I am updating a 1 dimensional mechanical FEA algorithm that integrates forward in time. It was written in the 1980's in Fortran and is not documented.
I am looking for: a) any guidance on a published reference on the numerical integration algorithm used. b) comments on the selection of theta - (currently used with theta = 0.67. c) calculation of maximum time step for stability
The algorithm is as follows:
M is the mass matrix. K is the stiffness matrix. C is the damping matrix = alpha*M + beta*K
delta is the timestep
u is the displacements v is the velocity f is the applied forces
a) Calculate the applied forces, f, for the time step.