ﻧاﻮﺗ ﺪﻨﭼ ﺪﻨﻧﺎﻣ .ﺪﻨﺷﺎﺑ ﻲﻋﻮﻧ ﺮﻫ زا ﺪﻨ

ﻞﻤﺟ يﺎﻫ ﻲﺗﺎﺒﺳﺎﺤﻣ تﺎﻌﻟﺎﻄﻣ ﺎﻣا ... و هاﻮﺨﻟد ﻪﺟرد زا نﺎﺸﻧ

ﺑﺎﺗ ﻪﻛ ﺖﺳا هداد .دراد ار ﻲﻫدزﺎﺑ ﻦﻳﺮﺘﻬﺑ ﺮﻳز ﻊ

)

4

φx, y = 1 + rx, y (

نآ رد ﻪﻛ r

نﺎﻴﻣ ﻪﻠﺻﺎﻓ هﺮﮔ

و ﺮﻈﻧ درﻮﻣ هﺮﮔ

ماk .ﺖﺳا

ﻦﻳاﺮﺑﺎﻨﺑ ﻲﻣ ناﻮﺗ : ﺖﺷﻮﻧ

) 5

α= ∑E$b$ (

$

نآ رد ﻪﻛ E

ﺲﻳﺮﺗﺎﻣ سﻮﻜﻌﻣ نﺎﻤﻫ φ

ﻪﺑ ﻲﮕﺘﺴﺑ ﻪﻛ ﺖﺳا

ﻊﺑﺎﺗ .دراﺪﻧb ضﺮﻓ لﺎﺣ ﻲﻣ

ﻢﻴﻨﻛ ﺎﻣ ﻲﻌﺑاﻮﺗ ﻪﻋﻮﻤﺠﻣ ﺪﻨﻧ

fk

ﻪﻛ دراد دﻮﺟو

:ﺪﻳﺎﻤﻧ ﺎﺿرا ار ﺮﻳز ﻪﻟدﺎﻌﻣ

) 6

∇f= φ (

ﻊﺑﺎﺗ ﻲﺘﺣاﺮﺑ f_k

ﻪﺑ ترﻮﺻ ﺮﻳز ﻪﺑ ﺖﺳد ﻲﻣ ﺪﻳآ :

) 7

f=^&₎^'⁽+^&₊^'^* (

ﻂﺑاور زا هدﺎﻔﺘﺳا ﺎﺑ ﻪﺑ

ﺖﺳد ﻊﺑﺎﺗ هﺪﻣآ ﻪﺑ b

ﺖﺳد آ ﻣ ﺪ رد و ه

ﻧ ﻳﺎﻬ نﺎﻴﺑ ﺮﻳز ﻞﻜﺷ ﻪﺑ نﻮﺳاﻮﭘ ﻪﻟدﺎﻌﻣ ﺖ ﻲﻣ

دﻮﺷ :

) 8

∇T = ∑∇fα (

ﻪﻤﺸﭼ ياﺮﺑ ﻪﻄﻘﻧ رد ﻪﻛ يا

) ﻢﻳراد ﺖﺳا ﻪﺘﻓﺮﮔ راﺮﻗ i

Gi

ﻊﺑﺎﺗ

(ﺖﺳا نزو

) 9

, G_Ω .∇TdΩ= , G_Ω .0∑∇fα1dΩ (

ﻲﻣ ار مﺮﺗ ود ﺮﻫ لﺎﺣ دﻮﻤﻧ ﻞﻘﺘﻨﻣ زﺮﻣ ﻪﺑ ناﻮﺗ

و ﺎﺑ

زا هدﺎﻔﺘﺳا شور

يﺎﻫ ﻪﺘﺴﺴﮔ يزﺎﺳ يدﺎﻋ هدﺎﻔﺘﺳا درﻮﻣ ، رد

شور ﻟا نﺎﻤ يزﺮﻣ ﺖﺑﺎﺛ نﺎﻤﻟا ياﺮﺑ

، ﻪﻟدﺎﻌﻣ ﭗﭼ ﺖﻤﺳ 9

ار

.ﺖﺷﻮﻧ فﻼﺧ ﺮﺑ ﻪﻛ ﺖﺳا ﻦﻳا ﺖﻤﺴﻗ ﻦﻳا رد ﺮﻛذ ﻞﺑﺎﻗ ﻪﺘﻜﻧ ياﺮﺑ ًﺎﺻﻮﺼﺨﻣ ،نﻮﺳاﻮﭘ ﻪﻟدﺎﻌﻣ رد ﻪﻤﺸﭼ سﻼﭘﻻ ﻪﻟدﺎﻌﻣ ﺎﻨﻌﻣ ﻦﻳا ﻪﺑ .ﺪﻨﻛ ﺖﻛﺮﺣ ﻢﻫ زﺮﻣ نورد ﺪﻳﺎﺑ ،ﻲﻄﺧﺮﻴﻏ ﺖﻟﺎﺣ ﺮﺑ هوﻼﻋ ﺪﻳﺎﺑ ﻪﻤﺸﭼ ﻪﻛ هﺮﮔ

ﺎﻫ ي يور يزﺮﻣ هﺮﮔ

ﺎﻫ ي ﻪﻧﺎﮔ يا

ﺰﻴﻧ .دﺮﻴﮔ راﺮﻗ

ﻪﻟدﺎﻌﻣ ﺖﺳار ﺖﻤﺳ ياﺮﺑ 9

ﺰﻴﻧ ﻲﻣ ناﻮﺗ سﻮﮔ يرﻮﺌﺗ زا -

ﻦﻳﺮﮔ و ﻲﺋﺰﺟ ﻖﺘﺸﻣ

، .ﺖﻓﺮﮔ ﻚﻤﻛ

ﺖﺳار ﺖﻤﺳ ﺐﻴﻛﺮﺗ ﺎﺑ ﭗﭼ و

ﻪﻟدﺎﻌﻣ 9 ﺮﮕﻳﺪﻜﻳ ﺎﺑ و

ﻒﻳﺮﻌﺗ

ﺐﻳاﺮﺿ ﺲﻳﺮﺗﺎﻣ ﻚﻳ ﻪﺑ

ترﻮﺻ

Mim

:ﺖﺷاد ﻢﻴﻫاﻮﺧ

(4)

ﺑ يزﺮﻣ نﺎﻤﻟا شور ﺎﺑ شﻮﺟ ﻲﻳﺎﻣد ﻪﭽﺨﻳرﺎﺗ ﻲﺳرﺮ ...

