SCILAB

-----------------------------------------

//Dane:

E=30000000;//[kPa]

b1=2.0;//[m]

h1=0.5;//[m]

b2=1.0;//[m]

h2=0.5;//[m]

k=28000;//[kN/m^3] - parametr sprężystości podłoża

lambda=0.1;

//Obliczenia pomocnicze:

J1=b1*h1^3/12;

J2=b2*h2^3/12;

k1=k*b1;

k2=k*b2;

//Wektor momentów bezwładności:

vJ=[J1*ones(1,53), J2*ones(1,52)];

vJ(53)=2*J1*J2/(J1+J2);

vJ(73)=0;

vJ(33)=0;

//Wektor podłoża sprężystego:

vk=zeros(1,105);

vk(53)=0.5*k2;

vk(54:102)=k2;

vk(103)=0.5*k2;

//Wektor pomocniczy dla uwzględnienia więzów jednostronnych:

vp=ones(1,105);

//Macierz główna układu równań MRS, bez uwzględnienia wpływu podłoża:

G=diag([vJ(2:$-3) 0 0], -2);

G=G+diag([0 -2*(vJ(2:$-3)+vJ(3:$-2)) 0 0], -1);

G=G+diag([0 0 (vJ(2:$-3)+4*vJ(3:$-2)+vJ(4:$-1)) 0 0]);

G=G+diag([0 0 -2*(vJ(3:$-2)+vJ(4:$-1)) 0 ], 1);

G=G+diag([0 0 vJ(4:$-1)], 2);

//Wektor obciążeń:

vo=zeros(1,105);

vo(33)=2.5;

vo(33:103)=5-linspace(0,5,71);

vo(73)=vo(73)+250;

vo=vo*lambda^4/E;

//Warunki brzegowe:

G(1,:)=0; G(1,3)=1; vk(1)=0; vo(1)=0;//w[3]==0

G(2,2)=-1; G(2,4)=1;//fi[3]==0

G(104,101)=1; G(104,102)=-2; G(104,104)=2; G(104,105)=-1; vo(104)=2*25*lambda^3/(E*J2);//T[123]==10

G(105,102)=1; G(105,103)=-2; G(105,104)=1;//M[103]==0

//Rozwiązanie (obliczenie wartości w_i w poszczególnych punktach modelu dyskretnego)

//z uwzględnieniem więzów dwustronnych:

w=(G+diag(vk)*lambda^4/E)\vo';

//Sprawdzenie mozliwości wystapienia więzów jednostronnych:

wj=(w(3:$-2)'.*vk(3:$-2).*vp(3:$-2))>=0;

twj=and(wj);

//Uwzględnienie więzów jednostronnych:

while ~twj

vp(3:$-2)=vp(3:$-2).*wj.*wj;

w2=(G+diag(vk.*vp)*lambda^4/E)\vo';

wj=(w2(3:$-2)'.*vk(3:$-2).*vp(3:$-2))>=0;

twj=and(wj);

else

w2=w;

end

//Kąty obrotu:

fi=1/(2*lambda)*(w2(4:($-1))-w2(2:($-3)));

//Momenty:

M=-E*vJ(3:($-2))'/(lambda^2).*(w2(2:($-3))-2*w2(3:($-2))+w2(4:($-1)));

//Tnące:

T=-E/(2*lambda^3)*(-vJ(2:102)'.*(w2(1:($-4))-2*w2(2:($-3))+w2(3:($-2)))+..

vJ(4:($-1))'.*(w2(3:($-2))-2*w2(4:($-1))+w2(5:$)));

//Odpór gruntu:

R=vk'.*vp'.*w2;

//Usunięcie wszystkich otwartych okien graficznych:

xdel(winsid());

//Wykres ugięć:

xinit();

plot2d((0:100)*lambda, w2(3:103), [1], rect=[0, 1.1*min(w2), 100*lambda, 1.1*max(w2)]);

plot2d((0:100)*lambda, zeros(1,101), [1]);

xname("Ugięcia");

xtitle('Ugięcia', 'x[m]', 'w[m]');

wy1=gcf();

wy1.children.axes_reverse = ["off","on","off"];

wy1.children.children.children(2).thickness=3;

//Wykres kątów obrotu:

xinit();

plot2d((0:100)*lambda, fi, [1], rect=[0, 1.1*min(fi), 100*lambda, 1.1*max(fi)]);

plot2d((0:100)*lambda, zeros(1,101), [1]);

xname("Kąty obrotu");

xtitle('Kąty obrotu', 'x[m]', 'fi[rad]');

wy2=gcf();

wy2.children.axes_reverse = ["off","on","off"];

wy2.children.children.children(2).thickness=3;

