以有限元素法模擬探討子彈衝擊編織布之行為

୯!ҥ!Ҭ!೯!ε!Ꮲ!

ᐒఓπำᏢس!

ᅺ

ᅺ!γ!ፕ!Ў!

! ! !

аԖज़ϡનݤኳᔕ

௖૸ηቸፂᔐጓᙃѲϐՉࣁ

Investigating Ballistic Impact Behaviors of Woven Fabric

Using Finite Element Analysis

!

! !

!ࣴ!ز!ғ!Ǻ݅ηః!

ࡰᏤ௲௤!Ǻጰ٫ᓄ!റγ!

!

!

ύ ๮ ҇ ୯

΋

̿ Β ԃ Ύ Д

аԖज़ϡનݤኳᔕ௖૸ηቸፂᔐጓᙃѲϐՉࣁ

Investigating Ballistic Impact Behaviors of Woven Fabric

Using Finite Element Analysis

ࣴ!ز!ғǺ݅ηః!!!!!!!!!!!!!!!!!!!!StudentǺTzu-Chen Lin ࡰᏤ௲௤Ǻጰ٫ᓄ AdvisorǺJia-Lin Tsai

୯ ҥ Ҭ ೯ ε Ꮲ

ᐒ ఓ π ำ Ꮲ س ᅺ γ ፕ Ў A Thesis

Submitted to Department of Mechanical Engineering College of Engineering

National Chiao Tung University in partial Fulfillment of the Requirements

for the Degree of Master

in

Mechanical Engineering July 2013

Hsinchu, Taiwan, Republic of China

аԖज़ϡનݤኳᔕ௖૸ηቸፂᔐጓᙃѲϐՉࣁ

ᏢғǺ݅ηః! ! ! ! ! ! ! ! ! ! ࡰᏤ௲௤Ǻጰ٫ᓄ ௲௤

୯ҥҬ೯εᏢᐒఓπำسᅺγ੤

ᄔ

ᄔा

ҁࣴزЬाճҔԖज़ϡનϩ݋(Finite element analysis)௖૸ᠼᆢጓᙃ

ѲڙηቸፂᔐࡕϐՉࣁᆶ֎ૈᐒڋǶ२Ӄᙖҗж߄܄ൂϡᡏٰᢀჸᠼᆢ ໔ነᔔΚჹܭ฻ਏᠼᆢથ״ϐ୊ΚኳኧޑቹៜǴᒿ๱થጕࠆࡋБӛᓸ ᔈ Κ೴ᅌቚуǴځ฻ਏ୊Κኳኧ཮ᒿϐቚуǴԶ྽ᓸᕭᔈΚ࣬ӕਔǴቚуᠼ ᆢ໔ነᔔ߯ኧҭ཮ගϲ฻ਏ୊ΚኳኧǶਥᏵൂቫጓᙃѲޑፂᔐኳᔕǴᢀჸ ༝ౚೲࡋᐕำᡂϯаϷጓᙃѲૈໆ֎ԏ௃׎ǴКၨጓᙃѲόӕ୊Κኳኧǵ ᠼᆢ໔ነᔔ߯ኧǵ൳Ֆ௨ӈ׎ރаϷᜐࣚచҹϐቹៜǶ่݀ᡉҢᠼᆢጓᙃ Ѳ׷਑ޑ୊Κኳኧཇե߾ၨόܰวғઇᚯǴ٠ૈۯᒨߔᏲፂᔐޑਔ໔Ǵ٬ ளלቸૈΚၨ٫ǹ྽ጓᙃѲᠼᆢ໔คነᔔΚҭ܈ጓᙃѲ൳Ֆ௨ӈࣁᚈၠ ຯጓᙃݤਔǴᠼᆢ໔೿཮৒ܰౢғྖ౽ϐ౜ຝǴᏤठܢלፂᔐૈΚ཮ၨৡǹ ᢀჸᠼᆢጓᙃѲӧόӕᜐࣚచҹϐΠڙፂᔐࡕϐՉࣁว౜ǴऩᜐࣚԖڙ

ډܥ״߾ᡂ׎ݢ໺ሀၨזǴόڙܥ״Бӛޑᡂ׎ݢ໺ሀၨᄌǴӢԜਥᏵፂ

ᔐނϐᎩೲว౜ѤᜐڰۓϐጓᙃѲჹܭלቸૈΚന٫Ƕ

ࣁΑԖਏ౗Ӧϩ݋ӭቫጓᙃѲڙᒳౚፂᔐϐՉࣁǴҁࣴزஒൂቫа

ϷΟቫӄጓᙃኳࠠ຾ՉᙁϯࣁൂЁࡋషӝϡનኳࠠ(single-scale hybrid

element model)Ǵࡌҥં׎฻ਏኳࠠ(central-patch model)аϷΜӷࠠ฻ਏኳ

ࠠ(center-cross model)଺КၨǴᒳౚϩձа 40m/sǵ100m/s Ϸ 300m/s ϐೲ ࡋፂᔐǴᢀჸጓᙃѲڙፂᔐࡕᒳౚϐೲࡋᐕำǵጓᙃѲ୏ૈϷᔈᡂૈᡂϯ ᆶነᔔ઻ૈᐕำǴ٠КၨӄጓᙃኳࠠᆶᙁϯኳࠠڙፂᔐࡕϐՉࣁϷၮᆉ ਔ໔Ƕࣴز่݀ᡉҢᙁϯኳࠠόՠё෧Ͽၮᆉਔ໔Ǵځύં׎฻ਏኳࠠӧ ᒳౚೲࡋ 300m/s ፂᔐΠၨૈᆶӄጓᙃኳࠠڙፂᔐ่݀ၲډ΋ठǴԶΜӷ ࠠ฻ਏኳࠠόፕڙډΟᅿೲࡋፂᔐΠࣣૈၲډᆶӄጓᙃኳࠠӕኬϐ่݀Ƕ

Investigating Ballistic Impact Behaviors of Woven Fabric

Using Finite Element Analysis

StudentǺTzu-Chen Lin! ! ! ! ! ! ! AdvisorǺDr. Jia-Lin Tsai

Department of Mechanical Engineering

National Chiao Tung University

Abstract

This research aims to investigate the ballistic impact behaviors of woven fabric and its energy absorption using finite element analysis. The representative volume element (RVE) model was employed to observe the inter-fiber friction effect on the effective shear modulus. With the increment of the compressive stress through thickness direction, the effective shear modulus gradually enhanced. Increasing the coefficient of inter-fiber friction enhanced the equivalent shear modulus with the same compressive stress. According to the simulation of the ballistic impact of a single-ply woven fabric, the effects of the equivalent shear modulus, friction between yarns, geometry and boundary conditions of woven fabric are studied by observing the projectile velocity and energy transformation histories. Modeling results show that the lower equivalent shear modulus of the woven fabric contributed to delaying fabric failure, and caused the anti-bullet capability enhanced. In the conditions such as no inter-fiber friction or double span woven fabrics, yarns are sliding

easily and causing poor resistance against bullets. In different boundary conditions of woven fabrics during ballistic impact, the strain wave propagated faster at the constrained boundaries than at the free boundaries. Thus the fabric can effectively reduce the projectile residual velocity when four edges were clamped.

In order to analyze multilayer woven fabric during ballistic impact effectively, this research presents a single-scale hybrid element model to simulate the 1-ply and 3-ply woven fabrics. This technique involves modeling the central-patch model and center-cross model. The projectile velocity histories, internal energy, kinetic energy and sliding energy of the woven fabrics with impact velocities of 40m/s, 100m/s and 300m/s were investigated. It was found that there is a good agreement between the central-patch model and the full woven model in the impact velocity of 300m/s. The center-cross model shows very good agreement with the full woven case in three kinds of impact velocity. Moreover, the effective models can reduce much computing time than the full woven model.

ठ

ठᖴ

ٿԃޑࣴزғࢲջஒ຾Ε׀ᖂǴཀښ๱ྗഢ፯ΕΓғќ΋ঁ໘ࢤǶ܍ ᆾࡰᏤ௲௤! ጰ٫ᓄറγ೭ࢤਔ໔ޑፌፌ௲ᇧǴӧࣴز΢๏ϒ೚ӭࡰᏤ ᆶᔅշǴ٬ךளډ೚ӭᏢಞᐒ཮аϷғࢲύࡑΓೀ٣ޑ࿶ᡍϷᄊࡋǴӧԜ ठ΢җ૱ޑགᖴǶӕਔགᖴమ๮εᏢ୏ᐒسယۏԵ௲௤کπ཰מೌࣴز ଣߋՙےറγኘϧᏼҺᏢғα၂ہ঩Ǵ٠Ъӧࣴز΢๏ϒᝊ຦ࡌ᝼Ǵ٬ள ҁፕЎૈ୼׳уֹ๓Ƕௗ๱ሡाགᖴჴᡍ࠻္΋ӕᏟᏯޑუՔॺ׵٫᫢ کᙎࠧЈǴаϷჴᡍ࠻Ꮲߏ೚༵ဂǵቅϿయǵᒘࡏᒺǵ໳଼ࢩǵЦੀϡǵ ಷЎࡏǵଯቺ࠶ӧ೭ٿԃٰ๏ϒ೚ӭᔅշϷࡌ᝼Ǵ٬ךԏᛘؼӭǶԜѦག ᖴᛥࠔ߷ǵ׵ದ྆ǵঞӀⲦǵڑࢃդӧࣴزᆶғࢲύޑഉՔǴ٬ளჴᡍ࠻ ғࢲ׳ӭߍӭ࠮Ƕ΋ၡ΢وٰ׳ሡाགᖴவεᏢਔය൩΋ଆոΚޑஞণ ᇬǵڑࣂᏌǵ໳ഩ╈ǵಷ࢙㩺ǵڬٵሺ฻ΓǴᗨฅεৎϩ႖ӭೀ٩ฅ཮ϕ ࣬уݨઉ᝝ǴᡣךഢགᆂЈǴ҂ٰᗋሡाӚՏޑڐշ٬ך׳Ԗ୏Κय़ჹϐ ࡕޑࡷᏯǶനࡕǴ׳ाགᖴৎР݅܍ѶӃғکৎ҆ֆᆧ࣓ζγǴӧᅐߏޑ ؃ᏢғఱύᓨᓨޑႴᓰǵЍ࡭ᆶᡏፊǴ٬ךૈ୼คࡕ៝ϐኁޑᏢಞǴа໩ ճֹԋᅺγᏢՏǶӵϞ؃Ꮲғఱջஒ֋΋ࢤပǴགᖴ΋ၡ΢Ѝ࡭ךǵᔅշ ךаϷ࣮ӳךޑΓǶ ݅ηః! ᙣᇞ ύ๮҇୯ 102 ԃ 7 Д

Ҟ

Ҟᒵ

ᄔा ... i Abstract ... iii ठᖴ ... v Ҟᒵ ... vi ߄Ҟᒵ ... ix კҞᒵ ... x ಃ΋ക! ᆣፕ ... 1 1.1 ࣴز୏ᐒᆶЎ᝘ӣ៝ ... 1 1.2 ࣴزҞ኱ᆶБݤ ... 11 ಃΒക! ௖૸ൂቫᠼᆢጓᙃѲڙፂᔐਔϐ୏ᄊៜᔈՉࣁ ... 12 2.1 ፂᔐϩ݋Бݤ ... 12 2.1.1 ᗦ܄؃ှݤᆶᡉ܄؃ှݤ ... 12

2.1.2 ਔ໔؁໘௓ڋ(Time Step Control) ... 14

2.2 ᠼᆢ׷਑୊Κኳኧޑቹៜ ... 15

2.3 ᠼᆢነᔔΚޑቹៜ ... 21

2.5 ጓᙃѲᜐࣚచҹޑቹៜ ... 27 ಃΟക! ࡌҥᙁϯ฻ਏᠼᆢጓᙃѲϩ݋ኳࠠ ... 30 3.1 ൂቫᠼᆢጓᙃѲᙁϯኳࠠࡌҥ ... 30 3.1.1 ӄጓᙃჴᡏϡનኳࠠࡌҥ ... 30 3.1.2 ฻ਏኳࠠࡌҥ ... 31 3.1.2.1 ં׎฻ਏኳࠠ ... 31 3.1.2.2 Μӷ׎฻ਏኳࠠ ... 32 3.1.3 ฻ਏ୔ୱϐ׷਑ୖኧ ... 33 3.2 ൂቫᠼᆢጓᙃѲᙁϯኳ่ࠠ݀૸ፕ ... 37 3.2.1 ፂᔐೲࡋ V0=40m/s ... 37 3.2.2 ፂᔐೲࡋ V0=100m/s ... 38 3.2.3 ፂᔐೲࡋ V0=300m/s ... 40 3.3 ΟቫᠼᆢጓᙃѲᙁϯኳࠠࡌҥ ... 41 3.4 ΟቫᠼᆢጓᙃѲኳ่ࠠ݀૸ፕ ... 42 3.4.1 ፂᔐೲࡋ V0=40m/s ... 42 3.4.2 ፂᔐೲࡋ V0=100m/s ... 43 3.4.3 ፂᔐೲࡋ V0=300m/s ... 44 3.5 ჴᡍ่݀Кၨ ... 46 ಃѤക! ่ፕᆶ҂ٰπբ ... 48

