Tarkibga o'tish

Sodda shaklli model yordamida verifikatsiya

Elastik statik tahlil

Ushbu verifikatsiyada 9.1.1-rasmda ko‘rsatilgandek to‘rga bo‘lingan konsol balka ko‘rib chiqildi. Verifikatsiya shartlari uchun 9.1.2-rasmda ko‘rsatilgan yuklash shartlari o‘zgartirilgan exA–exG yettita holat tahlil qilindi. exG holati exA bilan bir xil yuklash shartlariga ega, biroq unda to‘g‘ridan-to‘g‘ri yechuvchi ishlatiladigan verifikatsiya holatidir.

Har bir holat bo‘yicha verifikatsiya natijalari 9.1.1–9.1.7-jadvallarda keltirilgan.

Konsol balkaning to‘rga bo‘linish namunasi (geksaedral elementlar) Rasm 9.1.1　Konsol balkaning to‘rga bo‘linish namunasi (geksaedral elementlar)
(a) exA,G：jamlangan yuk
(b) exD：gravitatsiya
(c) exB：sirt bo‘ylab taqsimlangan yuk
(d) exE：markazdan qochma kuch
(e) exC：hajmiy yuk
(f) exF：termik yuk
Band Qiymat
Yung moduli \(E = 4000.0\ \mathrm{kgf/mm^2}\)
Uzunlik \(L = 10.0\ \mathrm{mm}\)
Puasson koeffitsiyenti \(\nu = 0.3\)
Ko‘ndalang kesim yuzi \(A = 1.0\ \mathrm{mm^2}\)
Massa zichligi \(\rho = 8.0102 \times 10^{-10}\ \mathrm{kgf}\;\mathrm{s}^2/\mathrm{mm}^4\)
Kesimning ikkinchi momenti \(I = 1.0/12.0\ \mathrm{mm^4}\)
Gravitatsion tezlanish \(g = 9800.0\ \mathrm{mm/s^2}\)
Chiziqli issiqlik kengayish koeffitsiyenti \(\alpha = 1.0 \times 10^{-5}\)

Rasm 9.1.2 Konsol balka modeli uchun verifikatsiya shartlari

Jadval 9.1.1　exA：jamlangan yuk masalasi bo‘yicha verifikatsiya natijalari

Holat nomi Elementlar soni Bashorat qiymati：\(\delta_{max}= -1.000\) Izoh
NASTRAN Tijoriy dastur FrontISTR
A231 40 -0.338 -0.371 -0.371 33 tugun / tekis kuchlanish masalasi
A232 40 -0.942 -1.002 -1.002 105 tugun / tekis kuchlanish masalasi
A241 20 -0.720 -0.711 -0.711 33 tugun / tekis kuchlanish masalasi
A242 20 -0.910 -1.002 -1.002 85 tugun / tekis kuchlanish masalasi
A341 240 -0.384 -0.384 -0.386 99 tugun
A342 240 -0.990 -0.990 -0.999 525 tugun
A351 80 -0.353 -0.355 -0.351 99 tugun
A352 80 -0.993 -0.993 -0.992 381 tugun
A361 40 -0.954 -0.985 -0.984 99 tugun
A362 40 -0.994 -0.993 -0.993 220 tugun
A731 40 - - -0.991 33 tugun / to‘g‘ridan-to‘g‘ri usul
A741 20 - - -0.996 33 tugun / to‘g‘ridan-to‘g‘ri usul

Jadval 9.1.2　exB：sirt bo‘ylab taqsimlangan yuk masalasi bo‘yicha verifikatsiya natijalari

Holat nomi Elementlar soni Bashorat qiymati：\(\delta_{max}= -3.750\) Izoh
NASTRAN Tijoriy dastur FrontISTR
B231 40 -1.281 -1.403 -1.403 33 tugun / tekis kuchlanish masalasi
B232 40 -3.579 -3.763 -3.763 105 tugun / tekis kuchlanish masalasi
B241 20 -3.198 -2.680 -2.680 33 tugun / tekis kuchlanish masalasi
B242 20 -3.426 -3.765 -3.765 85 tugun / tekis kuchlanish masalasi
B341 240 -1.088 -1.449 -1.454 99 tugun
B342 240 -3.704 -3.704 -3.748 525 tugun
B351 80 -3.547 -1.338 -1.325 99 tugun
B352 80 -0.3717 -3.716 -3.713 381 tugun
B361 40 -3.557 -3.691 -3.688 99 tugun
B362 40 -3.726 -3.717 -3.717 220 tugun
B731 40 - - -3.722 33 tugun / to‘g‘ridan-to‘g‘ri usul
B741 20 - - -3.743 33 tugun / to‘g‘ridan-to‘g‘ri usul

Jadval 9.1.3　exC：hajmiy yuk masalasi bo‘yicha verifikatsiya natijalari

Holat nomi Elementlar soni Bashorat qiymati：\(\delta_{max} = -2.944 \times 10^{-5}\) Izoh
NASTRAN Tijoriy dastur FrontISTR
C231 40 - -1.101e-5 -1.101e-5 33 tugun / tekis kuchlanish masalasi
C232 40 - -2.951e-5 -2.951e-5 105 tugun / tekis kuchlanish masalasi
C241 20 - -2.102e-5 -2.102e-5 33 tugun / tekis kuchlanish masalasi
C242 20 - -2.953e-5 -2.953e-5 85 tugun / tekis kuchlanish masalasi
C341 240 - -1.136e-5 -1.140e-5 99 tugun
C342 240 - -2.905e-5 -2.937e-5 525 tugun
C351 80 - -1.050e-5 -1.039e-5 99 tugun
C352 80 - -2.914e-5 -2.911e-5 381 tugun
C361 40 - -2.895e-5 -2.893e-5 99 tugun
C362 40 - -2.915e-5 -2.915e-5 220 tugun
C731 40 - - -2.922e-5 33 tugun / to‘g‘ridan-to‘g‘ri usul
C741 20 - - -2.938e-5 33 tugun / to‘g‘ridan-to‘g‘ri usul

