C HC VT RN BIN DNG
Chng 3. L thuyt bin dngI. Chuyn ng Bin dng Chuyn v
Chuyn ng, hay s thay i v tr ca mi trng lin tc l php bin i im hnh
thi ban u (hnh thi quy chiu) ca mt vt th hnh thi ca vt th khi b bin
dng
1Chng 3. L thuyt bin dngI. Chuyn ng Bin dng Chuyn vChuyn v ca im
P:
Cc thnh phn ca vect chuyn v:
Tp hp ca u to thnh trng chuyn v Bin dng l s thay i hnh dng ca vt
th:2Chng 3. L thuyt bin dngII. Tenx bin dngGi ds v ds l hai phn t
thng tng ng trong v Ta c:
M:
Nn:
3Chng 3. L thuyt bin dngIII. Tenx bin dngHiu s:
Ta c th biu din theo trng chuyn v:t:
Do :
- Tenx bin dng
T o hm ring:
4Chng 3. L thuyt bin dngIII. Tenx bin dngChn i lng gi l gradient
ca chuyn v
Ta c:
Hay:
5Chng 3. L thuyt bin dngII. Tenx bin dngQuan h bin dng - chuyn v
trong h trc ta Decartes
u, v, w l cc thnh phn ca vect chuyn vExx, Exx, Exx bin dng php
tuynExy, Exz, Eyz bin dng tip tuyn6Chng 3. L thuyt bin dngIII. Tuyn
tnh hnh hcGi thuyt tuyn tnh hnh hc: Gradient ca cc chuyn v rt b,
sao cho bnh phng v tch s ca chng khng ng k
Khi tenx bin dng Eij c n gin thnh tenx bin dng b ij:
7
Chng 3. L thuyt bin dngIV. Cch din gii v mt vt l
Bin dng php tuyn (bin dng di) biu din s thay i chiu di8Chng 3. L
thuyt bin dngIV. Cch din gii v mt vt l
Tng t: Bin dng tip tuyn (bin dng gc) biu din phn na s bin thin
ca gc vung9Chng 3. L thuyt bin dngIV. Cch din gii v mt vt l
Ta c: S trt biu din 2 ln bin dng tip tuyn:
Nu
10Chng 3. L thuyt bin dngIV. Cch din gii v mt vt l
Ta c: S trt biu din 2 ln bin dng tip tuyn:
Nu
11Chng 3. L thuyt bin dngIV. Cch din gii v mt vt l
Tenx bin dng c th c dng ma trn:
12Chng 3. L thuyt bin dngIV. Cc bin dng chnh Bt bin lchi vi tenx
bin dng ta cng kho st ging tenx ng sutTi mt im ca mi trng lin tc
lun tn ti 3 phng chnh vung gc, m dc theo khng c bin dng tip tuyn
no.
13Chng 3. L thuyt bin dngIV. Cc bin dng chnh Bt bin lch
OC3/2C2C1 I IIIII14Chng 3. L thuyt bin dngPhng trnh c trng:
Trong :
l cc bt bin ca tenx bin dng15Chng 3. L thuyt bin dngIV. Cc bin
dng chnh Bt bin lchBin dng tng qut c phn tch:S thay i th tch thun
tyS thay i hnh dng thun tyBin dng trung bnh:
Khi ny tenx bin dng c tch ra:16Chng 3. L thuyt bin dngBin dng
tng qut = Thay i th tch + Thay i hnh dng
IV. Cc bin dng chnh Bt bin lch17Chng 3. L thuyt bin dngV. Trng
thi phng ca bin dngTrng thi phng ca bin dng (trong mt phng xy), khi
ti mt im ca mi trng lin tc,
Khi tenx bin dng rt gn li 3 thnh phn:
18Chng 3. L thuyt bin dngV. Trng thi phng ca bin dngPhp bin di
trc trong mt phng, trn mt x:
dn di chnh:
19Chng 3. L thuyt bin dngIV. Cc phng trnh lin tc v bin dng
Cc phng trnh CauchyBit u(x,y,z) , v(x,y,z) , w(x,y,z)Bit
duy nht?20Chng 3. L thuyt bin dngIV. Cc phng trnh lin tc v bin
dngV mt ton hc s duy nht ca 3 thnh phn chuyn v chng t 6 thnh phn
bin dng khng phi c lp vi nhau m gia chng phi c cc quan h no 3 quan
h gia bin dng gc v bin dng di 3 quan h gia bin dng di v bin dng
gc21Chng 3. L thuyt bin dngNhm 1T phng tnh Cauchy:
22Chng 3. L thuyt bin dngTng t, t phng trnh
23Chng 3. L thuyt bin dngNhm 2
24Chng 3. L thuyt bin dng
25Chng 3. L thuyt bin dngPhng trnh Saint - Venant
Th hin s lin tc ca vt th trong qu trnh bin dng26Chng 3. L thuyt
bin dng
S lin tc ca vt th trong qu trnh bin dngCc phn t phi bin dng sao
cho chng c th xp kht c vi nhau
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