time integration

Can anyone suggest a time integration scheme for non constant mass (M), stiffness(K) and damping (C) matrices? I am trying to solve a dynamic system (Ma+Cv+Ku=R) where the matrices M,C and K are time dependent.

Any thoughts/ideas will be highly aprreciated. Thank you. 

Hello,

I am trying to implement the time integration scheme proposed by Combescure et. al [1] to simulate a dynamic crack propagation problem in XFEM (2D edge crack under impact loading). But I have an interesting question to ask.

Hi ,

 I'm working on simulation of wave propagation in a bar. I'm using
newmark time integration scheme to solve my problem. I have a bae
clamped at one end and under tensile at the other end. when I decrease
my time step ,at the beginning of the loading I see tiny negative
strains which is so weird. I used some numerical damping with the scheme
and I could reduce the time step but still I have this problem in
smaller time steps. Can anyone help me with this?

  Thank you very much!!!