ode15i
From
Kemal Can Struja@21:1/5 to
All on Wed Apr 12 13:37:03 2023
I am texting you regarding the assistance for the "Implicit Differential Equation Solver using ode15i in Matlab".
I have a 3DOF system of the slab with eccentric mass located with a distance of ex and ey.
I have already written the equation of motions and solved the system explicitly with ode45, but due to huge complex formulation and nonlinearity of the system I would like to also solve the system in an implicit form using ode15i and make comparison of
the results.
(mx+mecc)*u'' - mecc*ey*theta'' - F1x - F2x - F3x - F4x - fx = 0
(my+mecc)*v'' + mecc*ex*theta'' - F1y - F2y - F3y - F4y - fy = 0
-mecc*ey*u'' + mecc*ex*v'' + (Io+mecc*(ex^2+ey^2))*theta'' - A = 0
where for i=1,4 Fix and Fiy are the restoring forces, fx and fy are the seismic actions and A is the formulation about moments due to Fix and Fiy forces based on the center of Mass.
I already know that we should write the equation in the implicit form of f(t , y, y' , y'') but as the ODE's work on first order differential equations I have to convert it to the f(t, y, y').
u=y(1) -> u' = y(1)' = y(4) -> u'' = y(1)'' = y(4)'
v=y(2) -> v' = y(2)' = y(5) -> v'' = y(2)'' = y(5)'
theta=y(3) -> theta' = y(3)' = y(6) -> theta'' = y(3)'' = y(6)'
Thus, the output of the system will become as:
y = [ yP(1) - y(4) ; yP(2) - y(5) ; yP(3) - y(6) ;
(mx+mecc)*yP(4) - mecc*ey*yP(6) - F1x - F2x - F3x - F4x - fx ;
(my+mecc)*yP(5) + mecc*ex*yP(6) - F1y - F2y - F3y - F4y - fy ;
-mecc*ey*yP(4) + mecc*ex*yP(5) + (Io+mecc*(ex^2+ey^2))*yP(6) - A ]
Questions:
1. Is this definition of the variables with u=y(1) .. are correct?
2. Do I have any conceptual misunderstanding of the ode15i?
3. I don't understand so well the definition of y and yP for ode15i, while for ode45 it was quite straightforward to define the y'.
--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)