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Reference for FEA numerical integration algorithem
Posted:
Jul 9, 2013 5:27 AM


Hi,
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.
b) solve the following matrix equation for u
[C + M/(theta*delta) + theta * delta * K] * u = [C + M/(theta*delta)  (1theta)*delta*K]*u_old + theta*delta*f + (1theta)*delta*f_old + M*v_old/theta
c) Calculate the new velocity
v = (u  u_old)/(theta*delta)  (1theta)/theta*v_old
d) Update the old values
u_old = u v_old = v f_old = f
e) Repeat for the desired simulation time.
Any input is greatly appreciated.
Andrew



