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Resolucion de la ecuacion de placas planas de germain-lagrange

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RESOLUCION DE LA ECUACION DE PLACAS DE GERMAIN-LAGRANGE

Definimos la ecuacion diferencial de placas

 > EDO:=Diff(y(x),x\$4)+k=0;

Soluci?n general

 > dsolve (EDO,y(x));

Soluciones particulares seg?n las diferentes condiciones de borde

Condiciones de borde para apoyado-apoyado

 > AA:=y(0)=0,y(a)=0,D(D(y))(0)=0,D(D(y))(a)=0;

Solucion particular con tales condiciones

 > dsolve({EDO,AA},y(x));

Condiciones de borde para empotrado-libre

 > EL:=y(0)=0,D(y)(0)=0,D(D(y))(a)=0,D(D(D(y)))(a)=0;

Soluci?n particular con tales condiciones

 > dsolve({EDO,EL},y(x));

Condiciones de borde para empotrado-empotrado

 > EE:=y(0)=0,D(y)(0)=0,y(a)=0,D(y)(a)=0;

Solcion particular con tales condiciones

 > dsolve({EDO,EE},y(x));

Representaci?n gr?fica de los diferentes casos. Suponemos k = 0.001 y a = 4

Caso apoyado-apoyado

 > plot((-0.001/24)*(x^4)+(0.001*4/12)*(x^3)-(0.001*4^3)*x/24,x=0..4);

Caso empotrado-libre

 > plot((-0.001/24)*(x^4)+(0.001*4/6)*(x^3)-(0.001*4^2)*(x^2)/4,x=0..4);

Caso empotrado-empotrado

 > plot((-0.001/24)*(x^4)+(0.001*4/12)*(x^3)-(0.001*4^2)*(x^2)/24,x=0..4);

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