//Wykres momentów:

xinit();

plot2d((0:100)*lambda, M, [1], rect=[0, 1.1*min(M), 100*lambda, 1.1*max(M)]);

plot2d((0:100)*lambda, zeros(1,101), [1]);

xname("Momenty");

xtitle('Momenty', 'x[m]', 'M[kNm]');

wy3=gcf();

wy3.children.axes_reverse = ["off","on","off"];

wy3.children.children.children(2).thickness=3;

//Wykres tnących:

xinit();

plot2d((0:100)*lambda, T, [1], rect=[0, 1.1*min(T), 100*lambda, 1.1*max(T)]);

plot2d((0:100)*lambda, zeros(1,101), [1]);

xname("Tnące");

xtitle('Tnące', 'x[m]', 'T[kN]');

wy4=gcf();

wy4.children.axes_reverse = ["off","on","off"];

wy4.children.children.children(2).thickness=3;

//Wykres odporu gruntu:

xinit();

plot2d((0:100)*lambda, R(3:103), [1], rect=[0, 1.1*min(R), 100*lambda, 1.1*max(R)]);

plot2d((0:100)*lambda, zeros(1,101), [1]);

xname("Odpór gruntu");

xtitle('Odpór gruntu', 'x[m]', 'r[kN/m]');

wy5=gcf();

wy5.children.axes_reverse = ["off","on","off"];

wy5.children.children.children(2).thickness=3;

//Zapisanie wyników do plików:

savematfile('C:/ugiecia.txt', 'w2', '-ascii');

savematfile('C:/kąt_obrotu.txt', 'fi', '-ascii');

savematfile('C:/momenty.txt', 'M', '-ascii');

savematfile('C:/tnące.txt', 'T', '-ascii');

savematfile('C:/odpór_gruntu.txt', 'R', '-ascii');

savematfile('C:/G1.txt', 'G(:,1:50)', '-ascii');

savematfile('C:/G2.txt', 'G(:,51:105)', '-ascii');

savematfile('C:/vo.txt', 'vo(1,:)', '-ascii');