Jadval 9.1.4　exD：gravitatsiya masalasi bo‘yicha verifikatsiya natijalari

Holat nomi Elementlar soni Bashorat qiymati：\(\delta_{max} = -2.944 \times 10^{-5}\) Izoh
NASTRAN Tijoriy dastur FrontISTR
D231 40 -1.101e-5 -1.101e-5 -1.101e-5 33 tugun / tekis kuchlanish masalasi
D232 40 -2.805e-5 -2.951e-5 -2.951e-5 105 tugun / tekis kuchlanish masalasi
D241 20 -2.508e-5 -2.102e-5 -2.102e-5 33 tugun / tekis kuchlanish masalasi
D242 20 -2.684e-5 -2.953e-5 -2.953e-5 85 tugun / tekis kuchlanish masalasi
D341 240 -1.172e-5 -1.136e-5 -1.140e-5 99 tugun
D342 240 -2.906e-5 -2.905e-5 -2.937e-5 525 tugun
D351 80 -1.046e-5 -1.050e-5 -1.039e-5 99 tugun
D352 80 -2.917e-5 -2.914e-5 -2.911e-5 381 tugun
D361 40 -2.800e-5 -2.895e-5 -2.893e-5 99 tugun
D362 40 -2.919e-5 -2.915e-5 -2.915e-5 220 tugun
D731 40 - - -2.922e-5 33 tugun / to‘g‘ridan-to‘g‘ri usul
D741 20 - - -2.938e-5 33 tugun / to‘g‘ridan-to‘g‘ri usul

Jadval 9.1.5　exE：markazdan qochma kuch masalasi bo‘yicha verifikatsiya natijalari

Holat nomi Elementlar soni Bashorat qiymati：\(\delta_{max} = 2.635 \times 10^{-3}\) Izoh
NASTRAN Tijoriy dastur FrontISTR
E231 40 2.410e-3 2.616e-3 2.650e-3 33 tugun / tekis kuchlanish masalasi
E232 40 2.447e-3 2.627e-3 2.628e-3 105 tugun / tekis kuchlanish masalasi
E241 20 2.386e-3 2.622e-3 2.624e-3 33 tugun / tekis kuchlanish masalasi
E242 20 2.387e-3 2.627e-3 2.629e-3 85 tugun / tekis kuchlanish masalasi
E341 240 2.708e-3 2.579e-3 2.625e-3 99 tugun
E342 240 2.639e-3 2.614e-3 2.638e-3 525 tugun
E351 80 2.642e-3 2.598e-3 2.625e-3 99 tugun
E352 80 2.664e-3 2.617e-3 2.616e-3 381 tugun
E361 40 2.611e-3 2.603e-3 2.603e-3 99 tugun
E362 40 2.623e-3 2.616e-3 2.616e-3 220 tugun
E731 40 - - 2.619e-3 33 tugun / to‘g‘ridan-to‘g‘ri usul
E741 20 - - 2.622e-3 33 tugun / to‘g‘ridan-to‘g‘ri usul

Jadval 9.1.6　exF：termik kuchlanish yuklanishi masalasi bo‘yicha verifikatsiya natijalari

Holat nomi Elementlar soni Bashorat qiymati：\(\delta_{max} = 1.000 \times 10^{-2}\) Izoh
NASTRAN Tijoriy dastur FrontISTR
F231 40 - 1.016e-2 1.007e-2 33 tugun / tekis kuchlanish masalasi
F232 40 - 1.007e-2 1.007e-2 105 tugun / tekis kuchlanish masalasi
F241 20 - 1.010e-2 1.010e-2 33 tugun / tekis kuchlanish masalasi
F242 20 - 1.006e-2 1.006e-2 85 tugun / tekis kuchlanish masalasi
F341 240 - 1.047e-2 1.083e-2 99 tugun
F342 240 - 1.018e-2 1.022e-2 525 tugun
F351 80 - 1.031e-2 1.062e-2 99 tugun
F352 80 - 1.015e-2 1.017e-2 381 tugun
F361 40 - 1.026e-2 1.026e-2 99 tugun
F362 40 - 1.016e-2 1.016e-2 220 tugun

Jadval 9.1.7　exG：to‘g‘ridan-to‘g‘ri usul verifikatsiyasi natijalari (jamlangan yuk masalasi)

Holat nomi Elementlar soni Bashorat qiymati：δmax= -1.000 Izoh
NASTRAN Tijoriy dastur FrontISTR
G231 40 -0.338 -0.371 -0.371 33 tugun / tekis kuchlanish masalasi
G232 40 -0.942 -1.002 -1.002 105 tugun / tekis kuchlanish masalasi
G241 20 -0.720 -0.711 -0.711 33 tugun / tekis kuchlanish masalasi
G242 20 -0.910 -1.002 -1.002 85 tugun / tekis kuchlanish masalasi
G341 240 -0.384 -0.384 -0.386 99 tugun
G342 240 -0.990 -0.990 -0.999 525 tugun
G351 80 -0.353 -0.355 -0.351 99 tugun
G352 80 -0.993 -0.993 -0.992 381 tugun
G361 40 -0.954 -0.985 -0.984 99 tugun
G362 40 -0.994 -0.993 -0.993 220 tugun
G731 40 - - -0.991 33 tugun / to‘g‘ridan-to‘g‘ri usul
G741 20 - - -0.996 33 tugun / to‘g‘ridan-to‘g‘ri usul

Nochiziqli statik tahlil

(2-1) exnl1: Geometrik nochiziqli tahlil

exI verifikatsiya holatining modeli exA–exG holatlaridagi model bilan bir xil. 9.1.3-rasmda verifikatsiya modelining sxematik ko‘rinishi keltirilgan. Ushbu model uchun geometrik nochiziqli tahlil bajariladi. Verifikatsiya natijalari 9.1.8-jadvalda keltirilgan.

