Alex99dB

10 Reputation

One Badge

0 years, 188 days

MaplePrimes Activity


These are questions asked by Alex99dB

Hey everyone ! 

I want to get the analytical function from a piecewise differential equation defined on 6 intervals but Maple returns me a numerical result... I think it hides a Runge Kutta method.. However, it returned me an analytical function for a similar piecewise differential equation defined on 3 intervals.

Do you know how I could get the analytical function defined on the 6 intervals ?

Thank you very much for your time ! 

Alex

eq := diff(Uy(x), x, x)-piecewise(x < d1, 12*F*x/(E*b*h^3), d1 < x and x < d2, 12*((F+F1)*x-F1*d1)/(E*b*h^3), d2 < x and x < d3, 12*((F+F1+F2)*x-F1*d1-F2*d2)/(E*b*h^3), d3 < x and x < d4, 12*((F5+F4-F)*x+F*L-F5*d5-F4*d4)/(E*b*h^3), d4 < x and x < d5, 12*((F5-F)*x+F*L-F5*d5)/(E*b*h^3), 12*F*(L-x)/(E*b*h^3))

diff(diff(Uy(x), x), x)-piecewise(x < d1, 12*F*x/(E*b*h^3), d1 < x and x < d2, 12*((F+F1)*x-F1*d1)/(E*b*h^3), d2 < x and x < d3, 12*((F+F1+F2)*x-F1*d1-F2*d2)/(E*b*h^3), d3 < x and x < d4, 12*((F5+F4-F)*x+F*L-F5*d5-F4*d4)/(E*b*h^3), d4 < x and x < d5, 12*((F5-F)*x+F*L-F5*d5)/(E*b*h^3), 12*F*(L-x)/(E*b*h^3))

(1)

dsolve({eq, Uy(0) = 0, Uy(L) = 0}, Uy(x))

assign(dsolve({eq, Uy(0) = 0, Uy(L) = 0}, Uy(x)))

Uy_sol := unapply(Uy(x), x)

proc (x) options operator, arrow; Uy(x) end proc

(2)

E := 210*10^9; L := 4; d1 := (1/6)*L; d2 := 2*L*(1/6); d3 := 3*L*(1/6); d4 := 4*L*(1/6); d5 := 5*L*(1/6); b := 0.1e-1; h := 0.5e-2

210000000000

 

4

 

2/3

 

4/3

 

2

 

8/3

 

10/3

 

0.1e-1

 

0.5e-2

(3)

eq

diff(diff(Uy(x), x), x)-piecewise(x < 2/3, 0.4571428572e-1*F*x, 2/3 < x and x < 4/3, 0.4571428572e-1*(F+F1)*x-0.3047619048e-1*F1, 4/3 < x and x < 2, 0.4571428572e-1*(F+F1+F2)*x-0.3047619048e-1*F1-0.6095238096e-1*F2, 2 < x and x < 8/3, 0.4571428572e-1*(F5+F4-F)*x+.1828571429*F-.1523809524*F5-.1219047619*F4, 8/3 < x and x < 10/3, 0.4571428572e-1*(F5-F)*x+.1828571429*F-.1523809524*F5, 0.4571428572e-1*F*(4-x))

(4)

dsolve({eq, Uy(0) = 0, Uy(L) = 0}, Uy(x))

Uy(x) = -(1/4)*(Int(Int(piecewise(_z1 < 2/3, (1142857143/25000000000)*F*_z1, _z1 < 4/3, (1142857143/25000000000)*F*_z1-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1, _z1 < 2, (1142857143/25000000000)*F*_z1-(380952381/6250000000)*F2-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1+(1142857143/25000000000)*_z1*F2, _z1 < 8/3, -(1142857143/25000000000)*F*_z1-(1219047619/10000000000)*F4-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*F4*_z1+(1142857143/25000000000)*_z1*F5, _z1 < 10/3, -(1142857143/25000000000)*F*_z1-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*_z1*F5, 10/3 <= _z1, -(1142857143/25000000000)*F*_z1+(1142857143/6250000000)*F), _z1 = 0 .. _z1), _z1 = 0 .. 4))*x+Int(Int(piecewise(_z1 < 2/3, (1142857143/25000000000)*F*_z1, _z1 < 4/3, (1142857143/25000000000)*F*_z1-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1, _z1 < 2, (1142857143/25000000000)*F*_z1-(380952381/6250000000)*F2-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1+(1142857143/25000000000)*_z1*F2, _z1 < 8/3, -(1142857143/25000000000)*F*_z1-(1219047619/10000000000)*F4-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*F4*_z1+(1142857143/25000000000)*_z1*F5, _z1 < 10/3, -(1142857143/25000000000)*F*_z1-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*_z1*F5, 10/3 <= _z1, -(1142857143/25000000000)*F*_z1+(1142857143/6250000000)*F), _z1 = 0 .. _z1), _z1 = 0 .. x)

