I must solve ode equation system but dsolve gives me error

%Geometric and Inertial Parameters
E = 70000; %Young's Modulus [MPa]
h = 6; %Section Height [mm]
b = 25; %Section Width [mm]
A = b*h; %Section Area [mm^2]
I = [(b*h^3)/12] ; %Inertial Momentum [mm^4]
L = 200; %Beam Lenght [mm]
ni = 0.33; %Poisson's Ratio
G = E/(2*(1 + ni)); %Shear Modulus [MPa]
k = 0.5; %Shear Factor
A_t = k*A; %Shear Section Area [mm^2]
q = 0; %Distributed Load along the beam [N/mm]
c = 0; %Distributed Bending Moment along the beam [N]
P = -50; %Concentrated Load at the free wedge of the beam [N]
%Equations' Definition
syms v(s) psi(s)
T = G*A_t*[diff(v,s) + psi(s)];
M = E*I*diff(psi,s);
ode1 = diff(T,s) == q;
ode2 = diff(M,s) + c == T;
ode = [ode1; ode2]

ode(s) = 

%Boundary Condition Definition
c1 = v(0) == 0;
c2 = psi(0) == 0;
c3 = psi(L) == (P/(G*A_t))-diff(v,s);
psi1 = diff(psi,s);
c4 = psi1(L) == 0;
cond = [c1; c2; c3; c4]

cond(s) = 

[v_sol,psi_sol] = dsolve(ode,cond);

Warning: Number of equations greater than number of indeterminates. Trying heuristics to reduce to square system.

Error using mupadengine/evalin2sym
Unable to reduce to square system because the number of equations differs from the number of indeterminates.

Error in mupadengine/feval2sym_NaNsingularity

Error in dsolve>mupadDsolve (line 334)
T = feval2sym_NaNsingularity(symengine,'symobj::dsolve',sys,x,options);

Error in dsolve (line 203)
sol = mupadDsolve(args, options);

There is the message and the error it gives me:

Warning: symbolic:ode:MoreEquationsThanUnknowns∦Number of equations greater than number of indeterminates. Trying

heuristics to reduce to square system.∦

> In mupadengine/evalin2sym

In mupadengine/feval2sym_NaNsingularity

In dsolve>mupadDsolve (line 334)

In dsolve (line 203)

In Timoshenko_Beam_Model (line 40)

Error using mupadengine/evalin2sym

Unable to reduce to square system because the number of equations differs from the number of indeterminates.

Error in mupadengine/feval2sym_NaNsingularity

Error in dsolve>mupadDsolve (line 334)

T = feval2sym_NaNsingularity(symengine,'symobj::dsolve',sys,x,options);

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Error in dsolve (line 203)

sol = mupadDsolve(args, options);

^^^^^^^^^^^^^^^^^^^^^^^^^^

Error in Timoshenko_Beam_Model (line 40)

[v_sol,psi_sol] = dsolve(ode,cond);

^^^^^^^^^^^^^^^^

Answer 1

[Torsten]

The third boundary condition is wrong as stated. You must use dv/ds at some position s (e.g. 200).

%Geometric and Inertial Parameters
E = 70000; %Young's Modulus [MPa]
h = 6; %Section Height [mm]
b = 25; %Section Width [mm]
A = b*h; %Section Area [mm^2]
I = [(b*h^3)/12] ; %Inertial Momentum [mm^4]
L = 200; %Beam Lenght [mm]
ni = 0.33; %Poisson's Ratio
G = E/(2*(1 + ni)); %Shear Modulus [MPa]
k = 0.5; %Shear Factor
A_t = k*A; %Shear Section Area [mm^2]
q = 0; %Distributed Load along the beam [N/mm]
c = 0; %Distributed Bending Moment along the beam [N]
P = -50; %Concentrated Load at the free wedge of the beam [N]
%Equations' Definition
syms v(s) psi(s)
T = G*A_t*[diff(v,s) + psi(s)];
M = E*I*diff(psi,s);
ode1 = diff(T,s) == q;
ode2 = diff(M,s) + c == T;
ode = [ode1; ode2];
%Boundary Condition Definition
c1 = v(0) == 0;
c2 = psi(0) == 0;
dv = diff(v,s);
c3 = psi(L) == (P/(G*A_t))-dv(L);
psi1 = diff(psi,s);
c4 = psi1(L) == 0;
cond = [c1; c2; c3; c4];
[v_sol,psi_sol] = dsolve(ode,cond);
figure(1)
fplot(v_sol,[0 L])

●

figure(2)
fplot(psi_sol,[0 L])

[EDOARDO GELMI]

Thank you so much, i did the right thing for psi but i didn't modify the variable diff(v,s). Now it works fine, you saved me.