هداﺰﺑﺎﺼﻗ ﻲﻀﺗﺮﻣ رﺎﻜﻤﻫ و

نا

) 10

∑6 23454 (

4 − ∑6 8934:4

4 − ;3:3= ∑6><3==

=

ﻪﻄﺑار .ﺖﺳا هﺪﺷ ﻪﺘﺷﺎﮕﻧ زﺮﻣ يور ﻪﺑ ﻪﻟﺎﺴﻣ ﻦﻳاﺮﺑﺎﻨﺑ 10

ﻪﺘﺴﺴﮔ يزﺎﺳ شور ﻪﺑ نﻮﺳاﻮﭘ ﻪﻟدﺎﻌﻣ هﺪﺷ ﻪﻧﺎﮔود

يا ﻲﻣ ﺪﺷﺎﺑ .

ﻲﻠﻛ ﺖﻟﺎﺣ رد زا ﻲﻌﺑﺎﺗb

.ﺖﺳا نآ تﺎﻘﺘﺸﻣ وT ﻪﻧﻮﻤﻧ

زا يا ﻦﻳا

.ﺖﺳا هﺪﻣآ ﺮﻳز رد ﺖﻟﺎﺣ

) 11

b = T (

ﺷ مﺎﺠﻧا ﻲﺑﺎﻴﻧورد زا هدﺎﻔﺘﺳا ﺎﺑ ياﺮﺑ هﺪ

ﻪﻄﺑار ،

قﻮﻓ ﻪﺑ

ﻞﻳﺪﺒﺗ ﺮﻳز ﻪﻄﺑار ﻲﻣ

ددﺮﮔ .

) 12

b$= T$∑T?N$? (

? = ∑T$T?N$?

?

3 - تﻻدﺎﻌﻣ ﻢﻛﺎﺣ

ﺗراﺮﺣ ﻞﻴﻠﺤﺗرد ﻲ

شﻮﺟ

،شﻮﺟ لﺎﺣ رد قرو ﺖﻣﺎﺨﺿ ندﻮﺑ ﻚﭼﻮﻛ ضﺮﻓ ﺎﺑ ﻲﻣ

ناﻮﺗ

ﻪﺠﻴﺘﻧ رد و دﺮﻛ ضﺮﻓ يﺪﻌﺑ ود ار شﻮﺟ زا ﻲﺷﺎﻧ ﻲﻳﺎﻣد ﻊﻳزﻮﺗ ﻌﻣ ﻪﻟﺄﺴﻣ ﺮﺑ ﻢﻛﺎﺣ ﻪﻟدﺎ ﻪﺑ

ترﻮﺻ .دﻮﺷ نﺎﻴﺑ ﺮﻳز

) 13

− ^A^B+^A^C + D, , E = FG^HIJ,K,L_HL (

ﻪﻄﺑار ﻦﻳا رد ،هدﺎﻣ ﻲﺘﻬﺟ تراﺮﺣ لﺎﻘﺘﻧا ﺐﻳﺮﺿ K

خﺮﻧ Q

،ﻲﺟرﺎﺧ يﺪﻴﻟﻮﺗ يﺎﻣﺮﮔ و هدﺎﻣ هﮋﻳو يﺎﻣﺮﮔ ﺖﻴﻓﺮﻇ C

ρ

نآ ﻲﻟﺎﮕﭼ ﻲﻣ

ﺪﺷﺎﺑ دﺎﻌﻣ ﻦﻳا رد . تراﺮﺣ لﺎﻘﺘﻧا ﺐﻳﺮﺿ ًﻻﻮﻤﻌﻣ ﻪﻟ

درﻮﻣ ﻪﻟﺄﺴﻣ رد و (ﻚﻴﭘوﺮﺗوﺰﻳا هدﺎﻣ) هدﻮﺑ ﺖﻬﺟ نوﺪﺑ هدﺎﻣ ﺮﻔﺻ ﺮﺑاﺮﺑ يﺪﻴﻟﻮﺗ يﺎﻣﺮﮔ خﺮﻧ ﻲﺳرﺮﺑ ﻲﻣ

ﺪﺷﺎﺑ .

ﻪﻟﺄﺴﻣ ﻦﻳا ﺮﺑ ﻢﻛﺎﺣ ﻲﻠﻛ يزﺮﻣ طﺮﺷ ﻪﺑ

ترﻮﺻ نﺎﻴﺑ ﺮﻳز ﻲﻣ دﻮﺷ :

) 14

MJHI (

HJNJ+ MKHI

HKNK+ OP+ OQ+ OR= 0

ﻪﻄﺑار ﻦﻳا رد ،ﺎﻫزﺮﻣ راﺪﺘﻬﺟ سﻮﻨﻴﺴﻛN

qs

ﻲﻟﺎﻘﺘﻧا يﺎﻣﺮﮔ

،ﻢﺴﺟ ﺢﻄﺳ يور qc

و ﺖﻓﺮﻤﻫ ﺮﺛا رد ﻲﻟﺎﻘﺘﻧا يﺎﻣﺮﮔ qr

ﻲﻌﺸﻌﺸﺗ ﻲﻟﺎﻘﺘﻧا يﺎﻣﺮﮔ ﻲﻣ

ﺪﺷﺎﺑ تراﺮﺣ ﻦﻳا زا ﻚﻳﺮﻫ . يﺎﻫ

ﻨﺘﺴﻫ ﻪﺒﺳﺎﺤﻣ ﻞﺑﺎﻗ ﺮﻳز ﻂﺑاور سﺎﺳاﺮﺑ ﻲﻟﺎﻘﺘﻧا :ﺪ

) 15 (

OQ= ℎQ: − :U

) 16 (

OR= VW:⁾− :U)