(5)

Uy(x)[0]

Uy(x)[0]

(6)

assign(dsolve({eq, Uy(0) = 0, Uy(L) = 0}, Uy(x)))

Uy(x)[0]

(-(1/4)*(Int(Int(piecewise(_z1 < 2/3, (1142857143/25000000000)*F*_z1, _z1 < 4/3, (1142857143/25000000000)*F*_z1-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1, _z1 < 2, (1142857143/25000000000)*F*_z1-(380952381/6250000000)*F2-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1+(1142857143/25000000000)*_z1*F2, _z1 < 8/3, -(1142857143/25000000000)*F*_z1-(1219047619/10000000000)*F4-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*F4*_z1+(1142857143/25000000000)*_z1*F5, _z1 < 10/3, -(1142857143/25000000000)*F*_z1-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*_z1*F5, 10/3 <= _z1, -(1142857143/25000000000)*F*_z1+(1142857143/6250000000)*F), _z1 = 0 .. _z1), _z1 = 0 .. 4))*x+Int(Int(piecewise(_z1 < 2/3, (1142857143/25000000000)*F*_z1, _z1 < 4/3, (1142857143/25000000000)*F*_z1-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1, _z1 < 2, (1142857143/25000000000)*F*_z1-(380952381/6250000000)*F2-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1+(1142857143/25000000000)*_z1*F2, _z1 < 8/3, -(1142857143/25000000000)*F*_z1-(1219047619/10000000000)*F4-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*F4*_z1+(1142857143/25000000000)*_z1*F5, _z1 < 10/3, -(1142857143/25000000000)*F*_z1-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*_z1*F5, 10/3 <= _z1, -(1142857143/25000000000)*F*_z1+(1142857143/6250000000)*F), _z1 = 0 .. _z1), _z1 = 0 .. x))[0]

(7)

Uy(x < d1)

Uy(x < 2/3)

(8)

Uy(x)[x < d1]

(-(1/4)*(Int(Int(piecewise(_z1 < 2/3, (1142857143/25000000000)*F*_z1, _z1 < 4/3, (1142857143/25000000000)*F*_z1-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1, _z1 < 2, (1142857143/25000000000)*F*_z1-(380952381/6250000000)*F2-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1+(1142857143/25000000000)*_z1*F2, _z1 < 8/3, -(1142857143/25000000000)*F*_z1-(1219047619/10000000000)*F4-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*F4*_z1+(1142857143/25000000000)*_z1*F5, _z1 < 10/3, -(1142857143/25000000000)*F*_z1-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*_z1*F5, 10/3 <= _z1, -(1142857143/25000000000)*F*_z1+(1142857143/6250000000)*F), _z1 = 0 .. _z1), _z1 = 0 .. 4))*x+Int(Int(piecewise(_z1 < 2/3, (1142857143/25000000000)*F*_z1, _z1 < 4/3, (1142857143/25000000000)*F*_z1-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1, _z1 < 2, (1142857143/25000000000)*F*_z1-(380952381/6250000000)*F2-(380952381/12500000000)*F1+(1142857143/25000000000)*F1*_z1+(1142857143/25000000000)*_z1*F2, _z1 < 8/3, -(1142857143/25000000000)*F*_z1-(1219047619/10000000000)*F4-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*F4*_z1+(1142857143/25000000000)*_z1*F5, _z1 < 10/3, -(1142857143/25000000000)*F*_z1-(380952381/2500000000)*F5+(1828571429/10000000000)*F+(1142857143/25000000000)*_z1*F5, 10/3 <= _z1, -(1142857143/25000000000)*F*_z1+(1142857143/6250000000)*F), _z1 = 0 .. _z1), _z1 = 0 .. x))[x < 2/3]

(9)

NULL

Download cas_5v_F_inconnues.mw

Page 1 of 1