PHNG PHP PHN T HU HN - FEM

Trng i hc Cng nghip TP.HCM

ng Cng Truyn

Chng 4:

PHN T L XO

Phn t mt l xo

Hai nt : i, j

Chuyn v nt : ui, uj (in, m, mm)

Lc nt : fi, fj (lb, N)

cng : k (lb/in, N/m, N/mm)

Phn t mt l xo

Lin h gia lc bin dng l xo:

Phn t mt l xo

Phng trnh cn bng nt i:

Phng trnh cn bng nt j:

Vit di dng ma trn:

Phn t mt l xo

Hay:

k : ma trn cng phn t

u : vc t chuyn v nt phn t

f : vc t lc nt phn t

H l xo

Ba nt : 1, 2, 3

Chuyn v nt : u1, u2, u3 (in, m, mm)

Lc nt : F1, F2 , F3 (lb, N)

cng : k1, k2 (lb/in, N/m, N/mm)

H l xo

Phn t 1:

Phn t 2:

fim l ni lc tc ng

ln nt a phng ica phn t m (i=1,2)

H l xo

Lp rp ma trn cng tng th:

Phng trnh cn bng nt 1:

Phng trnh cn bng nt 2:

Phng trnh cn bng nt 3:

H l xo

Do :

Vit di dng ma trn:

Hay: , K l ma trn cng tng th

H l xo Cch khc lp ghp ma trn cng tng th

Tng kch thc cc ma trn phn t 1 v 2 t 22 thnh 33

Cng 2 ma trn bng nguyn l cng tc dng

H l xo iu kin bin v iu kin ti trng:

Gi s

Ta c:

Rt gn:

H l xo Gii h phng trnh

Ta c chuyn v

V phn lc

V d 1

H l xo chu lc nh hnh v, cho:

Tnh: Ma trn cng tng th Chuyn v nt 2 v 3 Phn lc nt 1 v 4

Lc l xo 2

V d 1

Cc ma trn cng phn t

V d 1 Ma trn cng tng th

V d 1 H phng trnh PTHH

(4)

V d 1 iu kin bin: u1 =u4 =0

Chuyn v nt 2 v 3

Phn lc nt 1 v 4

V d 1 Lc l xo 2

Phng trnh cn bng l xo 2

Lc l xo 2

BI TP V NH(Vit tay trn giy A4, tun sau np)