Nochiziqli hisoblashda \(P = 1.0\ \mathrm{kgf}\) tayanch yukidan foydalaniladi, yuk orttirmasi \(0.1P\) bo‘lgan 10 ta yuk qadamida.

Verifikatsiya modeli Rasm 9.1.3　Verifikatsiya modeli

Jadval 9.1.8　exI：verifikatsiya natijalari (maksimal egilish tarixi)

Holat nomi 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Chiziqli yechim
I231 - - - - - - - - - - -
I232 - - - - - - - - - - -
I241 - - - - - - - - - - -
I242 - - - - - - - - - - -
I341 0.039 0.077 0.116 0.154 0.193 0.232 0.270 0.309 0.348 0.386 0.386
I342 0.099 0.200 0.300 0.400 0.499 0.599 0.698 0.797 0.896 0.995 0.999
I351 0.035 0.070 0.105 0.141 0.176 0.211 0.246 0.281 0.316 0.351 0.351
I352 0.099 0.198 0.298 0.397 0.496 0.595 0.693 0.792 0.890 0.987 0.992
I361 0.070 0.139 0.209 0.278 0.348 0.417 0.487 0.556 0.625 0.694 0.984
I362 0.099 0.197 0.298 0.397 0.496 0.595 0.694 0.793 0.891 0.988 0.993

(2-2) exnl2: Elastoplastik deformatsiya tahlili

Ushbu verifikatsiya masalasi National Agency for Finite Element Methods and Standards (U.K.) tashkilotining NAFEMS Test NL1 sinoviga asoslangan, unda geometrik nochiziqlilik va bir nechta qattiqlashish qonunlari hisobga olinib elastoplastik deformatsiya tahlili bajarildi. 9.1.4-rasmda tahlil modeli ko‘rsatilgan.

Elastoplastik deformatsiya tahlili modeli

Rasm 9.1.4 Elastoplastik deformatsiya tahlili modeli

(1) Verifikatsiya shartlari

Band Qiymat
Material Mises elastoplastik materiali
Yung moduli \(E = 250\ \mathrm{GPa}\)
Puasson koeffitsiyenti \(\nu=0.25\)
Boshlang‘ich oqish kuchlanishi \(5\ \mathrm{MPa}\)
Boshlang‘ich oqish nisbiy deformatsiyasi \(0.25\times10^{-4}\)
Izotrop qattiqlashish koeffitsiyenti \(H_i = 0\) yoki \(62.5\ \mathrm{GPa}\)

(2) Chegaraviy shart

Band Chegaraviy shart Qiymat
Qadam1 2 va 3-tugunlarga berilgan ko‘chish \(u_x = 0.2500031251 * 10^{-4}\)
Qadam2 2 va 3-tugunlarga berilgan ko‘chish \(u_x = 0.25000937518 * 10^{-4}\)
Qadam3 3 va 4-tugunlarga berilgan ko‘chish \(u_y = 0.2500031251 * 10^{-4}\)
Qadam4 3 va 4-tugunlarga berilgan ko‘chish \(u_y = 0.25000937518 * 10^{-4}\)
Qadam5 2 va 3-tugunlarga berilgan ko‘chish \(u_x = -0.25000937518 * 10^{-4}\)
Qadam6 2 va 3-tugunlarga berilgan ko‘chish \(u_x = -0.2500031251 * 10^{-4}\)
Qadam7 3 va 4-tugunlarga berilgan ko‘chish \(u_y = -0.25000937518 * 10^{-4}\)
Qadam8 3 va 4-tugunlarga berilgan ko‘chish \(u_y = -0.2500031251 * 10^{-4}\)

Bu yerda ko‘rsatilmagan barcha tugunlar to‘liq mahkamlangan. Ushbu masalaning nazariy yechimi quyidagicha.

Nisbiy deformatsiya (\(\times10^{-4}\))
[\(\varepsilon_x\), \(\varepsilon_y\), \(\varepsilon_z\)]		 Ekvivalent kuchlanish (MPa)
[\(H_i=0\ H_k=0\); \(H_i=62.5\ H_k=0\)]
0.25, 0, 0 5.0; 5.0
0.50, 0, 0 5.0; 5.862
0.50, 0.25, 0 5.0; 5.482
0.50, 0.50, 0 5.0; 6.362
0.25, 0.50, 0 5.0; 6.640
0, 0.50, 0 5.0; 7.322
0, 0.25, 0 3.917; 4.230
0, 0, 0 5.0; 5.673

Taqqoslash uchun, hisoblash natijalari quyidagicha.

Nisbiy deformatsiya (\(\times10^{-4}\))
[\(\varepsilon_x\), \(\varepsilon_y\), \(\varepsilon_z\)]		 Ekvivalent kuchlanish (MPa)
[\(H_i=0\ H_k=0\); \(H_i=62.5\ H_k=0\)]
\(\varepsilon_{x}\) \(\varepsilon_{y}\)
0.25, 0, 0 5.0 (0.0%); 5.0 (0.0%)
0.50, 0, 0 5.0 (0.0%); 5.862 (0.0%)
0.50, 0.25, 0 5.0 (0.0%); 5.482 (0.0%)
0.50, 0.50, 0 5.0 (0.0%); 6.362 (-0.05%)
0.25, 0.50, 0 5.0 (0.0%); 6.640 (-0.21%)
0, 0.50, 0 5.0 (0.0%); 7.322 (-0.34%)
0, 0.25, 0 3.824 (-2.4%); 4.230 (-2.70%)
0, 0, 0 5.0 (0.0%); 5.673 (5.673 (-2.50%)

Kontakt tahlili (1)

Ushbu verifikatsiya masalasi National Agency for Finite Element Methods and Standards (U.K.) tashkilotining CGS-4 kontakt yamoq sinovi masalasiga asoslangan, va ishqalanishli chekli sirpanish kontakt funksiyasini sinaydi. 9.1.5-rasmda tahlil modeli ko‘rsatilgan.