4.1 ่ፕ ... 48

4.2 ҂ٰπբ ... 50

ୖԵЎ᝘ ... 52

ߕ߄ ... 55

߄

߄Ҟᒵ

߄ 2. 1 ᠼᆢϐ׷਑தኧ[11] ... 55 ߄ 2. 2 ጓᙃѲϐ൳Ֆୖኧ[11] ... 55 ߄ 2. 3 ጓᙃѲϐ׷਑தኧ[11] ... 56 ߄ 2. 4 ᒳ፦༝ౚϐ׷਑தኧ ... 56 ߄ 2. 5 ᚈၠຯጓᙃѲϐ൳Ֆୖኧ ... 56 ߄ 2. 6 ጓᙃѲϡનኧໆԏᔙ܄ ... 57 ߄ 2. 7 КၨόӕᜐࣚచҹጓᙃѲڙፂᔐࡕ༝ౚϐ҃ೲࡋ(t=80μs) ... 57 ߄ 3. 1 ฻ਏኳࠠϐ൳Ֆୖኧᆶ׷਑ୖኧ ... 58 ߄ 3. 2 ൂቫϷΟቫᠼᆢጓᙃѲኳࠠၮᆉਔ໔Кၨ ... 58

კ

კҞᒵ

კ 2. 1 ѳᙃѲᐉᄒय़ϐᡉ༾ྣТკ[11] ... 59 კ 2. 2 ጓᙃѲᠼᆢ״ᄒय़კ[23] ... 59 კ 2. 3 ጓᙃѲᠼᆢ״ᄒय़ (a)ᠼᆢ௨ӈ௃׎(b)ж߄܄ൂϡᡏ ... 60 კ 2. 4 ጓᙃѲᠼᆢϐж߄܄ൂϡᡏԖज़ϡનኳࠠ ... 60 კ 2. 5 ጓᙃѲᠼᆢж߄܄ൂϡᡏϐᜐࣚచҹ೛ۓ ... 61 კ 2. 6 ж߄܄ൂϡᡏޑ০኱س಍ϷЁκҢཀკ ... 61 კ 2. 7 ж߄܄ൂϡᡏኳࠠϐୁຎკ(a)࿯ᗺ Z БӛՏ౽ϩѲ (b)ᙁϯୁ ຎკ ... 62 კ 2. 8 ж߄܄ൂϡᡏᓸᔈΚᆶᓸᕭՏ౽ϐᜢ߯კ ... 62 კ 2. 9 ж߄܄ൂϡᡏ฻ਏ୊ΚኳኧᆶᓸᔈΚϐᜢ߯კ... 63 კ 2. 10 όӕነᔔ߯ኧΠǴ฻ਏ୊ΚኳኧᆶᓸᔈΚϐᜢ߯კ... 63 კ 2. 11 ᒳౚናᔐൂቫጓᙃѲ߃ۈރᄊϐ൳Ֆኳࠠ ... 64 კ 2. 12 ᠼᆢጓᙃѲԖज़ϡનኳࠠϐᐉᄒय़ ... 64 კ 2. 13 ൂቫጓᙃѲԖज़ϡનኳࠠ ... 65 კ 2. 14 ᠼᆢ״ϐϡન০኱Бӛ ... 65 კ 2. 15 όӕ୊ΚኳኧޑᠼᆢጓᙃѲڙፂᔐࡕ(a)༝ౚϐೲࡋᐕำ (b)ጓ ᙃѲᔈᡂૈᡂϯ(c)ጓᙃѲነᔔ઻ૈᡂϯ (d)ጓᙃѲ୏ૈᡂϯ ... 66 კ 2. 16 КၨጓᙃѲѤᜐڰۓਔᠼᆢነᔔ߯ኧϐᡂ׎კ(t=80μs) ... 67

კ 2. 17 όӕነᔔ߯ኧޑᠼᆢጓᙃѲڙፂᔐࡕ(a)༝ౚϐೲࡋᐕำ (b)ጓ ᙃѲᔈᡂૈᡂϯ(c)ጓᙃѲነᔔ઻ૈᡂϯ (d)ጓᙃѲ୏ૈᡂϯ ... 68 კ 2. 18 ጓᙃѲѤᜐڰۓڙፂᔐਔૈໆᙯ౽ԔጕკǴμ=0.5 ... 69 კ 2. 19 ጓᙃѲѤᜐڰۓڙፂᔐਔૈໆᙯ౽ԔጕკǴμ=0 ... 69 კ 2. 20 ᒳౚናᔐൂቫᚈၠຯጓᙃѲ߃ۈރᄊϐ൳Ֆኳࠠ... 70 კ 2. 21 ᚈၠຯѳᙃѲԖज़ϡનኳࠠϐᐉᄒय़ ... 70 კ 2. 22 ൂቫᚈၠຯጓᙃѲԖज़ϡનኳࠠ ... 71 კ 2. 23 КၨᚈၠຯጓᙃѲѤᜐڰۓਔᠼᆢነᔔ߯ኧϐᡂ׎კ(t=80μs) ... 71 კ 2. 24 όӕၠຯޑᠼᆢጓᙃѲڙፂᔐࡕ(a)༝ౚϐೲࡋᐕำ (b)ጓᙃѲ ᔈᡂૈᡂϯ(c)ጓᙃѲነᔔ઻ૈᡂϯ (d)ጓᙃѲ୏ૈᡂϯ ... 72 კ 2. 25 ᚈၠຯጓᙃѲѤᜐڰۓڙፂᔐਔૈໆᙯ౽ԔጕკǴμy-y =0.5 ... 73 კ 2. 26 КၨၠຯϷነᔔΚჹܭᒳౚϐೲࡋ-ਔ໔ᐕำ ... 73 კ 2. 27 ጓᙃѲѤᜐڰۓڙፂᔐϐୁຎკϷΠຎკǴμy-y =0.5 ... 74 კ 2. 28 ጓᙃѲٿᜐڰۓڙፂᔐϐୁຎკϷΠຎკǴμ=0.5 ... 75 კ 2. 29 ጓᙃѲѤᜐคܥ״ڙፂᔐϐୁຎკϷΠຎკǴμ=0.5 ... 76 კ 2. 30 όӕᜐࣚచҹޑᠼᆢጓᙃѲڙፂᔐࡕ(a)༝ౚϐೲࡋᐕำ (b)ጓ ᙃѲᔈᡂૈᡂϯ(c)ጓᙃѲነᔔ઻ૈᡂϯ (d)ጓᙃѲ୏ૈᡂϯ ... 77 კ 2. 31 ጓᙃѲڙፂᔐਔૈໆᙯ౽Ԕጕკ(a)ጓᙃѲٿᜐڰۓ (b)ጓᙃѲ Ѥᜐคܥ״ ... 78

კ 3. 1 ӄጓᙃჴᡏϡનኳࠠ΢ຎკ(Ѥϩϐ΋ኳࠠ) ... 79 კ 3. 2 ં׎฻ਏኳࠠ΢ຎკ(ӄኳࠠ) ... 79 კ 3. 3 ጓᙃ୔ୱᆶѳ݈୔ୱϐҬϟय़Ԗज़ϡનኳࠠკ... 80 კ 3. 4 Μӷ׎฻ਏኳࠠ΢ຎკ(ӄኳࠠ) ... 80 კ 3. 5 Ε৔ݢǵ೸৔ݢᆶϸ৔ݢҢཀკ ... 81 კ 3. 6 HEA ኳࠠ൳ՖЁκҢཀკ... 81 კ 3. 7 Кၨӄጓᙃኳࠠᆶ HEA ኳࠠܭ 40m/s ϐೲࡋፂᔐϐ่݀(a)༝ౚ ೲࡋ (b)ጓᙃѲᔈᡂૈ (c)ጓᙃѲύЈՏ౽ (d)ጓᙃѲ୏ૈ ... 82 კ 3. 8 ӄጓᙃኳࠠᆶ HEA ኳࠠڙ 40m/s ༝ౚፂᔐϐᡂ׎კ(a)ӄጓᙃኳ ࠠ (b)ં׎฻ਏኳࠠ (c)Μӷ׎฻ਏኳࠠ... 83 კ 3. 9 ӄጓᙃኳࠠᆶ HEA ኳࠠڙ 40m/s ༝ౚፂᔐϐЬᔈΚკ(a)ӄጓᙃ ኳࠠ (b)ં׎฻ਏኳࠠ (c)Μӷ׎฻ਏኳࠠ(t=200μs) ... 84 კ 3. 10 Кၨӄጓᙃኳࠠᆶ HEA ኳࠠܭ 100m/s ϐೲࡋፂᔐϐ่݀(a)༝ ౚೲࡋ (b)ጓᙃѲᔈᡂૈ (c)ጓᙃѲነᔔ઻ૈ (d)ጓᙃѲ୏ૈ ... 85 კ 3. 11 ӄጓᙃኳࠠᆶ HEA ኳࠠڙ 100m/s ༝ౚፂᔐϐᡂ׎კ(a)ӄጓᙃ ኳࠠ (b)ં׎฻ਏኳࠠ (c)Μӷ׎฻ਏኳࠠ ... 86 კ 3. 12 ӄጓᙃኳࠠᆶ HEA ኳࠠڙ 100m/s ༝ౚፂᔐϐЬᔈΚკ(a)ӄጓ ᙃኳࠠ (b)ં׎฻ਏኳࠠ (c)Μӷ׎฻ਏኳࠠ(t=60μs) ... 87 კ 3. 13 Кၨӄጓᙃኳࠠᆶ HEA ኳࠠܭ 300m/s ϐೲࡋፂᔐϐ่݀(a)༝

ౚೲࡋ (b)ጓᙃѲᔈᡂૈ (c)ጓᙃѲነᔔ઻ૈ (d)ጓᙃѲ୏ૈ ... 88 კ 3. 14 ӄጓᙃኳࠠᆶ HEA ኳࠠڙ 300m/s ༝ౚፂᔐϐᡂ׎კ(a)ӄጓᙃ ኳࠠ (b)ં׎฻ਏኳࠠ (c)Μӷ׎฻ਏኳࠠ ... 89 კ 3. 15 ӄጓᙃኳࠠᆶ HEA ኳࠠڙ 300m/s ༝ౚፂᔐϐЬᔈΚკ(a)ӄጓ ᙃኳࠠ (b)ં׎฻ਏኳࠠ (c)Μӷ׎฻ਏኳࠠ(t=10μs) ... 90 კ 3. 16 ΟቫጓᙃѲԖज़ϡનኳࠠ(a)฻فຎკ (b)ୁຎკ ... 91 კ 3. 17 КၨΟቫӄጓᙃኳࠠᆶ HEA ኳࠠܭ 40m/s ϐೲࡋፂᔐϐ่݀ (a)༝ౚೲࡋ (b)ጓᙃѲᔈᡂૈ (c)ጓᙃѲነᔔ઻ૈ (d)ጓᙃѲ୏ૈ 92 კ 3. 18 Οቫӄጓᙃኳࠠᆶ HEA ኳࠠڙ 40m/s ༝ౚፂᔐϐᡂ׎კ(a)ӄ ጓᙃኳࠠ (b)ં׎฻ਏኳࠠ (c)Μӷ׎฻ਏኳࠠ ... 93 კ 3. 19 Οቫӄጓᙃኳࠠᆶ HEA ኳࠠڙ 40m/s ༝ౚፂᔐϐЬᔈΚკ(a) ӄጓᙃኳࠠ (b)ં׎฻ਏኳࠠ (c)Μӷ׎฻ਏኳࠠ(t=60μs) ... 94 კ 3. 20 КၨΟቫӄጓᙃኳࠠᆶ HEA ኳࠠܭ 100m/s ϐೲࡋፂᔐϐ่݀ ... 95 კ 3. 21 Οቫӄጓᙃኳࠠᆶ HEA ኳࠠڙ 100m/s ༝ౚፂᔐϐᡂ׎კ(a)ӄ ጓᙃኳࠠ (b)ં׎฻ਏኳࠠ (c)Μӷ׎฻ਏኳࠠ ... 96 კ 3. 22 Οቫӄጓᙃኳࠠᆶ HEA ኳࠠڙ 100m/s ༝ౚፂᔐϐઇᚯ௃׎(a) ӄጓᙃኳࠠ (b)ં׎฻ਏኳࠠ (c)Μӷ׎฻ਏኳࠠ(ୁຎკ) ... 97 კ 3. 23 Οቫӄጓᙃኳࠠᆶ HEA ኳࠠڙ 100m/s ༝ౚፂᔐϐઇᚯ௃׎(a) ӄጓᙃኳࠠ(b)ં׎฻ਏኳࠠ (c)Μӷ׎฻ਏኳࠠ(΢ຎკ) ... 98

კ 3. 24 Οቫӄጓᙃኳࠠᆶ HEA ኳࠠڙ 100m/s ༝ౚፂᔐϐЬᔈΚკ(a) ӄጓᙃኳࠠ (b)ં׎฻ਏኳࠠ (c)Μӷ׎฻ਏኳࠠ(t=60μs) ... 99 კ 3. 25 КၨΟቫӄጓᙃኳࠠᆶ HEA ኳࠠܭ 300m/s ϐೲࡋፂᔐϐ่݀ (a)༝ౚೲࡋ (b)ጓᙃѲᔈᡂૈ (c)ጓᙃѲነᔔ઻ૈ (d)ጓᙃѲ୏ૈ ... 100 კ 3. 26 Οቫӄጓᙃኳࠠᆶ HEA ኳࠠڙ 300m/s ༝ౚፂᔐϐᡂ׎კ(a)ӄ ጓᙃኳࠠ (b)ં׎฻ਏኳࠠ (c)Μӷ׎฻ਏኳࠠ ... 101 კ 3. 27 Οቫӄጓᙃኳࠠᆶ HEA ኳࠠڙ 300m/s ༝ౚፂᔐϐЬᔈΚკ(a) ӄጓᙃኳࠠ (b)ં׎฻ਏኳࠠ (c)Μӷ׎฻ਏኳࠠ(t=10μs) ... 102 კ 3. 28 ൂቫጓᙃѲڙ༝ౚፂᔐࡕϐઇᚯϷྖ౽௃׎(a)ፂᔐೲࡋ 100m/s (b)ፂᔐೲࡋ 300m/s ... 103

