Advanced Search

Question: how i can pdsolve this nonlinear equations

Question:how i can pdsolve this nonlinear equations

torabi 85 Maple 18
nonlinear pdsolve
July 28 2016
0

hi...please help me for solve this nonlinear equations with pdsolve

thanksoffcenter2.mw

La := .25; Lb := 0.1e-1

h := 0.4e-2

rho := 7900

E := 0.200e12

nu := .3

ve := 5

g := 9.8

M := .5

Z0 := 0.1e-2

K := 5/6

C := sqrt(E/rho)

NULL

 

PDE[1] := diff(u(x, t), x, x)+(diff(w(x, t), x))*(diff(w(x, t), x, x)) = (diff(u(x, t), t, t))/C^2

diff(diff(u(x, t), x), x)+(diff(w(x, t), x))*(diff(diff(w(x, t), x), x)) = 0.3949999999e-7*(diff(diff(u(x, t), t), t))

 (1)

PDE[2] := K*(diff(phi(x, t), x)+diff(w(x, t), x, x))/(2*(1+nu))+(diff(w(x, t), x))*(diff(u(x, t), x, x))+(diff(u(x, t), x))*(diff(w(x, t), x, x))+(3/2)*(diff(w(x, t), x, x))*(diff(w(x, t), x))^2 = (diff(w(x, t), t, t))/C^2

.3205128205*(diff(phi(x, t), x))+.3205128205*(diff(diff(w(x, t), x), x))+(diff(w(x, t), x))*(diff(diff(u(x, t), x), x))+(diff(u(x, t), x))*(diff(diff(w(x, t), x), x))+(3/2)*(diff(diff(w(x, t), x), x))*(diff(w(x, t), x))^2 = 0.3949999999e-7*(diff(diff(w(x, t), t), t))

 (2)

 

PDE[3] := diff(phi(x, t), x, x)-6*K*(diff(w(x, t), x)+phi(x, t))/(h^2*(1+nu)) = (diff(phi(x, t), t, t))/C^2

diff(diff(phi(x, t), x), x)-240384.6154*(diff(w(x, t), x))-240384.6154*phi(x, t) = 0.3949999999e-7*(diff(diff(phi(x, t), t), t))

 (3)

 

 

#####################################

 (4)

at x= La

PDE[a1] := diff(u(x, t), x)+(1/2)*(diff(w(x, t), x))^2-M*(g-(diff(u(x, t), t, t))-Z0*(diff(phi(x, t), t, t)))/(E*Lb*h) = 0

diff(u(x, t), x)+(1/2)*(diff(w(x, t), x))^2-0.6125000000e-6+0.6250000000e-7*(diff(diff(u(x, t), t), t))+0.6250000000e-10*(diff(diff(phi(x, t), t), t)) = 0

 (5)

PDE[a2] := diff(phi(x, t), x)-12*M*Z0*(g-(diff(u(x, t), t, t))-Z0*(diff(phi(x, t), t, t)))/(E*Lb*h^3) = 0

diff(phi(x, t), x)-0.4593750000e-3+0.4687500000e-4*(diff(diff(u(x, t), t), t))+0.4687500000e-7*(diff(diff(phi(x, t), t), t)) = 0

 (6)

PDE[a3] := w(x, t) = 0

w(x, t) = 0

 (7)

NULL

############################################

``

at x=0 NULL

 (8)

PDE[b1] := u(x, t) = 0 

PDE[b2] := w(x, t) = 0

PDE[b3] := diff(phi(x, t), x) = 0

diff(phi(x, t), x) = 0

 (9)

################################################

at t=0 for x= [0,La]

u(x, t) = 0

u(x, t) = 0

 (10)

w(x, t) = 0

w(x, t) = 0

 (11)

phi(x, t) = 0

phi(x, t) = 0

 (12)

diff(phi(x, t), t) = 0

diff(phi(x, t), t) = 0

 (13)

diff(w(x, t), t) = 0

diff(w(x, t), t) = 0

 (14)

diff(phi(x, t), t, t) = 0

diff(diff(phi(x, t), t), t) = 0

 (15)

diff(w(x, t), t, t) = 0

diff(diff(w(x, t), t), t) = 0

 (16)

######################################################

at t=0 for x= [0,La)

diff(u(x, t), t) = 0

diff(u(x, t), t) = 0

 (17)

diff(u(x, t), t, t) = 0

diff(diff(u(x, t), t), t) = 0

 (18)

###################################################

at t=0 for x=La

NULL

diff(u(x, t), t) = -ve

diff(u(x, t), t) = -5

 (19)

diff(u(x, t), t, t) = g

diff(diff(u(x, t), t), t) = 9.8

 (20)

NULL

NULL

 

Download offcenter2.mw
Please Wait...