Kontakt tahlili modeli

Rasm 9.1.5 Kontakt tahlili modeli

Ushbu masalaning muvozanat sharti quyidagicha.

\[ F \cos \alpha - G \sin \alpha = \pm f_{c} \]

Yopishish ishqalanishi bosqichida ishqalanish kuchi

\[ f_{c} = E_t \Delta u \]

bo‘ladi, sirpanish ishqalanishi bosqichida esa

\[ f_{c} = \mu(G \cos \alpha + F \sin \alpha) \]

bo‘ladi.

Hisoblash natijalari bilan analitik yechimning taqqoslanishi quyidagicha.

\(\mu\) \(F/G\)analitik yechim \(F/G\)Hisoblash natijalari
0.0 0.1 0.1
0.1 0.202 0.202
0.2 0.306 0.306
0.3 0.412 0.412

Kontakt tahlili (2): Hertz kontakt masalasi

Ushbu verifikatsiyada cheksiz uzun silindr va cheksiz tekislik o‘rtasidagi Hertz kontakt masalasi tahlil qilindi. Silindr radiusi \(R = 8\ \mathrm{mm}\), deformatsiyalanuvchi jismning Yung moduli \(E\) va Puasson koeffitsiyenti \(\mu\) mos ravishda \(1100\ \mathrm{MPa}\) va \(0.0\). Kontakt yuzi silindr radiusiga nisbatan yetarlicha kichik deb qabul qilinadi; masala simmetriyasi hisobga olinib, silindrning chorak modeli tahlil qilinadi.

Hertz kontakt masalasi uchun tahlil modeli Rasm 9.1.6 Hertz kontakt masalasi uchun tahlil modeli

(1) Kontakt radiusini verifikatsiya qilish natijalari

Kontakt radiusini hisoblashning nazariy formulasi quyidagicha.

\[ a = \sqrt{\frac{4FR}{\pi E^{*}}} \]

bu yerda,

\[ E^{*} = E/2(1 - \mu^{2}) \]

bo‘ladi. Ushbu hisoblash sharoitida bosim \(F=100\) bo‘lganda kontakt radiusi \(a=1.36\) bo‘ladi.

9.1.7-rasmda kontakt nuqtalaridagi ekvivalent tugun kuchlari ko‘rsatilgan. Kontakt radiusi ushbu tugun kuchlari taqsimotini ekstrapolyatsiya qilish orqali olinadi.

Kontakt nuqtalaridagi ekvivalent tugun kuchlari taqsimoti

Rasm 9.1.7 Kontakt nuqtalaridagi ekvivalent tugun kuchlari taqsimoti

(2) Maksimal kesish kuchlanishini verifikatsiya qilish natijalari

Nazariy yechimda kontakt holati

\[ z = 0.78a \]

da maksimal siljish kuchlanishi

\[ \tau_{\max} = 0.30\sqrt{\frac{\text{FE}^{*}}{\pi R}} \]

bo‘ladi. Ushbu hisoblash sharoitida

\[ \tau_{\max} = 14.2 \]

bo‘ladi. Taqqoslash uchun,

\[ \tau_{\max} = 15.6 \]

hisoblash natijasi olindi.

Kesish kuchlanishining taqsimoti (maksimal qiymat = 15.6) Rasm 9.1.8 Kesish kuchlanishining taqsimoti (maksimal qiymat = 15.6)

(3) Modal tahlil

exJ va exK verifikatsiya holatlarining modellari exA–exG holatlaridagi modellar bilan bir xil. 9.1.9-rasmda verifikatsiya modelining sxematik ko‘rinishi keltirilgan. Ushbu model uchun modal tahlil bajariladi. Birinchi uchta tabiiy chastota hisoblanadi. exJ holatida iterativ yechuvchi, exK holatida esa to‘g‘ridan-to‘g‘ri yechuvchi ishlatiladi. Verifikatsiya natijalari 9.1.9–9.1.12-jadvallarda keltirilgan.

Verifikatsiya modeli Rasm 9.1.9　Verifikatsiya modeli

Konsol balkaning tabiiy chastotalari quyidagi tenglamalardan aniqlanadi.

Birinchi tabiiy chastota

\[ n_1 = \frac{1.875^2}{2 \pi l^2} \sqrt{ \frac{gEI}{\omega} } \]

Ikkinchi tabiiy chastota

\[ n_2 = \frac{4.694^2}{2 \pi l^2} \sqrt{ \frac{gEI}{\omega} } \]

Uchinchi tabiiy chastota

\[ n_3 = \frac{7.855^2}{2 \pi l^2} \sqrt{ \frac{gEI}{\omega} } \]

Verifikatsiya modelining xususiyat qiymatlari

Band Qiymat
\(I\) \(1.0/12.0\ \mathrm{mm}^4\)
\(E\) \(4000.0\ \mathrm{kgf/mm^2}\)
\(l\) \(10.0\ \mathrm{mm}\)
\(\omega\) \(7.85 \times 10^{-6}\ \mathrm{kgf/mm^3}\)
\(g\) \(9800.0\ \mathrm{mm/s^2}\)

Shunday qilib, birinchi uchta tabiiy chastota quyidagicha.