ಃ

ಃ΋ക! ᆣፕ

1.1 ࣴز୏ᐒᆶЎ᝘ӣ៝

ٛቸՊ(ballistic vest)ܭै᝾Ҕ೼ύתᄽ๱ཱུख़ाޑفՅǴځёϩࣁฯ Ԅǵ೬ԄϷ೬ฯፄӝԄǶฯԄٛቸङЈ೯தҗߎឦ܈ഏౠಔԋǴՠ፦ໆၨ εЪڙናᔐࡕ৒ܰᓫ຋ǹԶ೬ԄٛቸङЈ೯த٬Ҕ Kevlar ࣁ׷਑ǴKevlar ڀଯமࡋϐ੝܄ǴЪஏࡋ໻ࣁᒳ៓ޑϖϩϐ΋ǴᆶฯԄٛቸङЈ࣬КԖᇸ ѯϷᡫࢲ฻ᓬ༈ǶӢԜǴKevlar ᠼᆢጓᙃѲϐࣴزЇଆቶεޑख़ຎǴᙖҗ ፂᔐჴᡍёෳໆᠼᆢጓᙃѲڙηቸፂᔐࡕϐઇᚯՉࣁаϷלቸૈΚǴՠ εໆፂᔐჴᡍሡ޸຤εໆਔ໔ᆶԋҁǴࡺҁࣴز٬ҔԖज़ϡનϩ݋ݤኳ ᔕᠼᆢጓᙃѲڙηቸፂᔐϐՉࣁǴஒёε൯෧Ͽፂᔐჴᡍ܌ሡϐၗྍǴ٠ ᆶፂᔐჴᡍ่݀բКၨǴၲډႣ՗ᠼᆢጓᙃѲלቸૈΚϐਏ݀Ƕ ӧၸѐࣴزٛቸՊፂᔐϐЎ᝘ύǴᏢޣჹܭൂቫጓᙃѲڙፂᔐϐՉ

ࣁԖፏӭޑ௖૸ǶDuan ฻Γ[1]аԖज़ϡનݤ(finite element analysis)ࡌҥ

рൂቫѳᙃѲኳࠠǴ௖૸ѳᙃѲڙډখ܄༝ౚޑଯೲፂᔐΠǴѳᙃѲόӕ

ᜐࣚచҹаϷᠼᆢ״໔ነᔔ߯ኧჹܭ֎ԏፂᔐނ୏ૈӭჲޑቹៜǶ྽ό

ԵቾѳᙃѲޑઇᚯ௃׎ǴፂᔐނཞѨޑ୏ૈ(loss of projectile kinetic energy)

཮฻ܭጓᙃѲҁي୏ૈ(yarn kinetic energy)ǵᔈᡂૈ(yarn strain energy)Ϸ

ᜐڰۓਔǴፂᔐނཞѨޑ୏ૈЬाаᙯඤԋጓᙃѲᔈᡂૈࣁЬǹԶ྽ጓᙃ

ѲᜐࣚచҹࣁѤᜐࣣόڙܥ״ਔǴፂᔐނཞѨޑ୏ૈЬाаᙯඤԋጓᙃ

Ѳ୏ૈࣁЬǶ

Duan ฻Γ[2]ҭ௖૸྽ԵቾᜐࣚచҹࣁѤᜐڰۓϐѳᙃѲԖઇᚯՉ

ࣁਔځڙፂᔐϐ౜ຝǴۓကᠼᆢޑ von Mises ᔈΚ(von Mises stress)ࣁઇ

ᚯྗ߾ǴӢԜ྽ࢌ΋ϡનӧीᆉύၲډઇᚯྗ߾ਔǴԜϡન཮ӧीᆉύ೏ մନǴӢԜ྽ጓᙃѲ໒ۈวғઇᚯࡕǴጓᙃѲҁي୏ૈǵᔈᡂૈϷነᔔ઻ ૈϐᕴک߾཮λܭፂᔐނཞѨޑ୏ૈǶԜѦǴ྽ፂᔐނᆶጓᙃѲ໔ϐነᔔ ߯ኧཇεǴፂᔐނཞѨޑ୏ૈҭᒿϐᡂεǶ Duan ฻Γ[3]ҭ௖૸ᜐࣚచҹϩձࣁѤᜐڰۓϷٿᜐڰۓϐѳᙃѲ ӧԖઇᚯՉࣁਔڙፂᔐϐ౜ຝǴаᠼᆢޑ von Mises ᔈΚࣁᠼᆢϐઇᚯྗ ߾ǴКၨነᔔ߯ኧӧٿᅿόӕᜐࣚచҹϐΠጓᙃѲڙፂᔐޑቹៜǴ௖૸ጓ ᙃѲڙډፂᔐࡕখ܄༝ౚϐ҃ೲࡋǵፂᔐΚϷጓᙃѲ֎ԏϐᕴૈໆǶ่݀ ว౜Ǵነᔔ߯ኧၨεਔ཮ۯ጗ጓᙃѲઇᚯޑਔ໔Ǵ٠Ъჹܭ༝ౚ཮೷ԋၨ εޑፂᔐΚǴԶ྽ۯ጗ጓᙃѲઇᚯޑਔ໔ǴߡૈቚуጓᙃѲ֎ԏϐᕴૈໆǴ ٬༝ౚऀ೸ጓᙃѲࡕϐ҃ೲࡋၨեǶόӕᜐࣚచҹჹܭቚуነᔔ߯ኧϐ բҔҭԖቹៜǴ྽ጓᙃѲᜐࣚచҹࣁٿᜐڰۓਔǴቚуነᔔ߯ኧё٬ጓᙃ Ѳ֎ԏϐૈໆගϲၨӭǶ Duan ฻Γ[4]ҭࣴز༝ࢊ׎ϐፂᔐނჹܭൂቫጓᙃѲڙፂᔐϐՉࣁǴ

Եቾ྽ጓᙃѲԖઇᚯՉࣁวғਔǴ༝ࢊፂᔐܭጓᙃѲࡕǴፂᔐނϐೲࡋᡂ ϯǶӧեೲናᔐΠǴጓᙃѲᜐࣚచҹࣁѤᜐڰۓਔǴፂᔐނೲࡋΠफ़നזǴ ՠઇᚯ౜ຝวғനԐǹ྽ጓᙃѲᜐࣚచҹࣁѤᜐࣣόڙܥ״ਔǴፂᔐނೲ ࡋΠफ़നᄌǴځጓᙃѲၨό৒ܰวғઇᚯǴӢԜፂᔐނೲࡋ෧ϿໆၨӭǶ ԶӧଯೲናᔐΠǴጓᙃѲϐᜐࣚచҹჹܭፂᔐނϐೲࡋ߾คቹៜǶ Talebi ฻Γ[5]ࡌҥόӕفࡋϐ༝ᒷ׎ηቸǴ௖૸όӕηቸፂᔐܭጓ ᙃѲࡕǴηቸཞѨޑ୏ૈᆶቸᓐفࡋϐᜢ߯Ƕ่݀ว౜Ǵ྽ቸᓐفࡋၨλ ਔǴጓᙃѲϐઇᚯኳԄЬाаऀڈࠠ(wedging)ઇᚯࣁЬǹԶ྽ቸᓐفࡋ ၨεਔǴጓᙃѲϐઇᚯኳԄЬाа୊Κࠠ(shear)ઇᚯࣁЬǶӆਥᏵӚᅿف ࡋϐηቸཞѨޑ୏ૈаϷጓᙃѲᘐ຋ϐኧໆբ಍᏾Ǵว౜فࡋࣁ 60°ϐቸ ᓐჹܭጓᙃѲё೷ԋനεޑઇᚯǶ а΢Ў᝘[1-5]௖૸ΑൂቫᠼᆢጓᙃѲ׷਑܄፦ǵ൳Ֆచҹǵነᔔ߯ኧǵ ᜐࣚచҹаϷቸᓐ׎ރϐቹៜǶՠҗܭጓᙃѲޑ൳Ֆ׎ރၨፄᚇᏤठϡ નኧໆၨӭǴӧԖज़ϡનݤၮᆉύ཮޸຤೚ӭၮᆉਔ໔ǴӢԜԖᏢޣගр ᙁϯ฻ਏኳٰࠠ෧Ͽϩ݋ၮᆉਔ໔Ƕ Grujicic ฻Γ[6]ܭԖज़ϡનݤϩձճҔჴᡏϡનаϷᖓෘϡનࡌҥ ጓᙃѲኳࠠǴᢀჸηቸ-ጓᙃѲ໔ነᔔ߯ኧϷᠼᆢ״໔ነᔔ߯ኧჹܭηቸ ཞѨϐ୏ૈޑቹៜǴ٠КၨጓᙃѲڙፂᔐਔϐᡂ׎Ϸઇᚯ௃׎ǶਥᏵૈໆ Ӻࡡۓ౛ǴፂᔐނཞѨޑ୏ૈᔈ฻ܭጓᙃѲҁي୏ૈǵᔈᡂૈϷነᔔ઻ૈ

ϐᕴکǶ่݀ᡉҢǴόፕճҔჴᡏϡનϷᖓෘϡનࡌҥጓᙃѲኳࠠǴፂᔐ ނཞѨޑ୏ૈᆶጓᙃѲҁي୏ૈǵᔈᡂૈϷነᔔ઻ૈΟ໨ᕴکϐᇤৡࣣ եܭ 5%Ǵ߄ҢٿኳࣣࠠёၲډૈໆӺࡡǶኳᔕ่݀ᡉҢǴᖓෘϡનኳࠠ ጓᙃѲҁي୏ૈǵᔈᡂૈϷነᔔ઻ૈϐᖿ༈ᆶჴᡏϡનኳ่ࠠ݀όϼ΋ ठǴচӢࣁᖓෘϡનኳࠠځᆛ਱ၨಉǹԶჴᡏϡનኳࠠځᆛ਱ၨஏǴӢԜ ೷ԋٿޣ่݀ϐৡ౦ǶԜѦǴ٬Ҕᖓෘϡનኳᔕё෧եၮᆉਔ໔Ǵၮᆉໆ ऊࣁჴᡏϡનޑϖϩϐ΋Ƕ Nilakantan ฻Γ[7]٬ҔԖज़ϡનݤࡌҥჴᡏϡનጓᙃѲǴϩձ೛ۓௗ ᝻ᜪࠠࣁԾ୏ࠠൂय़ௗ᝻ϷԾ୏ࠠय़ჹय़ௗ᝻ǴаԜբࣁКၨϐ୷ྗǶ٠

٬ҔൂЁࡋషӝϡનϩ݋ݤ(scale hybrid element analysis,

single-scale HEA)ǴஒጓᙃѲௗ߈ናᔐ୔ୱޑ೽ϩࡌࣁჴᡏϡનǴᇻᚆናᔐ୔ୱ ޑ೽ϩࡌࣁᖓෘϡનǴٿϟय़ϐ໔೛ۓܥ״БำԄаᗉխᔈΚݢ໺ሀਔ ౢғϸ৔౜ຝǴኳᔕ่݀ว౜ HEA ኳࠠӧፂᔐၸำύǴፂᔐނϐೲࡋᐕ ำǵϣૈǵነᔔ઻ૈаϷௗ᝻ΚᆶჴᡏϡનጓᙃѲኳࠠϐ่݀࣬಄ӝǴЪ HEA ኳࠠё࿯࣪ၮᆉਔ໔Ǵ଺ࣁኳᔕϩ݋ϐБݤၨԖਏ౗Ƕ ฅԶǴൂЁࡋషӝϡનϩ݋ݤϝฅሡाࡌҥጓᙃ่ᄬ຾ՉኳᔕǴӢԜ ԖᏢޣஒጓᙃѲኳࠠᇻᚆናᔐ୔ୱޑ೽ϩׯࡌࣁ֡፦ᖓෘѳ݈ǴӃճҔ ჴᡍ่݀܈ӄጓᙃኳࠠբࣁКၨ୷ྗǴ௦Ҕ၂ᇤݤ(trial-and-error approach) аளډ֡፦ѳ݈ޑ׷਑܄፦[8, 9]Ƕҗܭ၂ᇤݤѸ໪ख़ፄ຾Չၮᆉפрന

ௗ߈୷ྗॶޑ่݀Ǵࡺ Nilakantan[10, 11]฻Γᇡࣁ၂ᇤݤ٠ߚ΋ঁԖਏ౗

ޑБݤǴӢԜගр΋঺Бݤٰ؃ள፦ѳ݈ޑ׷਑܄፦Ǻ྽ጓᙃѲڙፂᔐࡕǴ

ጓᙃ่ᄬᆶ֡፦ѳ݈ٿϟ፦໔ߔל(impedance)ᔈा࣬ӕǴᔈΚݢӧ໺ሀ

ਔό཮ౢғϸ৔ݢǴճҔԜᜢ߯ёள฻ਏ׷਑܄፦ǶNilakantan ฻Γ׳຾

΋؁௖૸ӭЁࡋϐషӝϡનϩ݋ኳࠠ(multi-scale HEA models)Ǵஒኳࠠന

᎞߈ናᔐᗺϐֽ೽୔ୱ(local region)ࡌࣁჴᡏϡનጓᙃѲǴԛाֽ೽୔ୱ ࡌࣁᖓෘϡનጓᙃѲǴനࡕ᏾ᡏ୔ୱ(global region)ࡌࣁ฻ਏᖓෘϡનѳ य़ǶӕኬܭჴᡏϡનጓᙃѲᆶᖓෘϡનጓᙃѲٿϟय़ϐ໔೛ۓܥ״Бำ ԄаᗉխᔈΚݢ໺ሀਔౢғϸ৔౜ຝǴԶӧ฻ਏᖓෘϡનѳय़೽ϩճҔ ٿϟय़໔ߔל࣬฻ࣁ฻ਏϐ٩ᏵǴीᆉр฻ਏѳ݈ޑ׷਑தኧǴࡌҥ΋ঁ ӭЁࡋϐషӝϡનϩ݋ኳࠠǴᢀჸፂᔐၸำύፂᔐނϐೲࡋᐕำǵϣૈǵ ነᔔ઻ૈаϷௗ᝻ΚǴ٠ᆶਥᏵЎ᝘[7]ϐኳᔕ่݀ǴӕਔКၨჴᡏϡન ጓᙃѲኳࠠǵൂЁࡋ HEA ኳࠠаϷӭЁࡋ HEA ኳࠠǴᢀჸΟᅿኳࠠޑ ፂᔐނೲࡋᐕำǵϣૈǵነᔔ઻ૈаϷௗ᝻ΚǶኳᔕ่݀КၨᡉҢǴൂЁ

