Non conservative loading
Article Stability analysis of a timoshenko beam subjected to distrib...
Generally, for a nonlinear problem, you must divide the problem to some increments. Each increment then is a linear problem (after linearization) with constant load. Thus, you can solve the linear problem with any iterative method. The result of an increment is a initial condition for the next increment.
Hello Fernando André Enciso,
As I see it there are two topics to discuss:
1. Solving non-linear problems using Newton-Raphson method.
2. Solving time-dependent problems.
You asked about equilibrium and time varying forces, which are two different things:
* If you want to solve an equilibrium problem then it is not time-dependent and Newton-Raphson's method is sufficient. If the load is "large" then you can use different approaches, i.e. incremental loading where you solve for lower values of the final load (i.e. 0.1F 0.3F 0.7F F) thus "helping" Newton-Raphson's method to approach the solution.
* If you want to solve a non-linear time dependent (dynamic) problem then you need to solve each time step using a scheme (i.e. Forward Euler, Backward Euler etc.) and at each time step you need to solve the equations using Newton-Raphson method, as explained above.
I hope this helps,
Doron
Hello,
if you are solving for the equilbrium in preparation for expand the response around it to obtain an approximate dynamic response around the equilbrium, then you keep only the DC/ time-invariant/ constant part of the load in the residual force vector and solve for the equilbrium. The time-varying part of the load will then show up when you solve for the dynamic response.
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