Rejim raqami Qiymat
\(n_1\) 3.609e3
\(n_2\) 2.262e4
\(n_3\) 6.335e4

Jadval 9.1.9　exJ: iterativ usuldagi verifikatsiya natijalari (birinchi tabiiy chastota)

Holat nomi Elementlar soni Bashorat qiymati：n1=3.609e3 Izoh
NASTRAN FrontISTR
J231 40 5.861e3 5.861e3 33 tugun / tekis kuchlanish masalasi
J232 40 3.596e3 3.593e3 105 tugun / tekis kuchlanish masalasi
J241 20 3.586e3 4.245e3 33 tugun / tekis kuchlanish masalasi
J242 20 3.590e3 3.587e3 85 tugun / tekis kuchlanish masalasi
J341 240 5.442e3 5.429e3 99 tugun
J342 240 3.621e3 3.595e3 525 tugun
J351 80 3.695e3 4.298e3 99 tugun
J352 80 3.610e3 3.609e3 381 tugun
J361 40 3.679e3 3.619e3 99 tugun
J362 40 3.611e3 3.606e3 220 tugun

Jadval 9.1.10　exJ: iterativ usuldagi verifikatsiya natijalari (ikkinchi tabiiy chastota)

Holat nomi Elementlar soni Bashorat qiymati：n2=2.262e4 Izoh
NASTRAN FrontISTR
J231 40 3.350e4 3.351e4 33 tugun / tekis kuchlanish masalasi
J232 40 2.163e4 2.156e4 105 tugun / tekis kuchlanish masalasi
J241 20 2.149e4 2.516e4 33 tugun / tekis kuchlanish masalasi
J242 20 2.149e4 2.143e4 85 tugun / tekis kuchlanish masalasi
J341 240 3.145e4 3.138e4 99 tugun
J342 240 2.171e4 2.155e4 525 tugun
J351 80 2.208e4 2.546e4 99 tugun
J352 80 2.156e4 2.149e4 381 tugun
J361 40 2.202e4 2.168e4 99 tugun
J362 40 2.154e4 2.144e4 220 tugun

Eslatma: uch o‘lchovli modellarda dastlabki ikki rejim degeneratsiyalangan. Shu sababli uchinchi hisoblangan tabiiy chastota jadvalda ikkinchi tabiiy chastota sifatida keltirilgan.

Jadval 9.1.11　exK: to‘g‘ridan-to‘g‘ri usuldagi verifikatsiya natijalari (birinchi tabiiy chastota)

Holat nomi Elementlar soni Bashorat qiymati：n1=3.609e3 Izoh
NASTRAN FrontISTR
J231 40 5.861e3 5.861e3 33 tugun / tekis kuchlanish masalasi
J232 40 3.596e3 3.593e3 105 tugun / tekis kuchlanish masalasi
J241 20 3.586e3 4.245e3 33 tugun / tekis kuchlanish masalasi
J242 20 3.590e3 3.587e3 85 tugun / tekis kuchlanish masalasi
J341 240 5.442e3 5.429e3 99 tugun
J342 240 3.621e3 3.595e3 525 tugun
J351 80 3.695e3 4.298e3 99 tugun
J352 80 3.610e3 3.609e3 381 tugun
J361 40 3.679e3 3.619e3 99 tugun
J362 40 3.611e3 3.606e3 220 tugun
J731 40 - 3.606e3 220 tugun
J741 20 - 3.594e3 220 tugun

Jadval 9.1.12　exK: to‘g‘ridan-to‘g‘ri usuldagi verifikatsiya natijalari (ikkinchi tabiiy chastota)

Holat nomi Elementlar soni Bashorat qiymati：n2=2.262e4 Izoh
NASTRAN FrontISTR
J231 40 3.350e4 3.351e4 33 tugun / tekis kuchlanish masalasi
J232 40 2.163e4 2.156e4 105 tugun / tekis kuchlanish masalasi
J241 20 2.149e4 2.516e4 33 tugun / tekis kuchlanish masalasi
J242 20 2.149e4 2.143e4 85 tugun / tekis kuchlanish masalasi
J341 240 3.145e4 3.138e4 99 tugun
J342 240 2.171e4 2.155e4 525 tugun
J351 80 2.208e4 2.546e4 99 tugun
J352 80 2.156e4 2.149e4 381 tugun
J361 40 2.202e4 2.168e4 99 tugun
J362 40 2.154e4 2.144e4 220 tugun
J731 40 - 2.156e4 220 tugun
J741 20 - 2.153e4 220 tugun

Eslatma: uch o‘lchovli modellarda dastlabki ikki rejim degeneratsiyalangan. Shu sababli uchinchi hisoblangan tabiiy chastota jadvalda ikkinchi tabiiy chastota sifatida keltirilgan.

(4) Issiqlik o‘tkazuvchanlik tahlili

Statsionar issiqlik o‘tkazuvchanlik tahlillari uchun umumiy shartlar 9.1.10-rasmda ko‘rsatilgan. exM–exT verifikatsiya holatlarining alohida shartlari 9.1.11-rasmda ko‘rsatilgan. To‘rga bo‘lish exA holatidagi bilan bir xil qilib olinadi.

Har bir holat bo‘yicha verifikatsiya natijasi bo‘lgan harorat taqsimoti jadvallari 9.1.13–9.1.20-jadvallarda keltirilgan.

Issiqlik o‘tkazuvchanlik tahlili
AB orasidagi uzunlik \(L = 10.0\ \mathrm{m}\)
Ko‘ndalang kesim yuzi \(A = 1.0\ \mathrm{mm^2}\)

Issiqlik o‘tkazuvchanligining haroratga bog‘liqligi

Issiqlik o‘tkazuvchanligi \(\lambda\) (W/(m·K)) Harorat (°C)
50.0 0.0
35.0 500.0
20.0 1000.0

Rasm 9.1.10　Statsionar issiqlik o‘tkazuvchanlik tahlilining verifikatsiya shartlari
exM:chiziqli material
exN:belgilangan harorat masalasi
exO:jamlangan issiqlik oqimi masalasi
exP:taqsimlangan issiqlik oqimi masalasi
exQ:konvektiv issiqlik uzatish masalasi
exR:radiatsion issiqlik uzatish masalasi
exS:hajmiy issiqlik ajralishi masalasi
exT:ichki tirqish masalasi

Rasm 9.1.11　Har bir verifikatsiya holati uchun tahlil shartlari

Jadval 9.1.13　exM: chiziqli material bilan statsionar hisoblash verifikatsiyasi natijalari