ﻪﻄﺑار ﻦﻳا رد ،يرﺎﻜﺷﻮﺟ ﻪﻴﺣﺎﻧ رد اﻮﻫ ﺖﻓﺮﻤﻫ ﺐﻳﺮﺿ h

T∞

،ﻂﻴﺤﻣ يﺎﻣد و هدﺎﻣ ﻊﺸﻌﺸﺗ ﺐﻳﺮﺿε

نﺎﻣﺰﺘﻟﻮﺑ ﺖﺑﺎﺛσ

ﻲﻣ ﺪﺷﺎﺑ نﺎﻤﻫ . ﻲﻣ هﺪﻫﺎﺸﻣ ﻪﻛ ﻪﻧﻮﮔ تراﺮﺣ لﺎﻘﺘﻧا ،دﻮﺷ

ﻂﺑار ﻲﻌﺸﻌﺸﺗ يﺎﻫ

ﻲﻄﺧ ياﺮﺑ و دراد ﻲﻄﺧﺮﻴﻏ زا نآ يزﺎﺳ

ﻪﻄﺑار .ﺖﺳا هﺪﺷ هدﺎﻔﺘﺳا ﻞﻴﻠﺤﺗ ﻞﺒﻗ ﻪﻠﺣﺮﻣ يﺎﻣد 16

ﻪﺑ ترﻮﺻ

هدﺎﺳ ﺮﻳز ﻲﻣ

دﻮﺷ :

) 17 (

O&= XεσT[\ + TU. T_[\ + TU^T − T_U

درﻮﻣ رد لﺪﻣ

يزﺎﺳ ﻲﻜﻳﺮﺘﻜﻟا سﻮﻗ زا ﻲﺷﺎﻧ تراﺮﺣ

ﻦﻳﺮﺗﺮﺒﺘﻌﻣ زا ﻲﻜﻳ ﻪﻛ ﺖﺳا هﺪﺷ نﺎﻴﺑ ﻲﻋﻮﻨﺘﻣ ﻂﺑاور يرﺎﻜﺷﻮﺟ ﻲﺳﻮﮔ ﻊﻳزﻮﺗ ﻪﻄﺑار نﺎﻴﺑ و سﻮﻗ طوﺮﺨﻣ ﻦﺘﻓﺮﮔ ﺮﻈﻧ رد ﺎﻬﻧآ تراﺮﺣ ﻪﺑ ترﻮﺻ ﻪﻄﺑار 18 ﻲﻣ ﺪﺷﺎﺑ ﻞﻜﺷ رد . 1

طوﺮﺨﻣ ﻦﻳا

ﻪﻈﺣﻼﻣ ﻣ ﻲ دﻮﺷ طوﺮﺨﻣ ﻦﻳا ﺮﻴﺛﺄﺗ شﻮﺟ ﺢﻄﺳ يور . ﻪﺑ

ترﻮﺻ

ﺎﺠﻧآ رد ار ﺰﻠﻓ ﻲﻜﻳﺮﺘﻜﻟا سﻮﻗ زا ﻲﺷﺎﻧ تراﺮﺣ ﻪﻛ ﺖﺳا يا هﺮﻳاد هﺪﻧاﻮﺧ باﺬﻣ ﻪﭽﺿﻮﺣ مﺎﻨﺑ و باﺬﻣ ﻲﻣ

دﻮﺷ .

) 18 (

OP= O, , E =^_`.a.b_c.R

d( exp −_R^_

d(g − h. E+ i

ﻪﻄﺑار ﻦﻳا رد rb

،ﻪﻌﻄﻗ ﺢﻄﺳ يور شﻮﺟ طوﺮﺨﻣ عﺎﻌﺷ s

،شﻮﺟ دوﺮﺘﻜﻟا ﻲﻄﺧ ﺖﻋﺮﺳ ،نﺎﻳﺮﺟ تﺪﺷ I

فﻼﺘﺧا V

و ﻞﻴﺴﻧﺎﺘﭘ ﻲﻜﻳﺮﺘﻜﻟا سﻮﻗ هدزﺎﺑη

ﻲﻣ ﺪﺷﺎﺑ . ﻠﺤﺗ ﻪﺑ ﻪﺟﻮﺗﺎﺑ ﻴ

ﻞ

شﻮﺟ يﺪﻌﺑ ود ،

دوﺮﺘﻜﻟا ﺖﻛﺮﺣ زا ﻲﺷﺎﻧ يدورو يﺎﻣﺮﮔ

ﻪﺑ ترﻮﺻ ﺎﻣد طﺮﺷ ﻲﻳ

هﺮﻳاد ﺮﺑ شﻮﺟ

ﺷ لﺎﻤﻋا ﻦﻳا رد و هﺪ

هﺮﮔ ﻲﻳﺎﻣد ﻪﻄﺑار ترﻮﺻ ﻪﺑ

ترﻮﺻ ﺮﻳز ﻲﻣ ﺪﺷﺎﺑ :

) 19 (

:6jkl= :=exp −_R^_

d(g − h. E+ i

ﻪﻄﺑار ﻦﻳا رد T_m

باﺬﻣ ﻪﭽﺿﻮﺣ يﺎﻣد ﺮﺜﻛاﺪﺣ ﻲﻣ

ﺪﺷﺎﺑ .

4 - يدرﻮﻣ تﺎﺒﺳﺎﺤﻣ و ﻪﻌﻟﺎﻄﻣ

ﻪﻟﺎﻘﻣ ﻦﻳا رد ﻲﺳرﺮﺑ درﻮﻣ ﻪﻟﺄﺴﻣ ﻪﺑ

د ﺖﺳ ﻲﻳﺎﻣد ﻊﻳزﻮﺗ ندروآ

ﻲﻠﻴﻄﺘﺴﻣ قرو ود يرﺎﻜﺷﻮﺟ زا ﻲﺷﺎﻧ ﻲﻣ

ﺪﺷﺎﺑ درﻮﻣ ﻪﺳﺪﻨﻫ .

