| 1 |
francois |
941 |
clc;
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| 2 |
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disp('Solution exercice 1 du chapitre elasticite 3D- Toutes les unites sont en SI');
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| 3 |
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E=100e9;
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| 4 |
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nu=0.3;
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| 5 |
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alpha=22e-6;
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| 6 |
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e=0.1e-3;
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| 7 |
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L=200e-3;
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| 8 |
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l=100e-3;
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| 9 |
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h=80e-3;
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| 10 |
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Ti=20;
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| 11 |
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Tf=50;
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| 12 |
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P=420e3;
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| 13 |
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epsxx=0;
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| 14 |
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epszzmax=e/L;
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| 15 |
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sigmay=-P/l/L;
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| 16 |
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syms sigmax sigmaz epszz;
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| 17 |
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disp('Hypothese pas de contact');
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| 18 |
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sigmazhyp1=0;
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| 19 |
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eq1=1/E*(sigmax-nu*(sigmay+sigmazhyp1))+alpha*(Tf-Ti)-epsxx;
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| 20 |
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eq2=1/E*(sigmazhyp1-nu*(sigmax+sigmay))+alpha*(Tf-Ti)-epszz;
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| 21 |
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R=solve(eq1,eq2);
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| 22 |
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if (eval(R.epszz)>epszzmax)
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| 23 |
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disp('hypothese de non contact fausse il y a contact epszz=epszzmax')
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| 24 |
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else
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| 25 |
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disp('hypothese de non contact correct')
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| 26 |
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end
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| 27 |
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eq3=1/E*(sigmax-nu*(sigmay+sigmaz))+alpha*(Tf-Ti)-epsxx;
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| 28 |
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eq4=1/E*(sigmaz-nu*(sigmax+sigmay))+alpha*(Tf-Ti)-epszzmax;
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| 29 |
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R2=solve(eq3,eq4);
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| 30 |
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disp('la valeur de sigmax est');
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| 31 |
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eval(R2.sigmax)
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| 32 |
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disp('la valeur de sigmaz est');
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| 33 |
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eval(R2.sigmaz)
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| 34 |
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disp('la valeur de epsilony est');
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| 35 |
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epsy=1/E*(sigmay-nu*(R2.sigmax+R2.sigmaz))+alpha*(Tf-Ti);
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| 36 |
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eval(epsy)
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| 37 |
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disp('le tenseur des contraintes est directement dans le repere principal (pas de cisaillement)');
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| 38 |
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sigma=[R2.sigmax 0 0; 0 sigmay 0; 0 0 R2.sigmaz];
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| 39 |
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eval(sigma)
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| 40 |
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disp('le cisaillement maximal vaut')
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| 41 |
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[D V]=eig(sigma);
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| 42 |
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taumax=(V(3,3)-V(1,1))/2;
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| 43 |
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eval(taumax)
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| 44 |
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disp('l allongement en y vaut');
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| 45 |
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v=epsy*h;
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| 46 |
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eval(v)
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