ࡋ HEA ኳࠠޑ่݀ᓬܭӭЁࡋ HEA ኳࠠǴՠࢂӭЁࡋ HEA ኳࠠ٩ฅૈ

߄౜ჴᡏϡનጓᙃѲኳࠠڙፂᔐϐՉࣁǴЪၮᆉਔ໔׳ࣁᕭอǴ۳ࡕటኳ

ᔕၨεЁκޑጓᙃѲኳࠠஒ׳ࣁߡճǶ

Ha-Minh ฻Γ[12]ஒ Nilakantan ฻ΓගрޑӭЁࡋషӝϡનϩ݋ኳࠠ

ᖓෘϡનጓᙃѲǴ᏾ᡏ୔ୱࡌࣁ฻ਏᖓෘϡનѳय़Ǵ٠ᆶӄጓᙃᖓෘϡન

ኳࠠ຾ՉКၨǴ௖૸฻ਏ୔ୱय़ᑈჹܭፂᔐނೲࡋᐕำǵϣૈǵነᔔ઻ૈ

аϷௗ᝻ΚϐቹៜǶኳᔕ่݀КၨᡉҢǴ྽ጓᙃѲڙፂᔐࡕϐୁӛᔈᡂ

(transverse strain wave)໺ሀԿ฻ਏ୔ୱਔǴځፂᔐނೲࡋᐕำϷௗ᝻Κᐕ

ำߡ཮ᆶӄጓᙃኳࠠϐ่݀ౢғৡ౦ǴӢԜ྽฻ਏ୔ୱय़ᑈཇλǴᆶӄጓ ᙃኳࠠޑኳᔕ่݀ཇ࣬߈Ƕ ౜ჴύٛቸՊ೯தࢂҗӭቫלቸѲ܌ಔԋǴፏӭᏢޣΨճҔԖज़ϡ નϩ݋ݤ௖૸ӭቫלቸѲڙፂᔐϐՉࣁǶChocron ฻Γ[13]ճҔԖज़ϡન ݤࡌҥΜቫჴᡏϡનጓᙃѲǴᙖҗ௖૸ጓᙃѲڙፂᔐࡕۭ೽ϐՏ౽(Apex position)аϷпഐᘉ৖ຯᚆ(Diagonal extent)Кၨٿᅿቸᓐ׎ރፂᔐϐ่ ݀Ǵ٠ᆶჴᡍ่݀բКၨǴ่݀ᡉҢጓᙃѲڙፂᔐࡕۭ೽ϐՏ౽ᆶпഐᘉ ৖ຯᚆӧኳᔕ΢ёྗዴႣ՗ፂᔐჴᡍϐ่݀Ƕ ӧӭቫጓᙃѲޑኳᔕБय़ǴGogineni ฻Γ[14]ჹܭൂቫϷӭቫጓᙃѲ

ҭԖుΕϐ௖૸Ǵ२Ӄۓကᠼᆢޑ܎՜ᔈᡂ(Failure strain in tension)ࣁઇ

ᚯྗ߾ǴႣෳൂቫጓᙃѲڙখ܄༝ࢊᡏፂᔐਔǴፂᔐނӧόӕ߃ೲࡋϐΠ

ऀ೸ጓᙃѲࡕϐ҃ೲࡋǴ٠ᆶ Tan ฻Γ[15]Ў᝘ϐჴᡍ่݀КၨǴ่݀ᡉ

ҢǴ٬ҔԖज़ϡનݤኳᔕёྗዴႣෳ༝ࢊᡏऀ೸ጓᙃѲࡕϐ҃ೲࡋǴᆶჴ

ᡍෳໆϐᇤৡࣣλܭ 6%Ƕځԛ௖૸ፂᔐނϐ߃ೲࡋჹܭጓᙃѲᔈᡂૈϷ

ઇᚯޑਔ໔Ǵ೷ԋጓᙃѲԖၨεޑᡂ׎ǴࡺጓᙃѲᔈᡂૈϷነᔔ઻ૈࣣ཮ ၨεǶᏢޣҭϩձ௖૸΋ԿѤቫጓᙃѲڙፂᔐϐՉࣁǴ่݀ว౜྽ጓᙃѲ ቫኧཇӭǴፂᔐނऀ೸ጓᙃѲࡕϐ҃ೲࡋཇλǴԶҗܭጓᙃѲวғઇᚯޑ ਔ໔ཇఁǴӢԜጓᙃѲᔈᡂૈၨεǶ ӧჴᡍБय़ǴTan ฻Γ[15]௖૸όӕηቸፂᔐܭᜐࣚచҹࣁٿᜐڰۓ ϐൂቫጓᙃѲࡕǴηቸཞѨޑ୏ૈᆶቸᓐ׎ރϐᜢ߯Ƕჴᡍύ٬Ҕቸᓐ׎ ރϩձࣁъ༝׎(hemispherical)ǵѳय़׎(flat)ǵӾഗ׎(ogival)Ϸ༝ᒷ׎ (conical)Ǵ२Ӄϩձҗ 50m/s Կ 700m/s ናᔐܭጓᙃѲ΢Ǵෳໆηቸऀ೸ ጓᙃѲϐ҃ೲࡋǴ่݀ว౜༝ᒷ׎ቸᓐऀ೸ጓᙃѲਔ܌ሡϐ߃ೲࡋനեǴ ځԛϩձࣁѳय़׎ቸᓐᆶӾഗ׎ቸᓐǴԶъ༝׎ቸᓐऀ೸ጓᙃѲ܌ሡϐ ߃ೲࡋനଯǶЪηቸӧ࣬ӕ߃ೲࡋϐΠǴ྽ъ༝׎ቸᓐፂᔐਔǴጓᙃѲ֎ ԏϐૈໆനεǹ྽༝ᒷ׎ቸᓐፂᔐਔǴጓᙃѲ֎ԏϐૈໆനλǶ

Rao ฻Γ[16]຾Չથጕ܎՜ෳ၂(yarn pull-out test)ٰෳໆጓᙃѲ໔ϐ

ነᔔ߯ኧǴෳளᠼᆢ໔୏ነᔔ߯ኧεऊϟܭ 0.15~0.20 ϐ໔Ƕௗ๱ճҔԖ

ज़ϡનݤኳᔕখ܄ౚᡏናᔐܭጓᙃѲ΢Ǵ௖૸ԖคነᔔΚჹܭౚᡏናᔐ

ࡕೲࡋᡂϯϐቹៜǶፂᔐኳᔕ่݀ว౜Ǵ྽ጓᙃѲ໔ԖነᔔΚਔǴౚᡏና

ᔐࡕೲࡋ෧եᖿ༈ၨזǶբޣ׳௖૸ጓᙃѲҁي׷਑܄፦ჹܭלፂᔐϐ

ቹៜǴᙖҗׯᡂጓᙃѲᠼᆢБӛϐླྀМ߯ኧ(longitudinal tensile modulus)

ᔕ่݀ёளޕǴ྽ጓᙃѲᠼᆢБӛϐླྀМ߯ኧၨεਔǴౚᡏናᔐࡕೲࡋ෧

ե౗(velocity decreasing rate)ၨεǹ྽ጓᙃѲᠼᆢБӛϐ܎՜மࡋၨεਔǴ

җܭځၨόܰวғઇᚯǴӢԜጓᙃѲբҔܭౚᡏޑਔ໔ၨߏǶ

Tan ฻Γ[17]ܭጓᙃѲҁيϐ׷਑܄፦ϷነᔔΚޑቹៜΨԖ࣬ᜢࣴزǴ

բޣஒటෳໆޑጓᙃѲ੆ݰܭόӕᐚࡋϐΒ਼ϯޖНྋనύ(silica-water

suspension,SWS)Ƕ२Ӄ຾Չથጕ܎՜ෳ၂ෳໆጓᙃѲ໔ነᔔ߯ኧǴӆճҔ

ޜ਻ᄳ຾Չηቸፂᔐ၂ᡍ(ballistic impact tests)ǴෳໆൂቫϷӭቫጓᙃѲڙ

ηቸፂᔐਔǴηቸёऀ೸ϐཱུज़ೲࡋ(ballistic limits)Ƕჴᡍ่݀ว౜Ǵ྽ ੆ݰޑΒ਼ϯޖНྋనᐚࡋࣁ 40%ਔǴጓᙃѲϐነᔔ߯ኧനଯǴηቸ৔ ᔐϐཱུज़ೲࡋၨεǴӢԜלቸૈΚΨനࣁؼӳǹԶ҂੆ݰΒ਼ϯޖНྋన ޑጓᙃѲነᔔ߯ኧၨեǴηቸ৔ᔐϐཱུज़ೲࡋၨλǴלቸૈΚΨܴᡉၨৡǶ Dong ᆶ Sun[18]׳຾΋؁௖૸ӚᅿᠼᆢጓᙃѲϐᐒఓՉࣁǺх֖ፂ ᔐ၂ᡍǵᠼᆢነᔔΚෳ၂ǵથጕ܎՜၂ᡍϷથጕ܎՜ኳᔕǶ२Ӄӧፂᔐ၂ ᡍБय़Ǵஒ΋ঁޔ৩ 7mm ޑᒳౚа 215m/s ϐೲࡋፂᔐܭٿᜐڰۓϐᠼ ᆢጓᙃѲ΢Ǵ٠КၨӚᠼᆢጓᙃѲ؂ൂՏख़ໆ܌੃઻ϐ୏ૈ(dissipated kinetic energy)Ǵ่݀ว౜ጓᙃཇᆙஏޑᠼᆢጓᙃѲځ੃઻ᒳౚϐ୏ૈཇ ӭǴ߄ҢځלቸૈΚཇ٫ǶᠼᆢነᔔΚෳ၂Бय़ǴෳໆӚጓᙃѲޑၠᠼᆢ ״ϐነᔔ߯ኧ(cross-yarn friction)ϷѳՉᠼᆢϐነᔔ߯ኧ(parallel-fiber friction)Ǵว౜ነᔔ߯ኧεऊϟܭ 0.2~0.39 ϐ໔Ƕӧથጕ܎՜၂ᡍБय़Ǵ

ϩձෳໆӚᠼᆢጓᙃѲځ࿶ጕ(warp)ᆶጎጕ(weft)Бӛޑ܎՜Κ(pull-out force)Ǵ่݀ว౜ጓᙃཇᆙஏޑᠼᆢጓᙃѲځ܎՜ΚཇεǴ߄Ңځሡाၨ εޑΚωૈ٬ᠼᆢ״໔ౢғྖ౽ǴӢԜ֎ԏ੃઻ϐ୏ૈҭၨӭǴԜѦҗܭ ᠼᆢጓᙃѲᇙำޑӢનǴ࿶ጕБӛޑ܎՜Κ཮εܭጎጕБӛϐΚǶӧથጕ ܎՜ኳᔕ೽ϩǴ٩ྣჴᡍෳໆϐᠼᆢጓᙃѲࡌҥ 2D ኳࠠ຾Չϩ݋٠ीᆉ ᠼᆢጓᙃѲϐ܎՜ΚǴ่݀ว౜ᆶჴᡍ่݀࣬಄ӝǴௗ๱ճҔԖज़ϡનݤ

ኳᔕ຾Չୖኧࣴز(parametric study)Ǵ௖૸થጕኧໆ(fabric count)ǵᠼᆢޔ

৩(fiber diameter)ǵᠼᆢླྀМ߯ኧ(fiber modulus)ǵથጕଆҷ(yarn waviness)

аϷነᔔΚ(friction)ჹܭ܎՜ΚϐቹៜǴനࡕёளޕ܎՜ΚϐڄኧǴӢԜ ճҔ܌ளډޑڄኧջёԖਏ౗ӦीᆉрӚᅿᠼᆢጓᙃѲޑ܎՜ΚǴЪว ౜ऩ໪ගϲᠼᆢጓᙃѲޑ܎՜ΚǴቚуથጕኧໆനԖਏ݀Ǵځԛࣁᠼᆢޔ ৩ǵᠼᆢླྀМ߯ኧǵથጕଆҷаϷነᔔΚǶ வ΢ॊЎ᝘᏾౛ǴჹܭᠼᆢጓᙃѲלቸૈΚࣴزǴёᙖҗηቸཞѨޑ ୏ૈǵηቸೲࡋᡂϯаϷᠼᆢጓᙃѲۭ೽Տ౽ໆ฻ނ౛ໆբࣁКၨϐ٩ ᏵǴٰ௖૸ᠼᆢጓᙃѲ׷਑܄፦ǵ൳Ֆచҹǵነᔔ߯ኧǵᜐࣚచҹаϷቸ ᓐ׎ރϐቹៜǶՠӧЎ᝘ύޑጓᙃѲ೿ࢂаથጕЁࡋ(yarn scale)ϐኳࠠբ ௖૸Ǵથጕ׷਑ޑ୊Κኳኧࣁ΋ঁଷ೛ϐୖኧǴۘคݤගٮԖਏֹ᏾ޑၗ ૻǶҁࣴزύஒჹܭᠼᆢЁࡋ(fiber scale)ޑᠼᆢ״уа௖૸Ǵीᆉрᙁϯ