ﻞﻜﺷ رد ﻲﺳرﺮﺑ 1

ﻲﻣ ﻪﻈﺣﻼﻣ .دﻮﺷ

ﺎﺑ ﻲﻠﻴﻄﺘﺴﻣ كزﺎﻧ قرو

رﻮﺤﻣ ﻪﻛ ﺺﺨﺸﻣ دﺎﻌﺑا رﻮﺤﻣ و شﻮﺟ ﻂﺧ يﺎﺘﺳار ﺮﺑ دﻮﻤﻋY

نآ يﺎﺘﺳار رد X ﻲﻣ

ﺪﺷﺎﺑ ﺖﻴﻌﻗﻮﻣ رد . ﻪﻜﻨﻳا ﻪﺑ ﻪﺟﻮﺗﺎﺑ ،y=0

(5)

3 / ﺰﻴﻳﺎﭘ 1390

ﺪﺣاو mm mm k k k w/m2.k

5.6697E w/m².k⁴

mm mm/s

A

V

لاوﮋﻳو ﻲﺴﻳﻮﻧ ﻪﻣﺎﻧﺮﺑ نﺎﺑز ﻪﺑ يﺪﻛ ﻪﻟﺄﺴﻣ ﻦﻳا ﻞﺣ ياﺮﺑ تﺎﻴﺿﺮﻓ و تﺎﻋﻼﻃا ،ﺪﻛ ياﺪﺘﺑا

و تﺎﺼﺘﺨﻣ ﺲﭙﺳ .دﻮﺷ ﺪﻌﺑ ﺖﻤﺴﻗ رد .دﻮﺷ

ﺎﻣد ،نﺎﻣز نﺪﺷ ﻪﻓﺎﺿا ﺎﺑ ،ﻲﻟاﻮﺘﻣ ﻪﻘﻠﺣ ود رد ،ﻪﻣﺎﻧﺮﺑ يﺎﻫ

هﺮﮔ ﺎﻫ

ﺎﻣد ،ﻲﻳاﺪﺘﺑا نﺎﻣز رد .ددﺮﮔ يﺎﻫ

ﻲﻜﻳﺮﺘﻜﻟا سﻮﻗ ﻲﺗراﺮﺣ طوﺮﺨﻣ ضﺮﻌﻣ رد ﺎﻳ و ﺪﻨﺷﺎﺑ سﻮﻗ زا رود

نﺪﺷ ﻚﻨﺧ مﺎﮕﻨﻫ رد ) ﺪﺷﺎﺑ يرﺎﻜﺷﻮﺟ زا ﺪﻌﺑ ﻲﻧﺎﻣز ﻪﻠﺣﺮﻣ

هدﺎﻔﺘﺳا ﺮﻳز شور

زا ﻚﻳﺮﻫ ياﺮﺑ ﻢﺴﺟ ﻲﺗراﺮﺣ لﺎﻘﺘﻧا رﺎﺘﻓر .ﺖﺳا هﺪﺷ 3

ﺖﻟﺎﺣ

ﻪﺒﺳﺎﺤﻣ ﻞﺑﺎﻗ ﻲﻠﻴﻠﺤﺗ شور ﻪﺑ و ﻲﻣ

ﺪﺷﺎﺑ ﻪﺑ .

هدﺎﻔﺘﺳا ﺪﻛ ﻲﻳﺎﻣزآ ﻲﺘﺳار ياﺮﺑ

ﻪﻌﻄﻗ ﻪﻴﻟوا يﺎﻣد شور ﻦﻳا

ﺖﺑﺎﺛ يﺎﻣد طﺮﺷ ﺎﺑ ﺎﻫزﺮﻣ ﻪﻤﻫ و هﺪﺷ ﺖﻟﺎﺣ ﻦﻳا رد .

ﺶﻴﭘ ﻲﻨﻴﺑ

رود ة

،ﻢﻫدزﺎﻳ ةرﺎﻤﺷ

ﻪﻟﺄﺴﻣ تﺎﻴﺿ

دﺎﻤﻧ راﺪﻘﻣ

Length 50

Berth 50

T∞ 298

T0

298

Tmold

2300

hc

10

0.08 ε

5.6697E^-8 σ Rb

3

S 20

0.8 η

I 200

V 10

ﻒﻳدر ﺮﺘﻣارﺎﭘ ﺎﺑ ( 5

زرا ﻢﻫ ﻲﻣ ﺪﺷﺎﺑ

.