Holat nomi Element turi Elementlar/tugunlar soni A uchidan masofa(m)
A uchi 2.0 4.0 6.0 8,0 B uchi
M361A 361 40／33 0.0 100.0 200.0 300.0 400.0 500.0
M361B 361 40／105 0.0 100.0 200.0 300.0 400.0 500.0
M361C 361 20／33 0.0 100.0 200.0 300.0 400.0 500.0
M361D 361 20／85 0.0 100.0 200.0 300.0 400.0 500.0
M361E 361 240／99 0.0 100.0 200.0 300.0 400.0 500.0
M361F 361 24／525 0.0 100.0 200.0 300.0 400.0 500.0
M361G 361 80／99 0.0 100.0 200.0 300.0 400.0 500.0

Jadval 9.1.14　exN: belgilangan harorat masalasi verifikatsiyasi natijalari

Holat nomi Element turi Elementlar/tugunlar soni A uchidan masofa(m)
A uchi 2.0 4.0 6.0 8,0 B uchi
Tijoriy dastur 361 40／99 0.0 87.3 179.7 278.2 384.3 500.0
N231 231 40／33 0.0 87.2 179.5 278.0 384.1 500.0
N232 232 40／105 0.0 86.0 178.3 276.8 382.9 500.0
N241 241 20／33 0.0 87.3 179.7 278.2 384.3 500.0
N242 242 20／85 0.0 87.3 179.7 278.2 384.3 500.0
N341 341 240／99 0.0 87.3 179.7 278.2 384.3 500.0
N342 342 24／525 0.0 87.9 179.9 278.0 383.6 500.0
N351 351 80／99 0.0 87.3 179.7 278.2 384.3 500.0
N352 352 80／381 0.0 87.3 179.7 278.2 384.3 500.0
N361 361 40／99 0.0 87.3 179.7 278.2 384.3 500.0
N362 362 40／330 0.0 87.3 179.7 278.2 384.3 500.0
N731 731 40／33 0.0 87.3 179.7 278.2 384.3 500.0
N741 741 20／33 0.0 87.3 179.7 278.2 384.3 500.0

Jadval 9.1.15　exO: jamlangan issiqlik oqimi masalasi verifikatsiyasi natijalari

Holat nomi Element turi Elementlar/tugunlar soni A uchidan masofa(m)
A uchi 2.0 4.0 6.0 8,0 B uchi
Tijoriy dastur 361 40／99 0.0 103.2 213.7 333.3 464.8 612.6
O231 231 40／33 0.0 103.2 213.7 333.3 464.8 612.6
O232 232 40／105 0.0 103.2 213.7 333.3 464.8 612.6
O241 241 20／33 0.0 103.2 213.7 333.3 464.8 612.6
O242 242 20／85 0.0 103.2 213.7 333.4 465.2 618.0
O341 341 240／99 - - - - - -
O342 342 24／525 0.0 104.4 214.9 334.7 466.3 614.6
O351 351 80／99 - - - - - -
O352 352 80／381 0.0 103.2 213.7 333.3 465.0 624.2
O361 361 40／99 0.0 103.2 213.7 333.3 464.8 612.6
O362 362 40／330 0.0 103.2 213.7 333.4 465.5 623.5
O731 731 40／33 0.0 103.2 213.7 333.3 464.8 612.5
O741 741 20／33 0.0 103.2 213.7 333.3 464.8 612.6

Jadval 9.1.16　exP: taqsimlangan issiqlik oqimi masalasi verifikatsiyasi natijalari

Holat nomi Element turi Elementlar/tugunlar soni A uchidan masofa(m)
A uchi 2.0 4.0 6.0 8,0 B uchi
Tijoriy dastur 361 40／99 0.0 103.2 213.7 333.3 464.8 612.6
P231 231 40／33 0.0 103.2 213.7 333.3 464.8 612.6
P232 232 40／105 0.0 103.2 213.7 333.3 464.8 612.6
P241 241 20／33 0.0 103.2 213.7 333.3 464.8 612.6
P242 242 20／85 0.0 103.2 213.7 333.3 464.8 612.6
P341 341 240／99 - - - - - -
P342 342 24／525 0.0 103.2 213.7 333.3 464.8 612.6
P351 351 80／99 - - - - - -
P352 352 80／381 0.0 103.2 213.7 333.3 464.8 612.6
P361 361 40／99 0.0 103.2 213.7 333.3 464.8 612.6
P362 362 40／330 0.0 103.2 213.7 333.4 465.5 612.6
P731 731 40／33 0.0 103.2 213.7 333.3 464.8 612.5
P741 741 20／33 0.0 103.2 213.7 333.3 464.8 612.6

Jadval 9.1.17　exQ: konvektiv issiqlik uzatish masalasi verifikatsiyasi natijalari

Holat nomi Element turi Elementlar/tugunlar soni A uchidan masofa(m)
A uchi 2.0 4.0 6.0 8,0 B uchi
Tijoriy dastur 361 40／99 0.0 89.2 183.8 284.8 393.9 513.2
Q231 231 40／33 0.0 89.2 183.8 284.8 393.9 513.2
Q232 232 40／105 0.0 89.2 183.8 284.8 393.9 513.2
Q241 241 20／33 0.0 89.2 183.8 284.8 393.9 513.2
Q242 242 20／85 0.0 89.2 183.8 284.8 393.9 513.2
Q341 341 240／99 - - - - - -
Q342 342 24／525 0.0 89.2 183.8 284.8 393.9 513.2
Q351 351 80／99 - - - - - -
Q352 352 80／381 0.0 89.2 183.8 284.8 393.9 513.2
Q361 361 40／99 0.0 89.2 183.8 284.8 393.9 513.2
Q362 362 40／330 0.0 89.2 183.8 284.8 393.9 513.2
Q731 731 40／33 0.0 89.2 183.8 284.8 393.9 513.2
Q741 741 20／33 0.0 89.2 183.8 284.8 393.9 513.2