ࣁથጕЁࡋࡕϐ୊ΚኳኧǴӆ٩ྣीᆉрޑ୊ΚኳኧࡌҥᠼᆢጓᙃѲԖ ज़ϡનኳࠠǴ௖૸൳Ֆచҹǵነᔔ߯ኧǵᜐࣚచҹჹܭלፂᔐૈΚϐቹៜǶ ӧ่ᄬБय़ǴЎ᝘ύჹܭጓᙃѲޑϩ݋εӭࣁൂၠຯѳᙃݤ຾Չ௖ ૸ǴჹځдጓᙃБݤϿԖࣴزǴࡺӧҁࣴزύ੝ձଞჹᚈၠຯѳᙃݤኳࠠ ຾Չፂᔐϩ݋ኳᔕǴ٠Кၨᆶൂၠຯѳᙃݤڙፂᔐϐৡ౦Ƕ ќ΋Бय़ǴЎ᝘ύჹܭᙁϯጓᙃѲኳࠠς௖૸ၸൂЁࡋ HEA ኳࠠа ϷӭЁࡋ HEA ኳࠠǴՠ΢ॊϐᙁϯኳࣣࠠԖ٬Ҕᖓෘϡનጓᙃ୔ୱǴԶ ᖓෘϡનၮҔܭጓᙃѲኳࠠ΢཮คݤ߄Ңᠼᆢ״ࠆࡋБӛϐᡂ׎ǶӢԜ ҁࣴزύஒ࣪ౣᖓෘϡનጓᙃ೽ϩٰࡌҥᙁϯጓᙃѲኳࠠǴКၨόӕޑ ᙁϯጓᙃѲኳࠠڙፂᔐϐՉࣁǶനࡕӆჹܭςᙁϯϐኳࠠ຾Չӭቫϩ݋Ǵ ԖਏӦၲډճҔኳᔕٰႣ՗ٛቸՊڙηቸፂᔐϐՉࣁǶ

1.2 ࣴ

ࣴزҞ኱ᆶБݤ

ҁࣴزЬाаᒳᇙ༝ౚᆶ Kevlar ׷਑לቸѲ຾Չ૸ፕǴ२Ӄࣴزᠼ ᆢ׷਑୊ΚኳኧޑቹៜǴа༾ᢀΚᏢޑفࡋࡌҥᠼᆢኳࠠǴ௖૸ᠼᆢ״җ ᠼᆢᙁϯࣁથጕЁࡋࡕϐ฻ਏ୊ΚኳኧǴௗ๱аԖज़ϡનϩ݋ࡌҥથጕ ЁࡋޑԖज़ϡનϩ݋ᠼᆢጓᙃѲኳࠠǴᢀჸڙ༝ౚናᔐࡕ༝ౚೲࡋᆶਔ ໔ϐᜢ߯аϷૈໆ੃ණ௃׎Ǵ٠௖૸ᠼᆢጓᙃѲ୊Κኳኧǵᜐࣚచҹǵ൳ Ֆ௨ӈϷᠼᆢ״໔ነᔔ߯ኧჹܭ༝ౚೲࡋϐቹៜǶௗ๱ӆஒൂቫӄጓᙃ ኳࠠ຾ՉᙁϯǴஒൂቫጓᙃѲௗ߈ናᔐ୔ୱޑ೽ϩࡌࣁჴᡏϡનǴᇻᚆና ᔐ୔ୱޑ೽ϩࡌࣁ฻ਏѳ݈ᖓෘϡનǴճҔٿϟ፦໔ߔל࣬ӕࣁ฻ਏ٩ ᏵǴளډ฻ਏ೽ϩϐ׷਑தኧǶനࡕǴࡌҥӭቫᙁϯኳٰࠠኳᔕჴሞٛቸ Պ׷਑ǴКၨӄጓᙃኳࠠᆶᙁϯኳࠠڙډᒳౚፂᔐࡕǴፂᔐނೲࡋᡂϯǵ ᠼᆢጓᙃѲՏૈᡂϯǵ୏ૈᡂϯаϷነᔔ઻ૈᡂǶ

ಃ

ಃΒക! ௖૸ൂቫᠼᆢጓᙃѲڙፂᔐਔϐ୏ᄊៜᔈՉࣁ

2.1 ፂᔐϩ݋Бݤ

ӧ౜ჴғࢲύǴ௞ပᆶፂᔐϐ౜ຝೀೀёـǴٯӵًؓ࿘ናǵЋᐒᄕ ပϷηቸፂᔐǴӧπ཰΢ϐሦୱ׳ࣁቶݱǴٯӵߎឦؑᓸԋࠠǵႝηሺᏔ ౢࠔ௞ပෳ၂ǵ᎜୏ୢᚒǵβЕ่ᄬϩ݋ǵ݈ߎԋࠠ…฻ǶԜᜪ౜ຝࣣឦ ܭᕓ໔ϸᔈǴ٠٬่ᄬౢғѮεϐᡂ׎ǴᇻຬၸᓉΚϩ݋܌ϷϐጄൎǴӢ

Ԝሡ٬ҔԖज़ϡનϩ݋ݤ(Finite Element Analysis)ޑኧॶϩ݋Бݤ຾Չኳ

ᔕǶԶӧηቸፂᔐၸำύ཮ౢғ׷਑ߚጕ܄ǵ൳Ֆߚጕ܄Ϸፄᚇϐௗ᝻ୢ ᚒǴځύ LS-DYNA[19]Ԗज़ϡનϩ݋೬ᡏڀഢᚳεޑ׷਑Ϸϡનၗ਑৤Ǵ ځᡉ܄؃ှݤ(Explicit Method)ჹܭፂᔐϷ࿘ናୢᚒёྗዴᄽᆉอਔ໔ϐ ኩᄊՉࣁǴࡺӧҁࣴزύ٬Ҕ LS-DYNA բࣁϩ݋ࣴزϐπڀǶ

2.1.1 ᗦ܄؃ှݤᆶᡉ܄؃ှݤ

ӧ LS-DYNA ύǴ௦Ҕᡉ܄ᑈϩݤೀ౛ᆶਔ໔ԖᜢϐᑈϩԄǴ፾Ҕܭ ୏ᄊᄽᆉᕓ໔วғޑՉࣁǴᆶᗦ܄؃ှݤ(Implicit Method)࣬ၨϐΠǴᓬ ᗺࢂόሡ޸຤εໆਔ໔ीᆉϸંତǶБำԄ(2-1)ࣁૈໆѳᑽБำԄǺ[20]

> @ > @ > @ > @

M x Cx K x P (2-1)

ځύ M ࣁ፦ໆǴC ࣁߔѭ߯ኧǴK ࣁቸ܄߯ኧǴP ࣁѦΚॄၩǶӧᗦ܄ ؃ှݤύǴ྽ਔ໔ࣁt ਔځඔॊБԄӵБำԄ(2-2)܌ҢǺ 't

> @

M xt't 

> @

C xt't 

> @

K xt't

> @

Pt't (2-2) ёว౜ᗦ܄؃ှݤ܌ඔॊϐՏ౽ǵೲࡋϷуೲࡋӧਔ໔ࣁt'tਔ཮ϕ࣬ ቹៜǴӢԜӧीᆉύѸ໪ख़ፄ᠄ж٬ளѦΚॄၩᆶՏ౽ǵೲࡋϷуೲࡋѳ ᑽ܈ԏᔙǴа຾ՉΠ΋ঁਔ໔؁໘ϐၮᆉǶԶӧᡉ܄؃ှݤύǴ྽ਔ໔ࣁ t t ਔځඔॊБԄӵБำԄ(2-3)܌ҢǺ '

> @

M xt't

> @ > @ > @

Pt  C xt  K xt (2-3) ёว౜ᡉ܄؃ှݤ܌ඔॊϐуೲࡋࢂҗਔ໔ࣁtਔϐՏ౽ǵೲࡋϷѦΚॄ ၩ܌ளǴόሡբख़ፄ᠄жϐၮᆉǴѝाਔ໔؁໘୼λ߾ीᆉᇤৡջё෧ϿǴ ӢԜᡉ܄؃ှݤᆶᗦ܄؃ှݤ࣬ၨϐΠё෧Ͽ೚ӭၮᆉਔ໔ǶӢԜᡉ܄ ؃ှݤёӃ؃ளӚ࿯ᗺӧਔ໔ࣁtਔϐуೲࡋӵБำԄ(2-4)Ǻ[19]

^ `

> @

1



> @ > @

int



t ext t t M F F a   (2-4) ځύ[F_text]ࣁѦΚϷᄍ܄ΚǴ[F_tint]ࣁϣ೽ᔈΚϷௗ᝻Κ฻ϣΚǶௗ๱ё؃ ှೲࡋॶӵБำԄ(2-5)аϷՏ౽ॶӵБำԄ(2-6)Ǻ

^

vt't/2

` ^

vt't/2

` ^ `

 at 'tt (2-5)

^ ` ^ ` ^

ut't ut  vt't/2

`

'tt't/2 (2-6)

നࡕёᙖҗՏ౽؃ளӚ࿯ᗺӧਔ໔ࣁt'tਔϐ൳ՖՏ࿼ӵБำԄ(2-7)Ǻ

^ ` ^ ` ^ `

xt't x0  ut't (2-7)

ځύ

^ `

x0 ࣁӚ࿯ᗺϐ߃ۈՏ࿼Ƕ

2.1.2 ਔ

ਔ໔؁໘௓ڋ(Time Step Control)

җܭᗦ܄ᑈϩݤࣁคచҹԄᛙۓǴջ٬ਔ໔؁໘ཱུεҭ཮ԏᔙǹϸϐǴ ᡉ܄ᑈϩݤࣁԖచҹԄᛙۓǴѸ໪ਔ໔؁໘ߚதλਔω཮ᛙۓǶӧ LS-DYNA ύǴਔ໔؁໘ޑ௓ڋࢂҗ೬ᡏԾՉᒧڗനλϡન܌،ۓǴځനλ ਔ໔؁໘ t' ϦԄीᆉӵБำԄ(2-8)܌ҢǺ U E l k C l k t ' ' ' _(2-8) ځύ l' ࣁനλϡનϐനεჹفጕߏࡋǴC ࣁቸ܄ݢӧϟ፦ύϐݢೲǴE ࣁ ׷਑ϐླྀМ߯ኧǴU ࣁ׷਑ϐஏࡋǶࣁΑᗉխਔ໔؁໘ၸεǴࡺ४΢΋ঁ Ӽӄ߯ኧ(Safe factor)ࣁ k (k1)ǴႣ೛ॶࣁ 0.9 аዴߥӧኳᔕϩ݋ύёᛙ ۓǶҁࣴزύࣁΑ؃ှ׳ᆒዴϐϩ݋่݀ǴӧԜஒӼӄ߯ኧᕭλࣁ 0.6Ƕ

2.2 ᠼ

ᠼᆢ׷਑୊Κኳኧޑቹៜ

΋૓೬ԄٛቸՊ೯தࣁӭቫѳᙃѲ܌ಔԋǴკ 2. 1 ࣁൂቫ Kevlar ѳ

ᙃѲᐉᄒय़ϐᡉ༾ྣТკ[10]ǶҗკύёᢀჸѳᙃѲޑጓᙃݤࣁ೚ӭ΢Π

ଆҷޑ࿶ጕ(warp yarns)Ϸጎጕ(fill yarns)࣬ϕࠟޔ௨ӈԶԋǴԶ؂΋״થ

ጕࢂҗคኧਥᠼᆢ܌ಔԋǴځᄒय़׎ރࣁᐍ༝ރǴ٠Ъݮ๱҅۰ݢϐၡ৩

ۯ՜ǶࣁΑ௖૸ᠼᆢ״җᠼᆢᙁϯࣁથጕЁࡋࡕϐ฻ਏ୊ΚኳኧǴ२Ӄҁ

ࣴز٬ҔԖज़ϡનϩ݋঺း೬ᡏ ANSYS[21]а༾ᢀΚᏢޑفࡋࡌҥᠼᆢ

ኳࠠǶკ 2. 2 ࣁጓᙃѲᠼᆢ״ᄒय़კ[22]Ǵёᢀჸᠼᆢޑ௨ӈ௃׎߈՟ࣁ

ᆙஏ௨ӈރǴӢԜଷ೛ᠼᆢ௨ӈࣁϤف׎௨ӈӵკ 2. 3(a)܌ҢǴӢԜڗ

ځж߄܄ൂϡᡏ(representative volume element , RVE)ӵკ 2. 3(b)܌ҢǴᠼ

ᆢޔ৩ࣁ 0.025mmǴ٩ྣკ 2. 3(b)܌ࡌҥϐԖज़ϡનኳࠠӵკ 2. 4 ܌ҢǴ Ьा٬Ҕޑϡનࣁ SOLID185Ǵᠼᆢߏࡋࣁ 0.05mmǴਥᏵЎ᝘[10]ύᠼᆢ Бӛϐ׷਑܄፦ǴӧԜ೛ᠼᆢࣁ฻ӛ܄׷਑ӵ߄ 2. 1Ǵ٠ࡌҥௗ᝻ϡન (TARGE170 Ϸ CONTA173)аٛЗᠼᆢ໔วғऀ೸౜ຝǶ җܭጓᙃѲޑᠼᆢ״ࣁᕵᐉҬᒱ٠΢ΠଆҷǴӢԜ൩ൂ״ᠼᆢٰᢀ ჸǴ཮ڙډݮࠆࡋБӛᓸᕭϐΚໆǴԶᒿ๱ԜᓸᕭΚޑόӕǴځᐒఓՉࣁ ҭԖ܌ৡ౦ǴࡺӧԜϩ݋ύϩࣁٿঁ؁ᡯǺಃ΋؁Ӄ๏ۓ Y БӛϐՏ౽ ܭ΢Π߄य़ǴځᜐࣚచҹҢཀკӵკ 2. 5(a)܌ҢǴ྽ಃ΋؁ᡯډၲѳᑽ ࡕջჹж߄܄ൂϡᡏ଺ຼය܄ᜐࣚచҹϐೀ౛Ǵځ০኱س಍ϷҢཀკӵ