لاوﮋﻳو ﻲﺴﻳﻮﻧ ﻪﻣﺎﻧﺮﺑ نﺎﺑز ﻪﺑ يﺪﻛ ﻪﻟﺄﺴﻣ ﻦﻳا ﻞﺣ ياﺮﺑ تﺎﻴﺿﺮﻓ و تﺎﻋﻼﻃا ،ﺪﻛ ياﺪﺘﺑا

ﻲﻣ ﻦﻴﻴﻌﺗ يدورو و تﺎﺼﺘﺨﻣ ﺲﭙﺳ .دﻮﺷ

ﻲﻣ ﺪﻴﻟﻮﺗ ﻲﺗﺎﺒﺳﺎﺤﻣ ﻪﻜﺒﺷ ﺪﻌﺑ ﺖﻤﺴﻗ رد .دﻮﺷ

ﺎﻣد ،نﺎﻣز نﺪﺷ ﻪﻓﺎﺿا ﺎﺑ ،ﻲﻟاﻮﺘﻣ ﻪﻘﻠﺣ ود رد ،ﻪﻣﺎﻧﺮﺑ ﺎﻣد ،ﻲﻳاﺪﺘﺑا نﺎﻣز رد .ددﺮﮔ

ﻲﻜﻳﺮﺘﻜﻟا سﻮﻗ ﻲﺗراﺮﺣ طوﺮﺨﻣ ضﺮﻌﻣ رد هﺮﮔ

ﺎﻫ ﺎﻳ و ﺪﻨﺷﺎﺑ سﻮﻗ زا رود

نﺪﺷ ﻚﻨﺧ مﺎﮕﻨﻫ رد ) ﺪﺷﺎﺑ يرﺎﻜﺷﻮﺟ زا ﺪﻌﺑ ﻲﻧﺎﻣز ﻪﻠﺣﺮﻣ ﻲﻣ ظﺎﺤﻟ ﻞﺒﻗ ﻪﻠﺣﺮﻣ

.ددﺮﮔ

ﻲﺗﺎﺒﺳﺎﺤﻣ ﺪﻛ ﻲﻳﺎﻣزآ ﻲﺘﺳار

زا هﺪﺷ ﻪﺘﺷﻮﻧ ﻪﻣﺎﻧﺮﺑ ﺖﺤﺻ لﺮﺘﻨﻛ ياﺮﺑ 3

هدﺎﻔﺘﺳا ﺮﻳز شور

زا ﻚﻳﺮﻫ ياﺮﺑ ﻢﺴﺟ ﻲﺗراﺮﺣ لﺎﻘﺘﻧا رﺎﺘﻓر .ﺖﺳا هﺪﺷ ﻪﺒﺳﺎﺤﻣ ﻞﺑﺎﻗ ﻲﻠﻴﻠﺤﺗ شور ﻪﺑ و

هدﺎﻔﺘﺳا ﺪﻛ ﻲﻳﺎﻣزآ ﻲﺘﺳار ياﺮﺑ

ﻪﻌﻄﻗ ﻪﻴﻟوا يﺎﻣد شور ﻦﻳا

ﺖﺑﺎﺛ يﺎﻣد طﺮﺷ ﺎﺑ ﺎﻫزﺮﻣ ﻪﻤﻫ و هﺪﺷ دﻮﺷ

ﺖﻟﺎﺣ ﻦﻳا رد .

رود

لوﺪﺟ ﺮﻓ1 ﻪﻟﺄﺴﻣ تﺎﻴﺿ

ناﻮﻨﻋ ﻪﻌﻄﻗ لﻮﻃ Length

ﻪﻌﻄﻗ ضﺮﻋ ﻂﻴﺤﻣ يﺎﻣد ﻪﻌﻄﻗ ﻪﻴﻟوا يﺎﻣد باﺬﻣ ﻪﭽﺿﻮﺣ يﺎﻣد اﻮﻫ ﺖﻓﺮﻤﻫ تراﺮﺣ لﺎﻘﺘﻧا ﺐﻳﺮﺿ

دﻻﻮﻓ ﻲﻌﺸﻌﺸﺗ روﺪﺻ ﺐﻳﺮﺿ نﺎﻣﺰﺘﻟﻮﺑ ﺖﺑﺎﺛ ﻲﻜﻳﺮﺘﻜﻟا سﻮﻗ طوﺮﺨﻣ عﺎﻌﺷ

دوﺮﺘﻜﻟا ﻲﻄﺧ ﺖﻋﺮﺳ ا سﻮﻗ ﻲﺗراﺮﺣ هدزﺎﺑ ﻲﻜﻳﺮﺘﻜﻟ

ﻲﻜﻳﺮﺘﻜﻟا سﻮﻗ نﺎﻳﺮﺟ تﺪﺷ ﻲﻜﻳﺮﺘﻜﻟا سﻮﻗ ﻞﻴﺴﻧﺎﺘﭘ فﻼﺘﺧا

11 ﺎﺗ 13 ﻒﻳدر ﺮﺘﻣارﺎﭘ ﺎﺑ (

لاوﮋﻳو ﻲﺴﻳﻮﻧ ﻪﻣﺎﻧﺮﺑ نﺎﺑز ﻪﺑ يﺪﻛ ﻪﻟﺄﺴﻣ ﻦﻳا ﻞﺣ ياﺮﺑ رد .ﺖﺳا هﺪﺷ ﻪﻴﻬﺗ ﻚﻴﺴﻴﺑ تﺎﻴﺿﺮﻓ و تﺎﻋﻼﻃا ،ﺪﻛ ياﺪﺘﺑا

ناﻮﻨﻋ ﻲﻣ ﻦﻴﻴﻌﺗ يدورو ﻲﻣ ﺪﻴﻟﻮﺗ ﻲﺗﺎﺒﺳﺎﺤﻣ ﻪﻜﺒﺷ

ﺎﻣد ،نﺎﻣز نﺪﺷ ﻪﻓﺎﺿا ﺎﺑ ،ﻲﻟاﻮﺘﻣ ﻪﻘﻠﺣ ود رد ،ﻪﻣﺎﻧﺮﺑ ﻲﻣ ﻪﺒﺳﺎﺤﻣ

ﺎﻣد ،ﻲﻳاﺪﺘﺑا نﺎﻣز رد .ددﺮﮔ

ﻲﻜﻳﺮﺘﻜﻟا سﻮﻗ ﻲﺗراﺮﺣ طوﺮﺨﻣ ضﺮﻌﻣ رد

ﻪﻛ ﻲﺗرﻮﺻرد و هﺪﺷ ﻪﺒﺳﺎﺤﻣ هﺮﮔ

نﺪﺷ ﻚﻨﺧ مﺎﮕﻨﻫ رد ) ﺪﺷﺎﺑ يرﺎﻜﺷﻮﺟ زا ﺪﻌﺑ ﻲﻧﺎﻣز ﻪﻠﺣﺮﻣ ﻲﻣ ظﺎﺤﻟ ﻞﺒﻗ ﻪﻠﺣﺮﻣ

ﻲﺗﺎﺒﺳﺎﺤﻣ ﺪﻛ ﻲﻳﺎﻣزآ ﻲﺘﺳار زا هﺪﺷ ﻪﺘﺷﻮﻧ ﻪﻣﺎﻧﺮﺑ ﺖﺤﺻ لﺮﺘﻨﻛ ياﺮﺑ زا ﻚﻳﺮﻫ ياﺮﺑ ﻢﺴﺟ ﻲﺗراﺮﺣ لﺎﻘﺘﻧا رﺎﺘﻓر .ﺖﺳا هﺪﺷ

ﻪﺒﺳﺎﺤﻣ ﻞﺑﺎﻗ ﻲﻠﻴﻠﺤﺗ شور ﻪﺑ و

ﻦﻳا زا ﺐﺒﺳ ﻦﻴﻤﻫ شور

ﺎﻫ هدﺎﻔﺘﺳا ﺪﻛ ﻲﻳﺎﻣزآ ﻲﺘﺳار ياﺮﺑ

رد :ﻪﻌﻄﻗ ﺎﺑ ﻲﻳﺎﻣﺪﻤﻫ :

