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Practice Sheet2 - 2D FEM

The document appears to contain a series of mathematical equations and expressions, possibly related to coordinate transformations and algebraic manipulations. It includes various symbols and notations that suggest a complex mathematical discussion. The overall context and specific purpose of the document are unclear due to the fragmented and disorganized nature of the content.

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naman Jain
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0% found this document useful (0 votes)
3 views10 pages

Practice Sheet2 - 2D FEM

The document appears to contain a series of mathematical equations and expressions, possibly related to coordinate transformations and algebraic manipulations. It includes various symbols and notations that suggest a complex mathematical discussion. The overall context and specific purpose of the document are unclear due to the fragmented and disorganized nature of the content.

Uploaded by

naman Jain
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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3o\1-

- ,\-B' -h>,i--c ~'O~ IL Qvo.j_tt.>-\~~cJ cl~~

\N ~ ~~ w '{\ -\;~ ·-::s:_ ~' '\ 0.$

X ==-
~z::_.l\V, t_, - 1\\' :x., ,t,- "-\2..l". ,__ + NJ 'X J -t-_ /\I'< X~

N \ 't l + 1'1.2-'( 1.. + N1"J + "' ~ '1 ~


~ ~ ~N,~: -

SoJ :X = :~{ G-~)(,-~j-+~CG~~)(,-rv)}iL~irv}1


-\"' --fy lc, -.. .\ c,.,.iv)j
X = ~l-1\-~~l\,i ~~G-t\,+ _'z._-k~J
--r \ l\ +l\,-t k -t-1\t 1,.J ,t- -ifL \+ l\;-1.11- ~j
'I ' .
j ' .

' , ; '

S;MJ· ~~

/= flt f [1- Tt&j -r ¾l 1-1-+ ~- ~~J:


t '- k

-t- *[1+~-rld f [ tp_j fv~ -t- /+~-~-


;
(

2 - 2-'\;-- ~~ -r 2J1,, ~ --t- 3- 3'1; - 3~'\; -t- G +-61v


--t- G212 ..+ Gt\,S£ + S- +r-,i,- S:&. - 5 ~A,)
I : :. b---r 3iv+9
. 2.. .

3 -:= 5 ~T 3 1; -t (
~'ti+ ·1
?( .
/2- . ~l.e. +;i-T 2R_ 'fll T /_s-c ' - 1 ! >@} ·
I

~o 3 ~ b-+31,c
,,..-
+ 2s' - J

2-

6 =
M ~ , pl,y oi
~+31,, +8'
2. ·uo ~ ~

,JcP.> . '
11- ==- 2.-~-+ S ,i,-+ t6 ~{f)
T""""' -------
J ow
I

N, ..:::,. /4 l, -H'.l, 2-"1 1 r)(, -r O• ~6 0.-,) 0 ·~


0
c; 'I- s- 2-

N2- ::= -h-( I ~ o. '.)__ 1-:;) ( t ~o


ti S& oir) -==- ('.). 2-1-ct-'\ '\'f-

f' -) (1 f o,\6~r) = C· o'+ E.1s2.


N !> :::,_ -4 L1 - cH,9\ I\
NL( -:,. ~ (,t-{J• 2-~1 .;) lr -o ,\6Y\) ::::.- 0 1
- ~~'1~1-

R~ 'Jctt_o b10-/\ , \~ ~~ '1,


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) _'a~ \ 0~
dv.-
; -
0 -- 0~
l a'>- o'\
o'v ~1\,,

. 5--& -t- 311.t + ~fv-+1 ~ -


we_ ~QvJ '3- ~
L-j ;
~ -
..-,
2.12. -,-<3,i., -+ r

-
- 3
cSo hoM ] CA\J s o.J(_ j~-

?& + 3 1r + ~ fv ·-t I f ~ 2.-~ + 61,--t- 16 .


·, I

JS., --31\v -t- )Q~ == j_

ZL [3-r'\t) - 2> 'v ~ -1-


-. ~ :::: l _,_Jt\;'
(__3 +'\I) ,--,, ®.
/'\Ill~ :Aor-l e:5j A . 70 4 I

l,.J<L cJ J.

l 2- = I G + bl\,+ 2/l r1-J1v)


9+tv

-- 11 : :,_ Gri,b-+l\t --t- 2--C,1 -t-Y\;


< (_3+1\1) .
.. .

G-1-1t,) ~ 6,i,()ffv}--r 2- CI+ 3'11 )


J

. . ......I,\

- l 2--:; % _:::: I8'I\,,+ 61/1- + 2- + G,1


.J
61\,,l..-t ')..~ Iv + )l.-f ~0
• I t_ \,.s o t, ;::: - C) • 5' 6 ~ s i
~ ' ,i,;. · ',
i

oJ &== I --3,.0 ,S"G 'l\


.> - 0 - f G '\ f' ·
~-== - 0 - 2-~,~ -
[ :cl'f r:n a 1r ,

-- t <1v X (.1) . ~oG ~r1- --t 8 (0 ~ 0 ° 2-t-~9 q.f-


+ S' ox O,. o 'f- G2S1- --t ~ o~ CJ, ts 8--'l'? 8-
Sol2 Cs) CG,4)

C)
Shape gia y

fas edge 2,3


So , =
(|-v)

Ny =
Now cquivalet edal ie
3-6)

ds

No
Consideny de d-5.

S=3r61

, S=
tds
:-C,t C2

2
CitC
| Cnd 2.

|80s

Now
=·8o

to

N,

180
4 6
?3. 3+x?

lootdinate trantrnatibn i x(<- 84+3

8+ (3¢t3)' 3dçx9dy
2+(214g)?

I =
3+9( y, 3r3(
3+9(%+J
2
3+9(

Q(244 4 0.38 5
9.354 +
(. 69 74 +
6

81-864

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