hw_4_solu

hw_4_solu - 5'! We represent the shape functions in terms...

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Unformatted text preview: 5'! We represent the shape functions in terms of the products of linear functions. We select the functions such that their product will produce a value of unity at the given node and a value of zero at other nodes. Ni(x)=C(x-xj)(x-xk)(x-XI) Ni(x) = c(x—%j[x—2?I)(x—l) Ni(0)=1 C(0—é)[O—%J(0—l)=l —9 c: 213 Nk(x)=c(x—xi)(x——xj)(x—x,) Nk(x)=c(x—O)[x—%J(x—I) ngjzl c£%ll%—éJ£%—IJ=I c: 213 Nk(x) = ‘22; x [x—é)(x—l) [VJ-()5)=c(x_xi)(x_xk)(x“x1) Nj(x)=c(x—0)[x—%)(x—l) C E 213 27 21 Nj(x)= 213 x(x—?)(x—I) N,(x) = c(x—x,.)(x.—xj)(x—xk) N,(x) =c(x—o)[x_1)(x_aj 3 3 N,(l) =1 l 21 c(l—0)[l—§)[l—?J—l 9 C = 213 N,(x) = 2913 x[x—é](x—%) (4‘ "5r ‘3 l4 A); - (fr-aw par/flap» 7h”, = “inky—550m : / +4 :ich 1,; 2. "' “32 am m n ( u(f).—Al;u;+djuj‘+dkuk ’0‘): act) = r; fU—HCU + {1.5953 4 3:; (gym) w‘x Sum) : —g(é)(~£)m +( ‘5ij 4 {(éKéxa) ., -J, 0' 9 , .«7 ‘ M443: w“? ,7‘: ’ {=3 (“(05) " égY’D'b-W and 1,6525 waml M .‘W c) = 33» DC: 9 (I 6 Amg=E(Yv£ : W.» 90‘ :J u, + fluf+ ggiuk) ,2; , 2. ,2, , , . z - L 2%}; 113:2)“; ¢§u§ a} figggggqu E :[(’§*§)"i '23”? ‘6’?)‘391 ‘%" xo‘xé =[(~§+§)(23 ~2 ?(>’J* (1% ‘4’)3] ’23,}, £1311 104x € (4;): ~ «EJJLJOJ ‘ 2(‘zl)(b~)+fé" (— >’+3")(21 (5) '5=£&.1 “J unaaéaj xJ- t .T. = {MAX = ’éI—éf(l~f)dj x I ’ u} I. = «:1 {é-é-r-é-taw] xk 1 (m m I: J N.‘JX=J(-°f-D<1'i—.)dm x. 1 1 = j; {Winn-1H“ = jjuth-slném 0 N°+ea how much easier?! was J" eva\ua:\'e, 1 “Skis hid-arc“ Ana lac-fl Coori§nu+es. 2 no‘l‘e jzif-l J¢=dxzi In 1 M W.) + Mum H.452) = * 1% (1-3)] ,= -33. [(-0-5‘7735'02 £901: 9.97735-och)] MU.) = “'23-‘7‘70‘701 “C(51) = "-2- [Sz‘éi-SIU Pig [0677359161 (1- o-S’WBs'ozcfifl “((3‘) = "O- 0610042371 I g (1X0. zL-ac'n €01 ) + (I) (—0- 041004 li‘be) ool£6666667427 ([22: I [IS I.ng 4 (d) 7"! mun-J? in evac-f Lia. fag:th £3549ch A; ufifi’fifiu’twd 9rd" J1: Z. uv-Q-(JIQ-Jn-‘WL lln}ar'¢+'1 624.412 fifij P‘fiv) ,1 unlar kc3( It —~ (2M4) ar‘ (5.5, ...
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hw_4_solu - 5'! We represent the shape functions in terms...

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