رﺎﻴﺘﺧا ﻂﻴﺤﻣ يﺎﻣد ﺖﺑﺎﺛ يﺎﻣد طﺮﺷ ﺎﺑ ﺎﻫزﺮﻣ ﻪﻤﻫ و هﺪﺷ

ﻪﺘﻓﺮﮔ ﺮﻈﻧ رد ﻦﻳﻮﻠﻛ ﻲﻣ

دﻮﺷ

ﻳ ناﻮﻨﻋ ﻒ

1 ﻪﻌﻄﻗ لﻮﻃ

2 ﻪﻌﻄﻗ ضﺮﻋ

3 ﻂﻴﺤﻣ يﺎﻣد

4 ﻪﻌﻄﻗ ﻪﻴﻟوا يﺎﻣد

5 باﺬﻣ ﻪﭽﺿﻮﺣ يﺎﻣد

6 اﻮﻫ ﺖﻓﺮﻤﻫ تراﺮﺣ لﺎﻘﺘﻧا ﺐﻳﺮﺿ

7 دﻻﻮﻓ ﻲﻌﺸﻌﺸﺗ روﺪﺻ ﺐﻳﺮﺿ

8 نﺎﻣﺰﺘﻟﻮﺑ ﺖﺑﺎﺛ

9 ﻲﻜﻳﺮﺘﻜﻟا سﻮﻗ طوﺮﺨﻣ عﺎﻌﺷ

10 دوﺮﺘﻜﻟا ﻲﻄﺧ ﺖﻋﺮﺳ

*11 ا سﻮﻗ ﻲﺗراﺮﺣ هدزﺎﺑ

*12 ﻲﻜﻳﺮﺘﻜﻟا سﻮﻗ نﺎﻳﺮﺟ تﺪﺷ

*13 ﻲﻜﻳﺮﺘﻜﻟا سﻮﻗ ﻞﻴﺴﻧﺎﺘﭘ فﻼﺘﺧا

ﻒﻳدر) ﺎﻫﺮﺘﻣارﺎﭘ ﻦﻳا يﺎﻫ

11

لاوﮋﻳو ﻲﺴﻳﻮﻧ ﻪﻣﺎﻧﺮﺑ نﺎﺑز ﻪﺑ يﺪﻛ ﻪﻟﺄﺴﻣ ﻦﻳا ﻞﺣ ياﺮﺑ

رد .ﺖﺳا هﺪﺷ ﻪﻴﻬﺗ ﻚﻴﺴﻴﺑ ﻪﻟﺄﺴﻣ ﻪﻴﻟوا ﻪﺑ

ناﻮﻨﻋ

هرﺎﻤﺷ هﺮﮔ ﺎﻫ ي ﻲﻣ ﺪﻴﻟﻮﺗ ﻲﺗﺎﺒﺳﺎﺤﻣ ﻪﻜﺒﺷ

ﺎﻣد ،نﺎﻣز نﺪﺷ ﻪﻓﺎﺿا ﺎﺑ ،ﻲﻟاﻮﺘﻣ ﻪﻘﻠﺣ ود رد ،ﻪﻣﺎﻧﺮﺑ ترﻮﺻ رود يﺎﻫ ﻲﻣ ﻪﺒﺳﺎﺤﻣ

يدور هﺮﮔ ﺎﻫ ي ﻲﻜﻳﺮﺘﻜﻟا سﻮﻗ ﻲﺗراﺮﺣ طوﺮﺨﻣ ضﺮﻌﻣ رد

ﻪﻛ ﻲﺗرﻮﺻرد و هﺪﺷ ﻪﺒﺳﺎﺤﻣ نﺪﺷ ﻚﻨﺧ مﺎﮕﻨﻫ رد ) ﺪﺷﺎﺑ يرﺎﻜﺷﻮﺟ زا ﺪﻌﺑ ﻲﻧﺎﻣز ﻪﻠﺣﺮﻣ ﺎﻣد ،(ﻪﻌﻄﻗ يﺎﻫ

ﻲﻣ ظﺎﺤﻟ ﻞﺒﻗ ﻪﻠﺣﺮﻣ

1 - ﻲﺗﺎﺒﺳﺎﺤﻣ ﺪﻛ ﻲﻳﺎﻣزآ ﻲﺘﺳار

زا هﺪﺷ ﻪﺘﺷﻮﻧ ﻪﻣﺎﻧﺮﺑ ﺖﺤﺻ لﺮﺘﻨﻛ ياﺮﺑ زا ﻚﻳﺮﻫ ياﺮﺑ ﻢﺴﺟ ﻲﺗراﺮﺣ لﺎﻘﺘﻧا رﺎﺘﻓر .ﺖﺳا هﺪﺷ ﻞﺑﺎﻗ ﺶﻴﭘ ﻲﻨﻴﺑ ﻪﺒﺳﺎﺤﻣ ﻞﺑﺎﻗ ﻲﻠﻴﻠﺤﺗ شور ﻪﺑ و

ﻦﻳا زا ﺐﺒﺳ ﻦﻴﻤﻫ .ﺖﺳا هﺪﺷ

شور لوا رد :ﻪﻌﻄﻗ ﺎﺑ ﻲﻳﺎﻣﺪﻤﻫ :

رﺎﻴﺘﺧا ﻂﻴﺤﻣ يﺎﻣد 1000 ﻪﺘﻓﺮﮔ ﺮﻈﻧ رد ﻦﻳﻮﻠﻛ

99

زا تراﺮﺣ لﺎﻘﺘﻧا و هدﻮﺑ راﺮﻗﺮﺑ نرﺎﻘﺗ زﺮﻣ ﻪﺳ ياﺮﺑ .

ترﻮﺻ

ﻲﻜﻳﺰﻴﻓ لﺪﻣ تﺎﻴﺿﺮﻓ ) لوﺪﺟ رد 1

(

دﻻﻮﻓ ﻲﻳﺎﻧﺎﺳر ﺐﻳﺮﺿ و ،k

نآ تاﺮﻴﻴﻐﺗ ﻲﻌﺑاﻮﺗ ﻚﻤﻛ ﻪﺑ و ﺖﺳا هﺪﺷ ضﺮﻓ ﺎﻣد ﺎﺑ ﺮﻴﻐﺘﻣ ﺪﺷﺎﺑ

.