Jadval 9.1.18　exR: radiatsion issiqlik uzatish masalasi verifikatsiyasi natijalari

Holat nomi Element turi Elementlar/tugunlar soni A uchidan masofa(m)
A uchi 2.0 4.0 6.0 8,0 B uchi
Tijoriy dastur 361 40／99 0.0 89.5 184.4 285.8 395.3 515.2
R231 231 40／33 0.0 89.5 184.4 285.8 395.3 515.2
R232 232 40／105 0.0 89.5 184.4 285.8 395.3 515.2
R241 241 20／33 0.0 89.5 184.4 285.8 395.3 515.2
R242 242 20／85 0.0 89.5 184.4 285.8 395.3 515.2
R341 341 240／99 - - - - - -
R342 342 24／525 0.0 89.5 184.4 285.8 395.3 515.2
R351 351 80／99 - - - - - -
R352 352 80／381 0.0 89.5 184.4 285.8 395.3 515.2
R361 361 40／99 0.0 89.5 184.4 285.8 395.3 515.2
R362 362 40／330 0.0 89.5 184.4 285.8 395.3 515.2
R731 731 40／33 0.0 89.5 184.4 285.8 395.3 515.2
R741 741 20／33 0.0 89.5 184.4 285.8 395.3 515.2

Jadval 9.1.19　exS: hajmiy issiqlik ajralishi masalasi verifikatsiyasi natijalari

Holat nomi Element turi Elementlar/tugunlar soni A uchidan masofa(m)
A uchi 2.0 4.0 6.0 8,0 B uchi
Tijoriy dastur 361 40／99 0.0 103.2 213.7 333.3 464.8 612.6
S231 231 40／33 0.0 103.2 213.7 333.3 464.8 612.6
S232 232 40／105 0.0 103.2 213.7 333.3 464.8 612.6
S241 241 20／33 0.0 103.2 213.7 333.3 464.8 612.6
S242 242 20／85 0.0 103.2 213.7 333.3 464.8 612.6
S341 341 240／99 - - - - - -
S342 342 24／525 0.0 103.2 213.7 333.3 464.8 612.6
S351 351 80／99 - - - - - -
S352 352 80／381 0.0 103.2 213.7 333.3 464.8 612.6
S361 361 40／99 0.0 103.2 213.7 333.3 464.8 612.6
S362 362 40／330 0.0 103.2 213.7 333.3 464.8 612.6
S731 731 40／33 0.0 103.2 213.7 333.3 464.8 612.6
S741 741 20／33 0.0 103.2 213.7 333.3 464.8 612.6

Jadval 9.1.20　exT: ichki tirqish masalasi verifikatsiyasi natijalari

Holat nomi Element turi Elementlar/tugunlar soni A uchidan masofa(m)
A uchi 2.0 4.0 6.0 8,0 B uchi
Tijoriy dastur 361 40／99 0.0 88.6 182.4 282.6 387.7 500.0
S231 231 40／33 0.0 88.6 182.4 282.6 387.7 500.0
S232 232 40／105 0.0 88.6 182.4 282.6 387.7 500.0
S241 241 20／33 0.0 88.6 182.4 282.6 387.7 500.0
S242 242 20／85 0.0 88.6 182.4 282.6 387.7 500.0
S341 341 240／99 - - - - - -
S342 342 24／525 0.0 88.6 182.4 282.6 387.7 500.0
S351 351 80／99 - - - - - -
S352 352 80／381 0.0 88.6 182.4 282.6 387.7 500.0
S361 361 40／99 0.0 88.6 182.4 282.6 387.7 500.0
S362 362 40／330 0.0 88.6 182.4 282.6 387.7 500.0
S731 731 40／33 0.0 88.6 182.4 282.6 387.7 500.0
S741 741 20／33 0.0 88.6 182.4 282.6 387.7 500.0

Chiziqli dinamik tahlil

exW holatida (1)-banddagi kabi konsol balka uchun chiziqli dinamik tahlil bajarildi. 9.1.12-rasmda verifikatsiya shartlari ko‘rsatilgan. Bu yerda bir xil to‘r bo‘linishi uchun vaqt qadamining natijalarga ta’siri verifikatsiya qilindi. Dinamik tahlilda nooshkor va oshkor usullarning ikkalasi ham qo‘llanildi, element turlari sifatida 361 va 342 ishlatildi. Verifikatsiya natijalari 9.1.22-jadval hamda 9.1.13–9.1.15-rasmlarda keltirilgan.

Tahlil modeli Tahlil modeli

Tashqi kuch F ning vaqt tarixi Tashqi kuch F ning vaqt tarixi

Qo‘zg‘atish nuqtasi ko‘chishining nazariy yechimi:

\[ F(t)=F_0 I(t) \]

bu yerda,

\[ \(F_0:\ \text{O‘zgarmas vektor}\) \]
\[ I(t)= \begin{cases} 0, t < 0 \\\ 1, 0 \leq t \end{cases} \]
\[ u(t) = \frac{F_0 l^3}{EI} \sum^{\infty}_{i=1} \frac{1-\cos{\omega_i t}}{{\lambda_i}^4} \left\lbrace \cosh{\lambda_i}-\cos{\lambda_i}-\frac{\cosh{\lambda_i} + \cos{\lambda_i}}{\sin{\lambda_i}+\sin{\lambda_i}} (\sinh{\lambda_i} - \sin{\lambda_i}) \right\rbrace^2 \]