კ 2. 6 ܌ҢǶ ӧx 0Ϸx aϐѳय़΢ϐ࿯ᗺǺ constant z) y, u(a, z) y, u(0,  (2-9a) constant z) y, v(a, z) y, v(0,  (2-9b) constant z) y, w(a, z) y, w(0,  (2-9c) ӧy 0Ϸy bϐѳय़΢ϐ࿯ᗺǺ constant z) b, u(x, z) u(x,0,  (2-10a) constant z) b, v(x, z) v(x,0,  (2-10b) constant z) b, w(x, z) w(x,0,  (2-10c) ӧz 0Ϸz cϐѳय़΢ϐ࿯ᗺǺ constant c) y, u(x, y,0) u(x,  (2-11a) constant c) y, v(x, y,0) v(x,  (2-11b) constant c) y, w(x, y,0) w(x,  (2-11c) ௗ๱໒ۈ຾ՉಃΒ؁ᡯǴஒΠ߄य़فပѤঁ࿯ᗺϩձܥ״ǴځԾҗࡋҢཀ კӵკ 2. 5(b)܌ҢǴ٠ஒ΢߄य़๏ۓ Z Бӛϐ༾λՏ౽ໆǴᙖҗीᆉ΢ ߄य़ϐय़ᑈаϷ࿯ᗺΚᕴکǴջё؃ளж߄܄ൂϡᡏኳࠠϐ୊ᔈΚǶ

A F ¦

W

_(2-12) ځύ¦Fࣁж߄܄ൂϡᡏኳࠠ΢߄य़࿯ᗺΚᕴکǴ A ࣁ΢߄य़ϐय़ᑈǴ z ' ࣁ΢߄य़ Z Бӛϐ༾λՏ౽ໆǶԶკ 2. 7(a)ࣁж߄܄ൂϡᡏኳࠠ࿯ᗺ Z БӛՏ౽ϩѲკϷᡂ׎ࡕϐୁຎკǴӧԜஒኳࠠᙁϯӵკ 2. 7(b)܌ҢǴ ीᆉ΢߄य़࿯ᗺϐՏ౽ໆջё؃ளж߄܄ൂϡᡏኳࠠϐ୊ᔈᡂǴځᜢ߯ ԄӵΠǺ h z '

J

_(2-13) ځύ z' ࣁ΢߄य़ Z Бӛϐ༾λՏ౽ໆǴhࣁж߄܄ൂϡᡏኳࠠϐଯࡋǶҗ Ԅ(2-12)ϷԄ(2-13)ёीᆉрᠼᆢ״җᠼᆢЁࡋᙁϯࣁથጕЁࡋࡕϐ฻ਏ ୊ΚኳኧǺ

J

W

G _(2-14) ᙖҗׯᡂಃ΋؁ᡯϐᓸᕭՏ౽ໆǴջё௖૸ൂ״ᠼᆢݮࠆࡋБӛᓸ ᕭΚޑόӕǴჹܭથጕЁࡋϐ฻ਏ୊ΚኳኧޑቹៜǴ२Ӄᢀჸ฻ਏൂϡᡏ ڙډᓸᕭՏ౽ໆࡕޑᓸᔈΚӵკ 2. 8Ǵёว౜྽ᠼᆢ״ᓸᕭՏ౽җ 0.6nm ቚуԿ 10nm ਔǴ߾ᓸᔈΚ཮җ 0.64MPa ೴ᅌ΢ϲࣁ 8.52MPaǶௗ๱ᢀჸ

όӕᓸᔈΚΠޑ฻ਏ୊ΚኳኧǴځϡનԏᔙ܄่݀ӵკ 2. 9 ܌ҢǶਥᏵ

ԏᔙϐϩ݋่݀ёว౜྽ᠼᆢ״ᓸᔈΚࣁ 0.64MPa ਔǴ฻ਏ୊Κኳኧऊ

ࣁ 0.43GPaǴԶᠼᆢ״ᓸᔈΚҗ 0.64MPa ቚуԿ 8.52MPaǴځीᆉр฻ਏ

୊Κኳኧ཮җ 0.43GPa ቚуԿ 5.22GPaǴ߄ҢᓸᔈΚჹܭ฻ਏ୊Κኳኧϐ ቹៜёၲډ 10 ७ৡ౦ǶऩКၨᠼᆢ໔ነᔔ߯ኧჹܭ฻ਏ୊Κኳኧϐቹៜ ӵკ 2. 10Ǵёว౜྽ᠼᆢ໔ነΚཇεǴीᆉр฻ਏ୊ΚኳኧҭᒿϐቚуǶ ӢԜӧҁ࿯ύஒᝩុ௖૸ᠼᆢጓᙃѲӧથጕЁࡋΠǴ୊Κኳኧჹܭጓᙃ ѲڙፂᔐਔޑቹៜǶ ҁࣴزаୖኧϯࡌҥᒳౚናᔐൂቫൂၠຯጓᙃѲϐԖज़ϡનኳࠠǴ კ 2. 11 ࣁ༝ౚᆶൂၠຯጓᙃѲ߃ۈރᄊϐ൳ՖኳࠠǺ΋ঁъ৩ࣁ 4mm ϐᒳౚࠟޔΕ৔ܭ҅Б׎ጓᙃѲޑύЈᗺ΢ǴጓᙃѲЁκࣁ 52.04mm × 52.04mmǴѳᙃѲԖज़ϡનኳࠠϐᐉᄒय़ӵკ 2. 12 ܌ҢǴځᄒय़ϐ൳Ֆ ୖኧӵ߄ 2. 2 ܌ҢǶ؂΋״થጕݮ๱Ꭹ۰ݢϐၡ৩ۯ՜Ǵځ࣬ᎃٿ״ᠼ ᆢޑڄኧӵБำԄ(2-15)ϷБำԄ(2-16)܌ҢǺ ) 2 cos( y A z

O

S

(2-15) ) 2 cos( y A z

O

S

 _(2-16) ځύ A ࣁᎩ۰ݢϐਁ൯ǴӧԜᆶᠼᆢࠆࡋ࣬ӕǹ

O

ࣁ҅۰ݢϐݢߏǴӧ

Ԝࣁၠࡋޑٿ७Ƕ ਥᏵკ 2. 11 Ϸკ 2. 12 ୷ҁЁκ܌ࡌҥޑԖज़ϡનኳࠠӵკ 2. 13 ܌ҢǴҗܭᠼᆢ״ݮ๱Ꭹ۰ݢϐၡ৩ۯ՜ǴӢԜሡۓကϡન০኱Бӛӵკ 2. 14 ܌ҢǶᜐࣚచҹࣁጓᙃѲѤᜐڰۓǴҗܭԜኳࠠჹᆀܭ x-z ѳय़а Ϸ y-z ѳय़ǴӢԜѝ໪ࡌҥѤϩϐ΋ٰኳࠠ຾Չϩ݋ǶԜኳࠠ௦Ҕ፾Ҕܭ ᡉ܄୏ᄊϩ݋ϐ΋໘Ζ࿯ᗺჴᡏϡન(SOLID164)բࣁϩ݋ϡનᜪࠠǴ؂ ঁ࿯ᗺԖ 9 ঁԾҗࡋ(ux, uy, uz, vx, vy, vz, ax, ay, az)ǴጓᙃѲ܄፦ࣁ҅Ҭጕቸ

܄׷਑(Orthotropic elastic material)Ǵ׷਑தኧӈܭ߄ 2. 3 ύǴځύࠟޔᠼ

ᆢБӛޑླྀМ߯ኧE22ᆶE33ၨλǴଷ೛ࣁᠼᆢБӛླྀМ߯ኧE11ޑԭϩϐ

΋ǶࣁΑ௖૸થጕЁࡋΠϐ୊ΚኳኧჹܭጓᙃѲڙፂᔐਔޑቹៜǴЪҗж

߄܄ൂϡᡏኳᔕளډϐ่ፕǴӧԜ୊Κኳኧϩձ೛ࣁ 0.328GPa аϷ

3.28GPa ଺КၨǶ٠٬Ҕ*MAT_ADD_EROSION ٰۓက׷਑ϐઇᚯՉࣁǴ

җܭᠼᆢБӛޑླྀМኳኧ(E )ၨځдٿБӛޑླྀМኳኧଯр೚ӭǴӢԜ11

നεЬᔈΚ(Maximum principle stress)཮ᖿ߈ܭᠼᆢБӛϐᔈΚǴࡺӧԜ

ஒઇᚯྗ߾೛ۓࣁനεЬᔈΚǴऩࢌ΋ϡનӧीᆉύϐᔈΚຬၸ܌೛ۓ

ϐઇᚯྗ߾Ǵӧ LS-DYNA ཮ஒԜϡનӧीᆉύմନǴӧԜ೛ۓനεЬᔈ

ΚຬၸᠼᆢБӛ܎՜மࡋ 3400MPa ջࣁઇᚯǶ༝ౚѝϢ೚ݮ๱ z Бӛ౽

୏Ǵ׷਑ࣁᒳ׷Ǵ߃ೲࡋ೛ࣁ 100m/sǴځ׷਑தኧӈܭ߄ 2. 4 ύǶ

аϷጓᙃѲ࿶ጕᆶጎጕϐ໔ነᔔ٬ҔԾ୏ࠠൂय़ௗ᝻(Contact Automatic Single Surface)ٰۓကௗ᝻ՉࣁǶҁࣴزஒ༝ౚᆶጓᙃѲ໔ነᔔ߯ኧаϷ ጓᙃѲᠼᆢϐ໔ነᔔ߯ኧ೛ࣁ 0.5ǴᢀჸᠼᆢጓᙃѲڙ༝ౚፂᔐࡕǴ༝ౚ ϐೲࡋᐕำǵጓᙃѲ୏ૈϷᔈᡂૈᡂϯᆶነᔔ઻ૈǴ௖૸ጓᙃѲᠼᆢ׷਑ ୊ΚኳኧϐቹៜǶ२ӃҁࣴزଞჹጓᙃѲ຾Չኳࠠᆛ਱ԏᔙ܄ᡍ᛾Ǵа୊ Κኳኧࣁ 3.28GPa ޑጓᙃѲࣁϩ݋ኳࠠǴᙖҗᒳౚፂᔐጓᙃѲࡕϐᎩೲ բࣁղᘐࢂցၲډϡનԏᔙϐ٩ᏵǴ߄ 2. 6 ࣁόӕϡનኧໆΠޑԏᔙ܄ ่݀Ǵ྽ϡનኧໆࣁ 173,052 ਔǴҗ߄ύёว౜ᒳౚፂᔐጓᙃѲࡕϐᎩೲ ᆶϡનኧໆࣁ 288,420 ޑጓᙃѲᇤৡࣁ 0.18%ǴࡺӧԜղᘐϡનςၲډԏ ᔙǴӧҁࣴزύஒᒧڗϡનኧໆࣁ 173,052 ޑᠼᆢጓᙃѲኳࠠ຾ՉКၨϩ ݋Ƕ ᠼᆢጓᙃѲڙፂᔐࡕϐ༝ౚϐೲࡋᐕำǵጓᙃѲᔈᡂૈᡂϯǵጓᙃѲ ነᔔ઻ૈᡂϯаϷጓᙃѲ୏ૈᡂϯӵკ 2. 15 ܌ҢǴკύᡉҢ྽୊Κኳኧ ࣁ 3.28GPa ਔǴ༝ౚ཮ܭፂᔐࡕ 40μs ਔऀ೸ጓᙃѲǹԶ྽୊Κኳኧࣁ 0.328GPa ਔǴ༝ౚ཮ܭፂᔐࡕ 67μs ਔऀ೸ጓᙃѲǴёܴᡉว౜྽୊Κኳ ኧၨեਔǴᠼᆢጓᙃѲวғઇᚯޑਔ໔ᗺၨఁǴӢԜ୊ΚኳኧၨեਔǴ༝ ౚऀ೸ጓᙃѲࡕϐ҃ೲࡋၨեǴӵკ 2. 15(a)܌ҢǴЪҗܭጓᙃѲբҔਔ ໔ቚߏ೚ӭǴࡺነᔔ઻ૈҭගϲ೚ӭǴӵკ 2. 15(c)܌ҢǶԜѦҗܭၨե ޑ୊ΚኳኧځጓᙃѲל៻ંૈΚၨৡǴӢԜڙፂᔐࡕᡂ׎ໆΨ཮ၨεǴࡺ