[m]	UGIĘCIA	KĄT OROTU	MOMENTY	TNĄCE	ODPÓR GRUNTU
	4.4860301E-07				0.0000000E+00
	1.1031222E-07				0.0000000E+00
0	0.0000000E+00	0.0000000E+00	-1.3789027E+01	4.5963423E+00	0.0000000E+00
	1.1031222E-07	2.1694736E-06	-1.3329393E+01	4.5963423E+00	0.0000000E+00
	4.3389472E-07	4.2654057E-06	-1.2869759E+01	4.5963423E+00	0.0000000E+00
	9.6339336E-07	6.2877963E-06	-1.2410124E+01	4.5963423E+00	0.0000000E+00
	1.6914540E-06	8.2366455E-06	-1.1950490E+01	4.5963423E+00	0.0000000E+00
	2.6107225E-06	1.0111953E-05	-1.1490856E+01	4.5963423E+00	0.0000000E+00
	3.7138446E-06	1.1913719E-05	-1.1031222E+01	4.5963423E+00	0.0000000E+00
	4.9934663E-06	1.3641944E-05	-1.0571587E+01	4.5963423E+00	0.0000000E+00
	6.4422334E-06	1.5296627E-05	-1.0111953E+01	4.5963423E+00	0.0000000E+00
	8.0527918E-06	1.6877769E-05	-9.6523189E+00	4.5963423E+00	0.0000000E+00
	9.8177872E-06	1.8385369E-05	-9.1926847E+00	4.5963423E+00	0.0000000E+00
	1.1729866E-05	1.9819428E-05	-8.7330505E+00	4.5963423E+00	0.0000000E+00
	1.3781673E-05	2.1179946E-05	-8.2734162E+00	4.5963423E+00	0.0000000E+00
	1.5965855E-05	2.2466921E-05	-7.8137820E+00	4.5963423E+00	0.0000000E+00
	1.8275057E-05	2.3680356E-05	-7.3541478E+00	4.5963423E+00	0.0000000E+00
	2.0701926E-05	2.4820249E-05	-6.8945135E+00	4.5963423E+00	0.0000000E+00
	2.3239107E-05	2.5886600E-05	-6.4348793E+00	4.5963423E+00	0.0000000E+00
	2.5879246E-05	2.6879410E-05	-5.9752450E+00	4.5963423E+00	0.0000000E+00
	2.8614989E-05	2.7798678E-05	-5.5156108E+00	4.5963423E+00	0.0000000E+00
	3.1438982E-05	2.8644405E-05	-5.0559766E+00	4.5963423E+00	0.0000000E+00
	3.4343870E-05	2.9416591E-05	-4.5963423E+00	4.5963423E+00	0.0000000E+00
	3.7322300E-05	3.0115235E-05	-4.1367081E+00	4.5963423E+00	0.0000000E+00
	4.0366917E-05	3.0740338E-05	-3.6770739E+00	4.5963423E+00	0.0000000E+00
	4.3470367E-05	3.1291899E-05	-3.2174396E+00	4.5963423E+00	0.0000000E+00
	4.6625297E-05	3.1769918E-05	-2.7578054E+00	4.5963423E+00	0.0000000E+00
	4.9824351E-05	3.2174396E-05	-2.2981712E+00	4.5963423E+00	0.0000000E+00
	5.3060176E-05	3.2505333E-05	-1.8385369E+00	4.5963423E+00	0.0000000E+00
	5.6325418E-05	3.2762728E-05	-1.3789027E+00	4.5963423E+00	0.0000000E+00
	5.9612722E-05	3.2946582E-05	-9.1926847E-01	4.5963423E+00	0.0000000E+00
	6.2914734E-05	3.3056894E-05	-4.5963423E-01	4.5963423E+00	0.0000000E+00
3	6.6224100E-05	5.5350481E-05	0.0000000E+00	4.3463423E+00	0.0000000E+00
	7.3984830E-05	7.7574526E-05	4.0963423E-01	3.8499138E+00	0.0000000E+00
	8.1739006E-05	7.7480157E-05	7.6998275E-01	3.3606281E+00	0.0000000E+00
	8.9480862E-05	7.7332018E-05	1.0817598E+00	2.8784852E+00	0.0000000E+00
	9.7205409E-05	7.7137823E-05	1.3456798E+00	2.4034852E+00	0.0000000E+00
	1.0490843E-04	7.6905172E-05	1.5624569E+00	1.9356281E+00	0.0000000E+00
	1.1258644E-04	7.6641551E-05	1.7328054E+00	1.4749138E+00	0.0000000E+00
	1.2023674E-04	7.6354331E-05	1.8574396E+00	1.0213423E+00	0.0000000E+00
	1.2785731E-04	7.6050770E-05	1.9370739E+00	5.7491377E-01	0.0000000E+00
	1.3544689E-04	7.5738010E-05	1.9724224E+00	1.3562806E-01	0.0000000E+00
	1.4300491E-04	7.5423080E-05	1.9641995E+00	-2.9651480E-01	0.0000000E+00
	1.5053151E-04	7.5112895E-05	1.9131194E+00	-7.2151480E-01	0.0000000E+00
	1.5802749E-04	7.4814254E-05	1.8198965E+00	-1.1393719E+00	0.0000000E+00
	1.6549436E-04	7.4533842E-05	1.6852450E+00	-1.5500862E+00	0.0000000E+00
	1.7293426E-04	7.4278232E-05	1.5098793E+00	-1.9536577E+00	0.0000000E+00
	1.8035000E-04	7.4053881E-05	1.2945135E+00	-2.3500862E+00	0.0000000E+00
	1.8774504E-04	7.3867131E-05	1.0398620E+00	-2.7393719E+00	0.0000000E+00
	1.9512343E-04	7.3724211E-05	7.4663913E-01	-3.1215148E+00	0.0000000E+00
	2.0248988E-04	7.3631235E-05	4.1555908E-01	-3.4965148E+00	0.0000000E+00
	2.0984968E-04	7.3594203E-05	4.7336168E-02	-3.8643719E+00	0.0000000E+00
5	2.1720872E-04	7.3633294E-05	-3.5731531E-01	-4.0730401E+00	3.0409221E+00
