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Resolucion de la ecuacion de Beltrami Mitchell

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RESOLUCION DE LA ECUACION DE BELTRAMI - MITCHEL 

PROF, ING, OSCAR BARRETO 

 

 

 

Ecuaciones de Compatibilidad 

 

 

`+`(`*`(`+`(1, mu), `*`(Diff(sigma(x), x, x))), `*`(3, `*`(Diff(sigma(x), x, x)))) = t (1)
 

Soluci?n General 

 

 

sigma(x) = `+`(`/`(`*`(`/`(1, 2), `*`(t, `*`(`^`(x, 2)))), `*`(`+`(4, mu))), `*`(_C1, `*`(x)), _C2) (2)
 

Las condiciones de borde ser?n 

 

 

sigma(0) = 0, sigma(1) = 0 (3)
 

 

Soluci?n Particular para las Condiciones 

 

 

sigma(x) = `+`(`/`(`*`(`/`(1, 2), `*`(t, `*`(`^`(x, 2)))), `*`(`+`(4, mu))), `-`(`/`(`*`(`/`(1, 2), `*`(t, `*`(x))), `*`(`+`(4, mu))))) (4)
 

 

Representaci?n Gr?fica 

Suponemos que los valores de t=1;μ=0.02 

 

 

Plot_2d  
 

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