F M

Gm:

ﻪﻜﺒﺷ

ﻖﻄﻨﻣ ﺎﺑ ﺖﺴﻳﺎﺑ

ﻒﻠﺘﺨﻣ ﻞﺣاﺮﻣ رد ﺎﺗ دﻮﺷ مﺎﺠﻧا

در ﻳ ﻒ 1 2 3 4 5 6 7 8 9 10

11 12 13

* ﻒﻳدر) ﺎﻫﺮﺘﻣارﺎﭘ ﻦﻳا

لاوﮋﻳو ﻲﺴﻳﻮﻧ ﻪﻣﺎﻧﺮﺑ نﺎﺑز ﻪﺑ يﺪﻛ ﻪﻟﺄﺴﻣ ﻦﻳا ﻞﺣ ياﺮﺑ

رد .ﺖﺳا هﺪﺷ ﻪﻴﻬﺗ ﻚﻴﺴﻴﺑ ﻪﻟﺄﺴﻣ ﻪﻴﻟوا هرﺎﻤﺷ ﺎﻣد ،نﺎﻣز نﺪﺷ ﻪﻓﺎﺿا ﺎﺑ ،ﻲﻟاﻮﺘﻣ ﻪﻘﻠﺣ ود رد ،ﻪﻣﺎﻧﺮﺑ ﻪﺑ ترﻮﺻ

و يدور ﻪﻛ ﻲﺗرﻮﺻرد و هﺪﺷ ﻪﺒﺳﺎﺤﻣ نﺪﺷ ﻚﻨﺧ مﺎﮕﻨﻫ رد ) ﺪﺷﺎﺑ يرﺎﻜﺷﻮﺟ زا ﺪﻌﺑ ﻲﻧﺎﻣز ﻪﻠﺣﺮﻣ ﺎﻣد ،(ﻪﻌﻄﻗ

4 - 1 زا هﺪﺷ ﻪﺘﺷﻮﻧ ﻪﻣﺎﻧﺮﺑ ﺖﺤﺻ لﺮﺘﻨﻛ ياﺮﺑ زا ﻚﻳﺮﻫ ياﺮﺑ ﻢﺴﺟ ﻲﺗراﺮﺣ لﺎﻘﺘﻧا رﺎﺘﻓر .ﺖﺳا هﺪﺷ ﻞﺑﺎﻗ ﻦﻳا زا ﺐﺒﺳ ﻦﻴﻤﻫ .ﺖﺳا هﺪﺷ شور رﺎﻴﺘﺧا ﻂﻴﺤﻣ يﺎﻣد 1000

زا تراﺮﺣ لﺎﻘﺘﻧا و هدﻮﺑ راﺮﻗﺮﺑ نرﺎﻘﺗ دﻮﺷ

زﺮﻣ ﻪﺳ ياﺮﺑ .

تراﺮﺣ لﺎﻘﺘﻧا ﺎﺑ و ﻦﻴﺑار ﻪﺑ

ترﻮﺻ

ﻲﻜﻳﺰﻴﻓ لﺪﻣ تﺎﻴﺿﺮﻓ 14 ) لوﺪﺟ رد [

يرﺎﻜﺷﻮﺟ دوﺮﺘﻜﻟا و قرو

دﻻﻮﻓ ﻲﻳﺎﻧﺎﺳر ﺐﻳﺮﺿ و

نآ تاﺮﻴﻴﻐﺗ ﻲﻌﺑاﻮﺗ ﻚﻤﻛ ﻪﺑ و ﺖﺳا هﺪﺷ ضﺮﻓ ﺎﻣد ﺎﺑ ﺮﻴﻐﺘﻣ ﺘﻧﺎﺳ ﻪﺟرد

ﻴ داﺮﮕ ﻲﻣ ﺪﺷﺎﺑ

: = −5.8 ∗ 10 : = q54 − 3.35

: = tu v

uw425 + 0.773:666 545

ﺪﻴﻟﻮﺗ و هﺮﮔ ﺎﻫ ي ﻪﻜﺒﺷ

ﻲﻣ ﺎﻬﻨﺗ ، ﻖﻄﻨﻣ ﺎﺑ ﺖﺴﻳﺎﺑ

ﻒﻠﺘﺨﻣ ﻞﺣاﺮﻣ رد ﺎﺗ دﻮﺷ مﺎﺠﻧا زا تراﺮﺣ لﺎﻘﺘﻧا و هدﻮﺑ راﺮﻗﺮﺑ نرﺎﻘﺗ

ضﺮﻓ ﻖﻳﺎﻋ ﻂﺧ ﻦﻳا و ﺮﻔﺻ ﺖﻬﺟ ﻦﻳا ﻲﻣ

دﻮﺷ

تراﺮﺣ لﺎﻘﺘﻧا ﺎﺑ و ﻦﻴﺑار

.ﺖﺳا هﺪﺷ ضﺮﻓ ﻲﻌﺸﻌﺸﺗ و ﺖﻓﺮﻤﻫ ﻲﻜﻳﺰﻴﻓ لﺪﻣ تﺎﻴﺿﺮﻓ

11 ، 12 ، 13 و 14

يرﺎﻜﺷﻮﺟ دوﺮﺘﻜﻟا و قرو

هﮋﻳو ﻲﺗراﺮﺣ ﺐﻳﺮﺿ ،

Cp

دﻻﻮﻓ ﻲﻳﺎﻧﺎﺳر ﺐﻳﺮﺿ و

نآ تاﺮﻴﻴﻐﺗ ﻲﻌﺑاﻮﺗ ﻚﻤﻛ ﻪﺑ و ﺖﺳا هﺪﺷ ضﺮﻓ ﺎﻣد ﺎﺑ ﺮﻴﻐﺘﻣ سﺎﺳاﺮﺑ ﺎﻫﺎﻣد .ﺖﺳا هﺪﺷ ﻒﻳﺮﻌﺗ ﺘﻧﺎﺳ ﻪﺟرد

:ﺖﺳا ﺮﻳز راﺮﻗ ﻪﺑ هﺪﺷ هدﺮﺑ

10^\{∗ : + 7870 35 ∗ 10^\∗ :