ጓᙃѲޑᔈᡂૈϷ୏ૈ཮ගϲ೚ӭǴӵკ 2. 15(b)ᆶკ 2. 15(d)܌ҢǶ ਥᏵҁ࿯௖૸୊ΚኳኧჹܭጓᙃѲڙፂᔐਔޑቹៜǴ่݀ว౜୊Κ ኳኧ཮ჹܭઇᚯวғਔ໔ౢғቹៜǴҗܭჴሞጓᙃѲϐל៻ૈΚཱུ১ǴӢ ԜӧϐࡕޑࣴزύǴஒڗ୊Κኳኧϐॶࣁ 0.328GPaǴ٠௖૸ځдୖኧϐ ቹៜǶ

2.3 ᠼ

ᠼᆢነᔔΚޑቹៜ

ࣁΑ௖૸ጓᙃѲነᔔ߯ኧϐቹៜǴҁࣴزύஒ༝ౚᆶጓᙃѲ໔ነᔔ ߯ኧаϷᠼᆢϐ໔ነᔔ߯ኧϩձӕਔ೛ࣁ 0 ᆶ 0.5Ǵ٠ஒઇᚯྗ߾౽ନа ߡᢀჸፂᔐၸำૈໆӺࡡϐ౜ຝǴКၨጓᙃѲᜐࣚచҹࣁѤᜐڰۓϐΠǴ ڙፂᔐਔᠼᆢ໔ነᔔ߯ኧჹܭጓᙃѲᡂ׎ǵፂᔐނೲࡋᡂϯǴаϷፂᔐނ ૈໆᙯ౽ϐ௃׎Ƕ ྽΋ঁፂᔐނናᔐܭጓᙃѲ΢Ǵ཮٬ጓᙃѲౢғᡂ׎ǴӢԶ੃઻ፂᔐ ނϐ୏ૈ٬ځೲࡋफ़եǴऩӧ᏾ঁፂᔐၸำύ҂ڙډځдѦΚբҔǴૈໆ س಍ᔈࣁӺࡡǶҁࣴزύፂᔐނࣁᒳౚǴ༝ౚᡂ׎ϐૈໆё۹ౣǴЪόԵ

ቾྕࡋϐቹៜǴӢԜ༝ౚཞѨޑ୏ૈ(Loss of projectile kinetic energy,ΔEpk)

ᔈ೏ጓᙃѲޑΟᅿૈໆֹӄ֎ԏǺጓᙃѲᔈᡂૈ(Yarn strain energy,ΔEys)ǵ

ጓ ᙃ Ѳ ୏ ૈ(Yarn kinetic energy,ΔEyk) а Ϸ ነ ᔔ ઻ ૈ (Frictional sliding

f yk ys pk E E E E ' ' ' ' (2-17) ༝ౚཞѨޑ୏ૈΔEpkۓကࣁ ) ( 2 1 2 2 r i pk m v v E  ' _(2-18) ځύ

m

ࣁ༝ౚޑ፦ໆǴviࣁ༝ౚ߃ೲࡋǴvrࣁ༝ౚᎩೲࡋǶࣁΑڗள༝ౚཞ Ѩޑ୏ૈᆶਔ໔ᜢ߯Ǵஒ༝ౚᎩೲࡋׯቪࣁਔ໔ t ޑڄኧǴӢԜБำԄ(2-18)ёׯቪࣁǺ ] ) ( [ 2 1 2 2 t v v m Epk i  ' _(2-19) ځύv(t)ࣁҺ΋ਔ໔༝ౚϐೲࡋǴӢԜճҔ༝ౚϐೲࡋᡂϯߡёளډځ ཞѨޑ୏ૈᆶਔ໔ϐᜢ߯ǶԶӧ LS-DYNA 3D ीᆉύǴࣁΑ࿯࣪ኧᏵᓯ Ӹک෧ϿၮᆉԛኧǴ೯த཮ӧჴᡏϡન٬ҔൂᗺଯථᑈϩၮᆉǴՠऩᔈΚ ໣ύуၩܭࢌ΋ϡન΢Ǵࠅёૈ׎ԋ؅ᅅኳᄊ(Hourglassing mode)ǴӢԜ ཮٬Ҕ؅ᅅ௓ڋٰቚуֽ೽ኳࠠখࡋٰᗉխౢғԜ౜ຝǴ྽ᡉ܄୏ᄊϩ ݋ਔǴ؅ᅅૈໆόຬၸᔈᡂૈޑ 10%ջ೏ᇡࣁࢂёௗڙޑϩ݋่݀[23]Ǵ ࡺӧҁࣴزύ؅ᅅૈໆࣣ௓ڋӧӝ౛ጄൎϐϣǶ ӧԜ௖૸ѤᜐڰۓϐᜐࣚచҹΠᠼᆢ໔ነᔔ߯ኧϐቹៜǴკ 2. 16 ࣁ ਔ໔ 80μs ᕓ໔Ǵᠼᆢ໔ነᔔ߯ኧϩձࣁ 0 Ϸ 0.5 ޑጓᙃѲڙډ༝ౚፂᔐ

ϐᡂ׎კǶว౜྽μ=0.5 ਔǴҗܭᠼᆢ໔ነᔔΚၨεǴӢԜڙፂᔐࡕᠼᆢ όܰวғྖ౽౜ຝǹ྽ μ=0 ਔǴҗܭᠼᆢ໔คነᔔΚբҔǴӢԜڙፂᔐ ࡕύЈ೽ϩᠼᆢܴᡉӛٿୁྖ౽Ƕ ऩКၨᠼᆢ໔ነᔔ߯ኧჹܭ༝ౚፂᔐೲࡋϐቹៜǴጓᙃѲѤᜐڰۓ ڙፂᔐਔ༝ౚೲࡋ-ਔ໔კӵკ 2. 17(a)܌ҢǶკύᡉҢ༝ౚϐ߃ೲࡋࣁ 100m/sǴࠟޔܭጓᙃѲѳय़БӛጓᙃѲύЈᗺፂᔐǴௗ᝻ډጓᙃѲࡕ༝ౚ ೲࡋ໒ۈΠफ़Ƕ྽ነᔔ߯ኧμ=0.5 ਔǴጓᙃѲᠼᆢ໔όܰڙ༝ౚፂᔐԶྖ ౽ǴӢԜ༝ౚೲࡋ෧Ͽᖿ༈ၨܴᡉǹϸϐ྽ μ=0 ਔǴጓᙃѲᠼᆢ໔৒ܰ ڙ༝ౚፂᔐԶྖ౽ǴӢԜ༝ౚೲࡋ෧ϿໆၨեǶӧૈໆБय़Ǵҗკ 2. 17 (c)ёว౜คነᔔΚբҔਔό཮Ԗነᔔ઻ૈǴԶКၨጓᙃѲڙፂᔐࡕϐᔈ ᡂૈϷ୏ૈӵკ 2. 17 (b)Ϸკ 2. 17 (d)܌ҢǴёว౜྽ᠼᆢ໔ԖነᔔΚբ ҔਔޑૈໆࣣКၨεǴж߄ጓᙃѲڙፂᔐࡕ཮֎ԏၨӭૈໆǴӢԜלቸૈ Κၨ٫ǶਥᏵ Tan ฻Γ[17]ϐჴᡍ่݀ǴෳໆጓᙃѲڙηቸፂᔐਔǴஒη ቸёֹӄऀ೸ጓᙃѲޑೲࡋۓကࣁཱུज़ೲࡋǴჴᡍ่݀߄Ңነᔔ߯ኧၨ ଯޑጓᙃѲǴځηቸ৔ᔐϐཱུज़ೲࡋၨεǴӢԜלቸૈΚΨനࣁؼӳǶҁ ࣴزϩ݋ύ௖૸࣬ӕ߃ೲࡋޑ༝ౚፂᔐܭጓᙃѲࡕޑೲࡋᐕำǴӧόԵ ቾጓᙃѲઇᚯޑ௃ݩΠǴளޕነᔔ߯ኧၨଯޑጓᙃѲځ༝ౚೲࡋ෧ե௃ ׎ၨܴᡉǴ߄Ңלቸૈၨ٫Ǵࡺӧҁࣴزϩ݋ύᆶჴᡍ่݀ޑᖿ༈ၲډ΋ ठǴԶӧ҂ٰஒԵቾጓᙃѲڙፂᔐࡕ཮วғઇᚯޑ௃ݩΠǴነᔔ߯ኧჹܭ

לቸૈΚޑቹៜǶ ྽μ=0.5 ਔǴጓᙃѲڙፂᔐਔૈໆᙯ౽Ԕጕკӵკ 2. 18 ܌ҢǴ܌Ԗ ૈໆࣣჹܭ༝ཞѨ୏ૈޑനεॶբ኱ྗϯǴҗკύᡉҢӧፂᔐၸำύǴਔ ໔0~40μs ਔጓᙃѲ୏ૈᆶᔈᡂૈ֎ԏૈໆ܌эКٯ࣬߈Ǵௗ๱ጓᙃѲ཮ ӢᜐࣚచҹѤᜐڰۓԶ٬ځ໒ۈวғ׳εᔈᡂǴᏤठጓᙃѲᔈᡂૈ֎ԏ ૈໆ܌эКٯ໒ۈ΢ϲԿ 66.8%ǴጓᙃѲ୏ૈ܌эКٯࣁ 29.5%ǴԶነᔔ ઻ૈ܌эКٯനλǴऊࣁ༝ౚཞѨ୏ૈޑ 4.5%Ƕ ྽μ=0 ਔǴጓᙃѲڙፂᔐਔૈໆᙯ౽Ԕጕკӵკ 2. 19 ܌ҢǴว౜ऩ ጓᙃѲᠼᆢ໔คነᔔΚբҔǴጓᙃѲ୏ૈᆶᔈᡂૈ֎ԏૈໆ܌эКٯ࣬ ߈ϐਔ໔ග߻Կ0~30μs ਔǴௗ๱ጓᙃѲ཮ӢᜐࣚచҹѤᜐڰۓԶ٬ځ໒ ۈวғ׳εᔈᡂǴӢԜጓᙃѲᔈᡂૈ֎ԏૈໆ܌эКٯ໒ۈ΢ϲǴၲډ 68.7%ǴԶጓᙃѲ୏ૈ܌эКٯࣁ 28.5%ǶӢԜёว౜྽ؒԖነᔔΚբҔ ਔǴᠼᆢጓᙃѲ৒ܰౢғྖ౽Ъᡂ׎ໆၨεǴᏤठᔈᡂૈ֎ԏૈໆϲଯޑ ਔ໔ග߻ǴלፂᔐϐૈΚΨӢԜၨৡǶ

2.4 ᠼ

ᠼᆢၠຯޑቹៜ

ҁ࿯ஒ௖૸ጓᙃѲ൳Ֆ௨ӈჹܭלቸਏ݀ϐቹៜǴᢀჸᚈၠຯጓᙃ ѲӧڙፂᔐၸำύǴᆶൂၠຯጓᙃݤޑৡ౦ǶӕኬӦǴ௖૸ጓᙃѲᜐࣚచ ҹᠼᆢϐ໔ነᔔ߯ኧϐቹៜǴճҔԖज़ϡનݤኳᔕǴᢀჸጓᙃѲӧΟᅿό ӕᜐࣚచҹϐΠǴڙፂᔐਔᠼᆢ໔ነᔔ߯ኧჹܭጓᙃѲᡂ׎ǵፂᔐނೲࡋ

ᡂϯǴ٠Кၨᜐࣚచҹჹܭፂᔐނૈໆᙯ౽ϐ௃׎Ƕ კ 2. 20 ࣁ༝ౚᆶጓᙃѲ߃ۈރᄊϐ൳ՖኳࠠǺ΋ঁъ৩ࣁ 4mm ϐ ᒳౚࠟޔΕ৔ܭ҅Б׎ጓᙃѲޑύЈᗺ΢ǴጓᙃѲЁκࣁ 52.04mm × 52.04mmǴᚈၠຯѳᙃѲԖज़ϡનኳࠠϐᐉᄒय़ӵკ 2. 21 ܌ҢǴځᄒय़ ϐ൳Ֆୖኧӵ߄ 2. 5 ܌ҢǴځၠࡋࣁൂၠຯጓᙃѲޑٿ७Ƕ؂΋״થጕ ݮ๱Ꭹ۰ݢϐၡ৩ۯ՜Ǵځ࣬ᎃٿ״ᠼᆢޑڄኧӵӕБำԄ(2-15)ϷБำ Ԅ(2-16)܌ҢǴځύ A ࣁᎩ۰ݢϐਁ൯ǴӧԜᆶᠼᆢࠆࡋ࣬ӕǹ

O

ࣁ҅۰ ݢϐݢߏǴӧԜࣁၠࡋޑٿ७Ƕ ਥᏵკ 2. 20 Ϸკ 2. 21 ୷ҁЁκ܌ࡌҥޑԖज़ϡનኳࠠӵკ 2. 22 ܌ҢǴᜐࣚచҹࣁѤᜐڰۓǶԜኳࠠᗨჹᆀܭ x-z ѳय़аϷ y-z ѳय़Ǵՠ җܭჹᆀືόӧᠼᆢ΢Ǵऩናᔐ୔ୱϐᠼᆢ۳ύЈБӛՏ౽Ǵ཮೷ԋኳᔕ ᆶჴሞ่݀ό಄ӝϐ௃׎ǴӢԜ໪ࡌҥӄኳࠠ຾Չϩ݋ǴጓᙃѲᕴी 342,720 ঁჴᡏϡનǴ२ӃෳໆጓᙃѲൂՏय़ᑈϐख़ໆ଺КၨǴൂၠຯጓ ᙃѲኳࠠࣁ 171.85g/m2_{ԶᚈၠຯጓᙃѲኳࠠࣁ 168.47g/m}2_{Ǵว౜җܭᚈ} ၠຯጓᙃѲޑᠼᆢ״΢Πଆҷ௃׎ၨѳ጗ǴӢԜख़ໆ཮ၨᇸǶҁࣴزύஒ ༝ౚᆶጓᙃѲ໔ነᔔ߯ኧаϷጓᙃѲᠼᆢϐ໔ነᔔ߯ኧଷ೛ࣁ 0.5Ǵ௖૸ ጓᙃѲᠼᆢၠຯϐቹៜǶ ࣁΑ௖૸ӧԜᜐࣚచҹΠᠼᆢ໔ነᔔ߯ኧϐቹៜǴკ 2. 23 ࣁਔ໔ 80μs ᕓ໔Ǵόӕነᔔ߯ኧޑጓᙃѲڙډ༝ౚፂᔐϐᡂ׎კǶว౜྽ μ=0.5

