C HC VT RN BIN DNG

Chng 5. nh lut ng x ca vt liuI. nh lut ng x ca vt liu

Quan h gia ng sut v bin dng l tuyn tnhTrong : Cijkl cc hng s n hi vt liu. Cc hng s ny to thnh mt tenx hng 4. S hng s n hi c lp khng th ln hn 21

1Chng 5. nh lut ng x ca vt liuII. nh lut Hooke theo trc chnhng sut ti mt im:

Bin dng ti mt im:

2.1. Trng thi ng sut n:

2.1. Trng thi ng hai chiu:Xt phn t hnh ch nht c b dy mng u, chu trng thi ng sut phng

2Chng 5. nh lut ng x ca vt liu2.1. Trng thi ng sut hai chiu:

L lun tng t theo phng 2:

Bin dng di theo phng 1:V ngc li:

(2.1)(2.2)3Chng 5. nh lut ng x ca vt liu2.2. Trng thi ng sut ba chiu:L lun tng t bi ton trng thi ng sut phng, ta c:

4Chng 5. nh lut ng x ca vt liuIII. Muyn trtTrng thi trt thun ty

Tng t:

(3.1)321- m un n hi trt

(3.2)5Chng 5. nh lut ng x ca vt liuIV. nh lut Hooke tng qut

Trng thi ng sut ba chiuTrng thi ng sut hai chiu

(4.1)(4.2)6Chng 5. nh lut ng x ca vt liuIV. nh lut Hooke tng qut

Theo k hiu ch s: gin n th tch:

Hay:

(4.3)(4.4)7Chng 5. nh lut ng x ca vt liuIV. nh lut Hooke tng qut

Trong : - ng sut trung bnh

- moduyn nn khi

thay t biu thc (4.4) vo (4.3), ta c nh lut Hooke ngc:

(4.5)8Chng 5. nh lut ng x ca vt liuIV. nh lut Hooke tng qutHoc ta cn c th vit:

(4.5)Hoc ta c th thay cc hng s E, G, bng cc hng s Lam:

(4.6)9Chng 5. nh lut ng x ca vt liuIV. nh lut Hooke tng qutKhi nh lut Hooke ngc c vit di dng:

(4.7)Ta li c:

(4.8)=(4.4)

(4.9)10Chng 5. nh lut ng x ca vt liuVI. nh lut Hooke khiPhng trnh (4.8) din t s thay i th tch m khng b xon

Biu thc (4.8) th hin nh lut Hooke khi

Phng trnh (4.9) din t s thay i hnh dng m khng lm thay i th tch11Chng 5. nh lut ng x ca vt liuV. nh lut Hooke trong trng hp bin dng phng trng thi bin dng phng, ta c:

Thay z = 0 vo biu thc (4.1c), ta c

(5.1)Thay (5.1) vo (4.8a) v (4.8b)12Chng 5. nh lut ng x ca vt liuV. nh lut Hooke trong trng hp bin dng phng trng thi bin dng phng, ta c:

Thay z = 0 vo biu thc (4.1c), ta c

(5.1)Thay (5.1) vo (4.8a) v (4.8b), ta c nh lut Hooke cho trng thi ng sut phng:13Chng 5. nh lut ng x ca vt liuV. nh lut Hooke trong trng hp bin dng phngThay (5.1) vo (4.8a) v (4.8b), ta c nh lut Hooke cho trng thi ng sut phng:

(5.2)

(5.3)14Chng 5. nh lut ng x ca vt liuVI. Cc hng s n hi ca vt liu:Nu vt liu ng hng:

15Chng 5. nh lut ng x ca vt liuVI. Cc hng s n hi ca vt liu:Nu vt liu d hng:

- cc hng s vt liu

(4.13)16Chng 5. nh lut ng x ca vt liuVI. Cc hng s n hi ca vt liu:Trong trng hp tng qut ch c 21 hng s n hi c lp

17Chng 5. nh lut ng x ca vt liuVI. Cc hng s n hi ca vt liu:Vt liu c mt mt i xng

18Chng 5. nh lut ng x ca vt liuVI. Cc hng s n hi ca vt liu:Vt liu ch cn 13 hng s c lp

19Chng 5. nh lut ng x ca vt liuVI. Cc hng s n hi ca vt liu:Vt liu c 3 mt i xng

20Chng 5. nh lut ng x ca vt liuVI. Cc hng s n hi ca vt liu:Vt liu ch cn 9 hng s c lp

21Chng 5. nh lut ng x ca vt liuVII. Cc phng trnh c bn ca CHVRBD v phng php gii - Ba phng trnh cn bng

Cc phng trnh ca CHVRBD(I)22Chng 5. nh lut ng x ca vt liu - Su phng trnh Cauchy hoc 6 phng trnh tng thch bin dng:

(II)(II)23Chng 5. nh lut ng x ca vt liu - Su phng trnh nh lut Hooke:

(III)(III)24Chng 5. nh lut ng x ca vt liuiu kin bin:

- Trng ng sut tha iu kin cn bng trn bin tnh hc

- Trng chuyn v tha iu kin chuyn v trn bin ng hc 25Chng 5. nh lut ng x ca vt liu 1. Phng php chuyn v

Cc phng php gii bi ton LTHThay (II) vo (III) ri thay vo (I) sau bin di, ta c phng trnh LamTrong - ton t Laplace

26Chng 5. nh lut ng x ca vt liu* iu kin bin tnh hc

27Chng 5. nh lut ng x ca vt liu 2. Phng php lc

Thay (III) vo (II) ta c (IV) , sau thay (I) vo (IV), ta c h phng trnh Beltrami - MichellVi

28Chng 5. nh lut ng x ca vt liuVI. nh l v s duy nht nghim Mt vt th n hi chu tc ng ca lc th tch v lc b mt trn bin tnh hc v chuyn v cng bc trn bin ng hc th ch c duy nht mt trng ng sut, bin dng v chuyn v trong vt th.29