27.3 800

− 0.00169:+ 2.22 ∗ 666 +_{~_\I}^_}} 600 545 +_{~_\I}^~ 735 650 900

هدﺎﺳ ﻞﻜﺷ ﻪﻟﺄﺴﻣ ﻦﻳا رد ﻲﻣ

ﺪﺷﺎﺑ ﺪﻴﻟﻮﺗ و

ﻲﻣ دﻮﺷ ﻲﻣ ﺎﻬﻨﺗ ، ﻒﻠﺘﺨﻣ ﻞﺣاﺮﻣ رد ﺎﺗ دﻮﺷ مﺎﺠﻧا

.دﺮﻛ ﻲﻧاﻮﺧاﺮﻓ ﻲﺘﺳرد

ﻚ سرﺪﻣ

ﺪﺷﺎﺑ ﻂﻳاﺮﺷ ، زا تراﺮﺣ لﺎﻘﺘﻧا و هدﻮﺑ راﺮﻗﺮﺑ نرﺎﻘﺗ

ضﺮﻓ ﻖﻳﺎﻋ ﻂﺧ ﻦﻳا و ﺮﻔﺻ ﺖﻬﺟ ﻦﻳا يزﺮﻣ طﺮﺷ ﺮﮕﻳد ﻪﺑ

ترﻮﺻ تراﺮﺣ لﺎﻘﺘﻧا ﺎﺑ و ﻦﻴﺑار

.ﺖﺳا هﺪﺷ ضﺮﻓ ﻲﻌﺸﻌﺸﺗ و ﺖﻓﺮﻤﻫ زا ﻦﺘﻓﺮﮔ ﻚﻤﻛ ﺎﺑ شﻮﺟ 11]

ﻜﺷ ﻞ يرﺎﻜﺷﻮﺟ دوﺮﺘﻜﻟا و قرو1

هﮋﻳو ﻲﺗراﺮﺣ ﺐﻳﺮﺿ ،

نآ تاﺮﻴﻴﻐﺗ ﻲﻌﺑاﻮﺗ ﻚﻤﻛ ﻪﺑ و ﺖﺳا هﺪﺷ ضﺮﻓ ﺎﻣد ﺎﺑ ﺮﻴﻐﺘﻣ سﺎﺳاﺮﺑ ﺎﻫﺎﻣد .ﺖﺳا هﺪﺷ ﻒﻳﺮﻌﺗ :ﺖﺳا ﺮﻳز راﺮﻗ ﻪﺑ هﺪﺷ هدﺮﺑ

7870 ⁄ ^_

20 : 800 800 :

∗ 10^\:^_ 20 :

: 735

: 900

:

هدﺎﺳ ﻞﻜﺷ ﻪﻟﺄﺴﻣ ﻦﻳا رد مﺎﺠﻧا ﻲﺘﺣار ﻪﺑ ﻲﺗﺎﺒﺳﺎﺤﻣ ﻲﻣ

يراﺬﮔ هﺮﮔ ﺎﻫ ﻒﻠﺘﺨﻣ ﻞﺣاﺮﻣ رد ﺎﺗ دﻮﺷ مﺎﺠﻧا

ﺎﻫ ﺑ ار ﻪ .دﺮﻛ ﻲﻧاﻮﺧاﺮﻓ ﻲﺘﺳرد

ﻲﺳﺪﻨﻬﻣ ﻧﺎﻜﻣ ﻴ ﻚ

شﻮﺟ زرد ﻲﻣ

ﺪﺷﺎﺑ

ضﺮﻓ ﻖﻳﺎﻋ ﻂﺧ ﻦﻳا و ﺮﻔﺻ ﺖﻬﺟ ﻦﻳا يزﺮﻣ طﺮﺷ ﺮﮕﻳد .ﺖﺳا هﺪﺷ ضﺮﻓ ﻲﻌﺸﻌﺸﺗ و ﺖﻓﺮﻤﻫ زا ﻦﺘﻓﺮﮔ ﻚﻤﻛ ﺎﺑ شﻮﺟ نﺎﻴﺑ .ﺖﺳا هﺪﺷ

ﻲﻟﺎﮕﭼ هﮋﻳو ﻲﺗراﺮﺣ ﺐﻳﺮﺿ ،ρ

نآ تاﺮﻴﻴﻐﺗ ﻲﻌﺑاﻮﺗ ﻚﻤﻛ ﻪﺑ و ﺖﺳا هﺪﺷ ضﺮﻓ ﺎﻣد ﺎﺑ ﺮﻴﻐﺘﻣ سﺎﺳاﺮﺑ ﺎﻫﺎﻣد .ﺖﺳا هﺪﺷ ﻒﻳﺮﻌﺗ ﻂﺑاﻮﺿ ﻪﺑ رﺎﻛ :ﺖﺳا ﺮﻳز راﺮﻗ ﻪﺑ هﺪﺷ هدﺮﺑ

) 20 (

) 21 (

800

) 22 (

600

هدﺎﺳ ﻞﻜﺷ ﻪﻟﺄﺴﻣ ﻦﻳا رد مﺎﺠﻧا ﻲﺘﺣار ﻪﺑ ﻲﺗﺎﺒﺳﺎﺤﻣ

هرﺎﻤﺷ ﻲﺘﺳرد يراﺬﮔ

ناﻮﺘﺑ ﻞﺣ هﺮﮔ

ﺎﻫ

شﻮﺟ زرد ضﺮﻓ ﻖﻳﺎﻋ ﻂﺧ ﻦﻳا و ﺮﻔﺻ ﺖﻬﺟ ﻦﻳا يزﺮﻣ طﺮﺷ ﺮﮕﻳد .ﺖﺳا هﺪﺷ ضﺮﻓ ﻲﻌﺸﻌﺸﺗ و ﺖﻓﺮﻤﻫ زا ﻦﺘﻓﺮﮔ ﻚﻤﻛ ﺎﺑ شﻮﺟ نﺎﻴﺑ

نآ تاﺮﻴﻴﻐﺗ ﻲﻌﺑاﻮﺗ ﻚﻤﻛ ﻪﺑ و ﺖﺳا هﺪﺷ ضﺮﻓ ﺎﻣد ﺎﺑ ﺮﻴﻐﺘﻣ سﺎﺳاﺮﺑ ﺎﻫﺎﻣد .ﺖﺳا هﺪﺷ ﻒﻳﺮﻌﺗ ﻂﺑاﻮﺿ )

)

مﺎﺠﻧا ﻲﺘﺣار ﻪﺑ ﻲﺗﺎﺒﺳﺎﺤﻣ هرﺎﻤﺷ ﻲﺘﺳرد ناﻮﺘﺑ ﻞﺣ