Một trường hợp tính tấm chữ nhật chịu uốn xét ảnh hưởng của biến dạng trượt ngang

KHOA HOC CdNt NGHE & CUDC SONt

MOTTRl/OfNGHOPTINHTAMCHl/NHAT

CHIUUONXETANHHl/dNGCUA

BIEN DANG TRaOT NGANG

Nguyen Thuy Anh

ABSTRACT

The current method for calculating

bent plate under the effect of

horizontal slide deformation

uses deflection function W and

rotation angle cp^ caused by

bending moment Mx, rotation

angle cp caused by bending

moment My,which are three

implicit functions of the problem

(see [2,3,4]). However, the above

solution still has certain difficulty

(shearlocking phenomenon). In

this paper, the author studies the

case of bent rectangular plate

under the effect of horizontal slide

deformation on the basic of using

deflection function W, shear force

function Q^, shear force function Q

which are three target functions

Th.S Nguyen Thuy Anh

Trirdng Cao dang Giao thong

van tai

Df): 0988087009

odi vdi ti m tda khdp d chu vi (hinh 1),

h i m dp vdng tam cd the dUOc viet theo

dang chuoi lupng giic kep Navier:

mnx . nrty W(X'y) = 2^2 . amn sin ^ ^ ,„,

m-l n-1

Vl Q^ li m thay doi gde xoay cua mat

trung hda theo

ehieu X nen hi m luc ci t Q^ ed the viet

dudi dang sau: X X

m-l n=l

Tuong tu hi m lUc cit Q^ cd dang sau:

TTty

a "b~

m=l n=l

Cic he sd a^^, b^^, e^^ la cie an can tim.

TU (b) va (e) xie dinh bien dang trUOt y^

mn:x nny cos —s,n — (b,

„ '^~' V . rnTTX nn

Qy = 2^2 ^ ^mn sin—-cos - (c)

vay :

^v=^Q v

Gh = Eh 6D(1-|a)

2(1+1.1) h^

E: mddun di n hdi eua vi t lieu,

p: he sd Poat-xdng

(d)

(e)

Eh^

D = -: dp cdng tru eua tim .

12(1-^")

a: l i he sd xet in h hudng cua sU ti p

trung lUe cit tai mat trung hda. Odi vdi tam

cd tiet dien die cd the lay a = 1.2 [1,3]

h: chieu day tam.

Cic gde xoay do md men udn IVI^, M

gi y ra duoc xic dinh:

5W a ^

dx Gh

X X

V^'V"' mjt mrtx . nny

=2.z.^-v^°^^^'"ir m-l n^l " X X

m=1 n=l

aw a „

(f)

'X X

v-'V- ' nn: . mnx nny = > 7 a„n—si n cos

m-l n=1

X X

a v^X" ' rnnx nrty + > > CmnSin COS

Gh^ ^ """ . a b

Cic bien dang udn hay dp cong eua

mat vdng:

x2

I mn

Xx .5Px

dx

CO -x

m -l n-1 " k

"^' "

mnx . I

sin sin￾a

Py - W

m=l n=l

5Px , SPy

a nn

"Gh'"^"V

mnx . r

sin sin￾a

Kxy - + -

dy dx

(g)

•ZZ m=l n=l

mn nn

~3mn ~ +

a b

a , nn

mn a

mnx . nny

eos sin

a b

Cac cdng thdc xac dinh ndi lUc md men:

Mx=D(zx+ii-/.y )

M„ = D(zy-FnXx ) (h)

Mxy=D(1-n)Xxy

Cic hi m dp vdng (a), hi m luc cit Q__ (b),

ham lUc cat Q^ (c) thda mi n dieu kien bien

tren canh ti m dupc the hien tren hinh 2.

5 0 iSDniiifSl 02.2011 i