Rasm 9.1.12　Chiziqli dinamik tahlilning verifikatsiya shartlari

Verifikatsiya shartlari:
Uzunlik \(L\) \(10.0\ \mathrm{mm}\)
Ko‘ndalang kesim eni \(a\) \(1.0\ \mathrm{mm}\)
Ko‘ndalang kesim balandligi \(b\) \(1.0\ \mathrm{mm}\)
Yung moduli \(E\) \(4000.0\ \mathrm{kgf/mm^2}\)
Puasson koeffitsiyenti \(\nu\) \(0.3\)
Zichlik \(\rho\) \(1.0 \times 10^{-9}\ \mathrm{kgf}\;\mathrm{s}^2/\mathrm{mm}^4\)
Gravitatsion tezlanish \(g\) \(9800.0\ \mathrm{mm/s^2}\)
Tashqi kuch \(F_0\) \(1.0\ \mathrm{kgf}\)
Element Birinchi tartibli geksaedral element
Ikkinchi tartibli tetraedral element
Yechish usuli nooshkor usul
Newmark-\(\beta\) usuli parametri\(\gamma\) 1/2
Newmark-\(\beta\) usuli parametri\(\beta\) 1/4
oshkor usul
So‘nish Yo‘q

Jadval 9.1.21　Chiziqli dinamik tahlilning verifikatsiya shartlari (davomi)

Holat nomi Element turi Tugunlar soni Elementlar soni Yechish usuli Vaqt qadami \(\Delta t\) (s)
W361_c0_im_m2_t1 361 99 40 nooshkor usul 1.0E-06
W361_c0_im_m2_t2 361 99 40 nooshkor usul 1.0E-05
W361_c0_im_m2_t3 361 99 40 nooshkor usul 1.0E-04
W361_c0_ex_m2_t1 361 99 40 nooshkor usul 1.0E-08
W361_c0_ex_m2_t2 361 99 40 nooshkor usul 1.0E-07
W361_c0_ex_m2_t3 361 99 40 nooshkor usul 1.0E-06
W342_c0_im_m2_t1 342 525 240 oshkor usul 1.0E-06
W342_c0_im_m2_t2 342 525 240 oshkor usul 1.0E-05
W342_c0_im_m2_t3 342 525 240 oshkor usul 1.0E-04
W342_c0_ex_m2_t1 342 525 240 oshkor usul 1.0E-08
W342_c0_ex_m2_t2 342 525 240 oshkor usul 5.0E-08
W342_c0_ex_m2_t3 342 525 240 oshkor usul 1.0E-07

Jadval 9.1.22　exW: konsol balka uchun chiziqli dinamik tahlil verifikatsiyasi natijalari

Holat nomi Element turi Tugunlar soni Elementlar soni Yechish usuli \(t = 0.002\ \mathrm{s}\) vaqtdagi z yo‘nalishidagi ko‘chish (mm)
W361_c0_im_m2_t1 361 99 40 nooshkor usul 1.9753 1.9302
W361_c0_im_m2_t2 361 99 40 nooshkor usul 1.9753 1.8686
W361_c0_im_m2_t3 361 99 40 nooshkor usul 1.9753 0.3794
W361_c0_ex_m2_t1 361 99 40 nooshkor usul 1.9753 1.9302
W361_c0_ex_m2_t2 361 99 40 nooshkor usul 1.9753 1.9247
W361_c0_ex_m2_t3 361 99 40 nooshkor usul 1.9753 yaqinlashmadi
W342_c0_im_m2_t1 342 525 240 oshkor usul 1.9753 1.9431
W342_c0_im_m2_t2 342 525 240 oshkor usul 1.9753 1.8719
W342_c0_im_m2_t3 342 525 240 oshkor usul 1.9753 0.3873
W342_c0_ex_m2_t1 342 525 240 oshkor usul 1.9753 1.9359
W342_c0_ex_m2_t2 342 525 240 oshkor usul 1.9753 1.9358
W342_c0_ex_m2_t3 342 525 240 oshkor usul 1.9753 yaqinlashmadi

Konsol balkaning deformatsiya ko‘rinishi va ekvivalent kuchlanish taqsimoti Rasm 9.1.13　Konsol balkaning deformatsiya ko‘rinishi va ekvivalent kuchlanish taqsimoti

(a) Element turi 361:nooshkor usul (a) Element turi 361:nooshkor usul

(b) Element turi 361:oshkor usul (b) Element turi 361:oshkor usul

Rasm 9.1.14 qo‘zg‘atish nuqtasi ko‘chishi \(u_z\) ning vaqt tarixi

(a) Element turi 342:nooshkor usul (a) Element turi 342:nooshkor usul

(b) Element turi 342:oshkor usul (b) Element turi 342:oshkor usul

Rasm 9.1.15　qo‘zg‘atish nuqtasi ko‘chishining \(u_z\)vaqt tarixi

Chastotaviy javob tahlili

Ushbu verifikatsiyada konsol balka uchun chastotaviy javob tahlili bajarilib, natijalar umumiy maqsadli tijoriy yechuvchi natijalari bilan taqqoslandi. Tahlil modeli va verifikatsiya shartlari quyida keltirilgan.

Tahlil shartlari:
Yung moduli \(E\) \(210000\ \mathrm{N/mm^2}\)
Puasson koeffitsiyenti \(\nu\) \(0.3\)
Zichlik \(\rho\) \(7.89 \times 10^{-9}\ \mathrm{t/mm^3}\)
Gravitatsion tezlanish \(g\) \(9800.0\ \mathrm{mm/s^2}\)
Yuk \(F_0\) \(1.0\ \mathrm{N}\)
Rayleigh so‘nish parametri \(R_m\) \(0.0\)
Rayleigh so‘nish parametri \(R_k\) \(7.2E-07\)

Rasm 9.1.16 Tahlil modeli (birinchi tartibli tetraedral elementlar: 126 ta element, 55 ta tugun)

Modal tahlildan olingan birinchi beshta tabiiy chastota va qo‘zg‘atish nuqtasining chastotaviy javobi quyida keltirilgan.

Rejim FrontISTR Tijoriy dastur
1 14952 14952
2 15002 15003
3 84604 84539
4 84771 84697
5 127054 126852

Qo‘zg‘atish nuqtasi ko‘chish kattaligining chastotaga bog‘liqligi Rasm 9.1.17　Qo‘zg‘atish nuqtasi ko‘chish kattaligining chastotaga bog‘liqligi