ਔǴҗܭᠼᆢ໔ၠຯၨεǴӢԜڙፂᔐࡕᠼᆢς࿶วғྖ౽౜ຝǹ྽μ=0 ਔǴҗܭᠼᆢ໔คነᔔΚբҔǴӢԜڙፂᔐࡕᠼᆢܴᡉӛٿୁྖ౽Ƕӆᆶ კ 2. 16 ൂၠຯጓᙃѲᡂ׎࣬КǴёว౜྽ μ=0 ਔǴᚈၠຯጓᙃѲᠼᆢྖ ౽ϐ௃׎׳ࣁܴᡉǶ ऩӕਔКၨൂၠຯᆶᚈၠຯጓᙃѲڙፂᔐࡕǴ༝ౚϐೲࡋᐕำӵკ 2. 24(a)܌ҢǴёܴᡉ࣮рൂၠຯጓᙃѲڙፂᔐࡕ༝ౚೲࡋ෧Ͽᖿ༈ၨࣁ ܴᡉǴځԛࣁᚈၠຯጓᙃѲǴЪԖነᔔΚբҔਔځ༝ౚೲࡋ෧Ͽᖿ༈Ξ཮ ၨӭǶӧૈໆБय़Ǵҗკ 2. 24(c)ёว౜ӧናᔐ߃යነᔔ઻ૈ൳Я࣬ӕǴ җܭᚈၠຯጓᙃѲၨܰౢғྖ౽ǴӢԜࡕයነᔔ઻ૈၨൂၠຯጓᙃѲλ ೚ӭǶԶКၨጓᙃѲڙፂᔐࡕϐᔈᡂૈϷ୏ૈӵკ 2. 24(b)Ϸკ 2. 24(d) ܌ҢǴёว౜྽ൂၠຯጓᙃѲޑૈໆࣣКၨεǴҗԜёޕൂၠຯጓᙃѲڙ ፂᔐࡕ཮֎ԏၨӭૈໆǴӢԜלቸૈΚ཮КᚈၠຯጓᙃѲቚம೚ӭǶ ᚈၠຯጓᙃѲڙፂᔐਔૈໆᙯ౽Ԕጕკӵკ 2. 25 ܌ҢǴ܌Ԗૈໆ߄ Ңࣣჹܭ༝ౚཞѨ୏ૈޑനεॶբ኱ྗϯǴҗკύᡉҢӧፂᔐၸำύǴጓ ᙃѲ୏ૈᆶᔈᡂૈ֎ԏૈໆ܌эКٯ࣬߈Ǵϩձࣁ 40.2%Ϸ 54.4%ǴԶነ ᔔ઻ૈ܌эКٯၨλǴऊࣁ 0.2%ǶҗܭᚈၠຯጓᙃѲڙፂᔐࡕၨ৒ܰว ғྖ౽Ǵ༝ౚፂᔐܭጓᙃѲࡕ཮ޔௗҗᠼᆢ໔ሜύऀ೸ǴϸԶό཮ჹጓᙃ Ѳ೷ԋεໆᡂ׎ǴӢԜᆶკ 2. 18 ൂၠຯጓᙃѲૈໆᙯ౽Ԕጕკ࣬КǴጓ ᙃѲᔈᡂૈ܌эКٯ཮ౣλ೚ӭǶКၨၠຯϷነᔔΚჹܭᒳౚϐೲࡋ-ਔ

໔ᐕำӵკ 2. 26ǴᆕӝКၨว౜ǴൂၠຯคነᔔΚ(Single span, μ=0)ϐጓ ᙃѲޑלቸૈΚ཮ᓬܭᚈၠຯԖነᔔΚ(Double span, μ=0.5)ϐጓᙃѲǴӢ ԜᠼᆢၠຯჹܭלቸૈΚϐቹៜ཮ᓬܭነᔔΚϐቹៜǶ

2.5 ጓ

ጓᙃѲᜐࣚచҹޑቹៜ

ࣁΑ௖૸ጓᙃѲᜐࣚచҹϐቹៜǴҁ࿯ύஒΟᅿᜐࣚచҹϩձᔈҔ ܭൂၠຯጓᙃѲ΢ǺϩձࣁѤᜐڰۓǵٿᜐڰۓаϷѤᜐคܥ״Ƕᢀჸጓ ᙃѲڙፂᔐਔጓᙃѲᜐࣚచҹჹܭځᡂ׎ǵፂᔐނೲࡋᡂϯǴ٠Кၨᜐࣚ చҹჹܭፂᔐނૈໆᙯ౽ϐ௃׎Ƕ२ӃǴკ 2. 27 ࣁጓᙃѲᜐࣚచҹࣁѤ ᜐڰۓǴᠼᆢ໔ነᔔ߯ኧࣁ 0.5ǴڙፂᔐਔୁຎკаϷΠຎკǴᢀჸਔ໔ ໔਱ࣁ20μs ϐୁӛᡂ׎ǴҗკύጓᙃѲᡂ׎ϐᖿ༈ว౜ǴҗܭځѤᜐԾ җࡋڙܥ״Ǵڙፂᔐࡕϐୁӛᡂ׎཮և౜ߎӷ༣׎ރ೴ᅌӛѦۯ՜Կᜐ ࣚǶ კ 2. 28 ࣁጓᙃѲᜐࣚచҹࣁٿᜐڰۓǴᠼᆢ໔ነᔔ߯ኧࣁ 0.5Ǵڙ ፂᔐਔୁຎკаϷΠຎკǴᢀჸਔ໔໔਱ࣁ20μs ϐୁӛᡂ׎Ǵҗკύጓ ᙃѲᡂ׎ϐᖿ༈ว౜ǴҗܭځٿᜐԾҗࡋڙܥ״Ǵڙፂᔐࡕόڙܥ״Бӛ ޑᡂ׎ݢ໺ሀၨᄌǴӢԜҗ΢ຎკᢀჸୁӛᡂ׎୔ୱǴڙܥ״Бӛᡂ׎୔ ୱჹفጕߏࡋၨεǴόڙܥ״Бӛᡂ׎୔ୱჹفጕߏࡋၨλǶ კ 2. 29 ࣁጓᙃѲᜐࣚచҹࣁѤᜐคܥ״Ǵᠼᆢ໔ነᔔ߯ኧࣁ 0.5Ǵ ڙፂᔐਔୁຎკаϷΠຎკǴᢀჸਔ໔໔਱ࣁ20μs ϐୁӛᡂ׎Ǵҗკύ

ጓᙃѲᡂ׎ϐᖿ༈ว౜ǴҗܭځѤᜐόڙܥ״Ǵࡺᡂ׎ݢ໺ሀၨᄌǴᆶკ 2. 27 Ѥᜐڰۓϐᡂ׎კКၨёว౜ӧ࣬ӕਔ໔ΠǴѤᜐڰۓϐጓᙃѲୁ ӛᡂ׎ጄൎၨεǴѤᜐคܥ״ϐጓᙃѲୁӛᡂ׎ጄൎၨλǶԶ྽ᡂ׎ݢ໺ ሀԿጓᙃѲѤڬਔǴᜐࣚ཮ڙ༝ౚፂᔐԶӛύЈ౽୏Ƕ ࣁΑ௖૸ጓᙃѲόӕᜐࣚచҹቹៜჹܭ༝ౚೲࡋቹៜϐำࡋǴόӕ ᜐࣚచҹޑጓᙃѲڙፂᔐਔ༝ౚϐೲࡋᐕำӵკ 2. 30(a)܌ҢǴҗკύё ܴᡉ࣮рѤᜐڰۓϐጓᙃѲڙፂᔐࡕ༝ౚೲࡋΠफ़നזǴԶѤᜐคܥ״ ϐጓᙃѲڙፂᔐࡕ༝ౚೲࡋΠफ़നᄌǶ྽ጓᙃѲڙፂᔐࡕᡂ׎ݢ໺ሀԿ ᜐࣚϐਔ໔ऊࣁ80μsǴКၨԜਔӚኳࠠ༝ౚೲࡋӵ߄ 2. 7 ܌ҢǴёว౜ ྽ጓᙃѲᜐࣚచҹࣁѤᜐڰۓǵٿᜐڰۓаϷѤᜐคܥ״ਔǴፂᔐނӧ 80μs ϐᎩೲϩձࣁ 51.9m/sǵ75.9m/s аϷ 90.6m/sǴ߄ҢѤᜐڰۓϐጓᙃ ѲჹܭלቸૈΚၨ٫ǴځԛࣁٿᜐڰۓϐጓᙃѲǴԶѤᜐคܥ״ϐጓᙃѲ לቸૈΚന১Ƕௗ๱ᢀჸૈໆᖿ༈Ǵკ 2. 30(c)ࣁόӕᜐࣚచҹޑᠼᆢጓ ᙃѲڙፂᔐࡕϐነᔔ઻ૈᐕำǴӕኬёว౜ӧናᔐ߃යነᔔ઻ૈ࣬߈Ǵҗ ܭܥ״ၨϿޑጓᙃѲၨܰౢғྖ౽ǴӢԜډናᔐࡕයѤᜐڰۓϐነᔔ઻ ૈനଯǴځԛࣁٿᜐڰۓϷѤᜐคܥ״ǶԶКၨጓᙃѲڙፂᔐࡕϐᔈᡂૈ Ϸ୏ૈӵკ 2. 30(b)Ϸკ 2. 30(d)܌ҢǴҭёว౜ཇ৒ܰౢғྖ౽ޑጓᙃ ѲځૈໆཇλǴӢԜѤᜐคܥ״ޑጓᙃѲڙፂᔐࡕ֎ԏૈໆၨϿǴӢԜל ቸૈΚനৡǴԶԜᖿ༈ҭᆶ Duan ฻Γ[1]аԖज़ϡનݤ௖૸ᠼᆢόӕᜐࣚ

చҹΠڙፂᔐϐՉࣁၲډ΋ठǶ ӧጓᙃѲѤᜐڰۓਔǴڙፂᔐਔૈໆᙯ౽Ԕጕკςܭ 2.3 ࿯௖૸Ǵӵ კ 2. 18 ܌ҢǴԶጓᙃѲٿᜐڰۓϷѤᜐคܥ״ਔૈໆᙯ౽Ԕጕკӵკ 2. 31 ܌ҢǴёว౜྽ጓᙃѲޑᜐࣚచҹόӕਔǴځૈໆᙯ౽Ԕጕҭό࣬ӕǶ ٿᜐڰۓޑጓᙃѲૈໆᙯ౽Ԕጕკӵკ 2. 31(a)܌ҢǴҗܭጓᙃѲѝԖٿ ᜐڙܥ״Ǵڙፂᔐࡕ৒ܰӛጓᙃѲύЈྖ౽ǴӢԜጓᙃѲ୏ૈ֎ԏૈໆ܌ эКٯၨεǴԶጓᙃѲᔈᡂૈౣλǴነᔔ઻ૈ܌эКٯനλǶ྽ᡂ׎ݢ໺ ሀԿѤڬᜐࣚ΢ࡕǴጓᙃѲޑᡂ׎೴ᅌᡂεǴӢԜᔈᡂૈ܌эКٯຬၸጓ ᙃѲ୏ૈǶѤᜐคܥ״ޑጓᙃѲૈໆᙯ౽Ԕጕკӵკ 2. 31(b)܌ҢǴᡉҢ ӧፂᔐၸำύǴҗܭጓᙃѲѤᜐࣣ҂ڙܥ״Ǵڙፂᔐࡕ৒ܰӛጓᙃѲύЈ ྖ౽ǴӢԜӧ᏾ঁፂᔐၸำύǴጓᙃѲ୏ૈ֎ԏૈໆ܌эКٯၨεǴԶጓ ᙃѲᔈᡂૈᆶነᔔ઻ૈ܌эКٯၨλǶ ӧҁക࿯ύǴ௖૸ΑൂቫᠼᆢጓᙃѲϐ܄፦ڙፂᔐࡕޑቹៜǴϩձࣁ ᠼᆢ׷਑୊ΚኳኧǵᠼᆢጓᙃѲነᔔΚǵᠼᆢၠຯаϷጓᙃѲᜐࣚచҹǴ ёว౜ᠼᆢጓᙃѲҁي׷਑܄፦Ϸ൳Ֆ׎ރ฻ࣣ཮ჹܭלቸૈΚౢғቹ ៜǴӢԜӧჴቸ৔ᔐਔǴ೭٤ୖኧ೿཮ࢂ،ۓٛቸՊᄬ೷ޑख़ाӢનǶࣁ Α׳߈΋؁ܭԖज़ϡનϩ݋ύǴஒٛቸՊڙፂᔐՉࣁ଺຾΋؁ޑ௖૸Ǵҁ ЎஒᝩុࣴزൂቫᠼᆢጓᙃѲޑᙁϯኳࠠǴӆჹܭӭቫᠼᆢጓᙃѲ຾Չ ௖૸ϩ݋Ƕ