	2.2457634E-04	7.3798936E-05	-7.6727186E-01	-3.9601586E+00	6.2881374E+00
	2.3196851E-04	7.4105595E-05	-1.1493470E+00	-3.6674244E+00	6.4951182E+00
	2.3939745E-04	7.4529611E-05	-1.5007567E+00	-3.3467977E+00	6.7031287E+00
	2.4687443E-04	7.5060725E-05	-1.8187066E+00	-2.9981600E+00	6.9124840E+00
	2.5440960E-04	7.5687781E-05	-2.1003887E+00	-2.6213623E+00	7.1234688E+00
	2.6201198E-04	7.6398719E-05	-2.3429790E+00	-2.2162293E+00	7.3363355E+00
	2.6968934E-04	7.7180578E-05	-2.5436346E+00	-1.7825617E+00	7.5513016E+00
	2.7744810E-04	7.8019478E-05	-2.6994914E+00	-1.3201407E+00	7.7685468E+00
	2.8529324E-04	7.8900622E-05	-2.8076627E+00	-8.2873139E-01	7.9882107E+00
	2.9322822E-04	7.9808287E-05	-2.8652377E+00	-3.0808705E-01	8.2103903E+00
	3.0125490E-04	8.0725809E-05	-2.8692801E+00	2.4204646E-01	8.4351371E+00
	3.0937339E-04	8.1635587E-05	-2.8168284E+00	8.2192605E-01	8.6624548E+00
	3.1758201E-04	8.2519062E-05	-2.7048949E+00	1.4318065E+00	8.8922964E+00
	3.2587720E-04	8.3356720E-05	-2.5304671E+00	2.0719351E+00	9.1245616E+00
	3.3425336E-04	8.4128076E-05	-2.2905079E+00	2.7425464E+00	9.3590940E+00
	3.4270281E-04	8.4811671E-05	-1.9819578E+00	3.4438565E+00	9.5956788E+00
	3.5121569E-04	8.5385062E-05	-1.6017366E+00	4.1760567E+00	9.8340394E+00
	3.5977983E-04	8.5824819E-05	-1.1467464E+00	4.9393076E+00	1.0073835E+01
	3.6838066E-04	8.6106519E-05	-6.1387509E-01	5.7337322E+00	1.0314658E+01
7	3.7700113E-04	9.0051581E-05	0.0000000E+00	-5.9405904E+00	1.0556032E+01
	3.8639097E-04	9.4186743E-05	-1.8019932E+00	-1.7582556E+01	1.0818947E+01
	3.9583848E-04	9.5037704E-05	-3.5165112E+00	-1.6691006E+01	1.1083477E+01
	4.0539851E-04	9.6422776E-05	-5.1401944E+00	-1.5765703E+01	1.1351158E+01
	4.1512303E-04	9.8312352E-05	-6.6696517E+00	-1.4806258E+01	1.1623445E+01
	4.2506098E-04	1.0067573E-04	-8.1014460E+00	-1.3812144E+01	1.1901708E+01
	4.3525818E-04	1.0348109E-04	-9.4320804E+00	-1.2782697E+01	1.2187229E+01
	4.4575720E-04	1.0669550E-04	-1.0657985E+01	-1.1717132E+01	1.2481202E+01
	4.5659728E-04	1.1028486E-04	-1.1775507E+01	-1.0614550E+01	1.2784724E+01
	4.6781417E-04	1.1421389E-04	-1.2780895E+01	-9.4739457E+00	1.3098797E+01
	4.7944006E-04	1.1844608E-04	-1.3670296E+01	-8.2942184E+00	1.3424322E+01
	4.9150339E-04	1.2294368E-04	-1.4439739E+01	-7.0741832E+00	1.3762095E+01
	5.0402879E-04	1.2766766E-04	-1.5085133E+01	-5.8125810E+00	1.4112806E+01
	5.1703692E-04	1.3257764E-04	-1.5602255E+01	-4.5080890E+00	1.4477034E+01
	5.3054432E-04	1.3763188E-04	-1.5986750E+01	-3.1593325E+00	1.4855241E+01
	5.4456330E-04	1.4278722E-04	-1.6234122E+01	-1.7648961E+00	1.5247772E+01
	5.5910177E-04	1.4799904E-04	-1.6339730E+01	-3.2333641E-01	1.5654849E+01
	5.7416311E-04	1.5322120E-04	-1.6298789E+01	1.1668058E+00	1.6076567E+01
	5.8974601E-04	1.5840603E-04	-1.6106369E+01	2.7069929E+00	1.6512888E+01
	6.0584431E-04	1.6350423E-04	-1.5757390E+01	4.2986765E+00	1.6963641E+01
	6.2244685E-04	1.6846487E-04	-1.5246633E+01	5.9432841E+00	1.7428512E+01
	6.3953729E-04	1.7323533E-04	-1.4568734E+01	7.6422048E+00	1.7907044E+01
	6.5709392E-04	1.7776124E-04	-1.3718192E+01	9.3967742E+00	1.8398630E+01
	6.7508953E-04	1.8198645E-04	-1.2689379E+01	1.1208260E+01	1.8902507E+01
	6.9349121E-04	1.8585300E-04	-1.1476540E+01	1.3077844E+01	1.9417754E+01
	7.1226013E-04	1.8930105E-04	-1.0073810E+01	1.5006610E+01	1.9943284E+01
	7.3135142E-04	1.9226890E-04	-8.4752183E+00	1.6995524E+01	2.0477840E+01
	7.5071391E-04	1.9469289E-04	-6.6747053E+00	1.9045415E+01	2.1019990E+01
	7.7029000E-04	1.9650742E-04	-4.6661353E+00	2.1156963E+01	2.1568120E+01
	7.9001540E-04	1.9764493E-04	-2.4433127E+00	2.3330677E+01	2.2120431E+01
10	8.0981898E-04	1.9803586E-04	0.0000000E+00	2.5000000E+01	1.1337466E+01
	8.2962257E-04				0.0000000E+00
	8.4934434E-04				0.0000000E+00

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