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Time Integration scheme for non constant M, C and K matrices?

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. 

Time integration scheme for XFEM? (dynamic crack propagation)

Hello everyone,

 

Can somebody suggest an implicit/explicit time integration scheme when the matrices involved(M,C,K) are time dependent? (They change at every time step because of the crack tip enrichment functions which are time dependent).

 

I used the implicit Newmark scheme (trapezoidal/constant average acceleartion method) but just discovered that all my matrices (M,C,K) are time dependent where the original scheme is probably for constant M,C and K matrices. I used the scheme as in reference [1]. 

 

Time Integration Schemes for 2D Dynamic Crack Propagation

1. Is there anyone familiar/working with the time integration schemes for 2D dynamic crack propagation in XFEM? I would like to discuss some of the issues I am facing. I will really appreciate any kind of help/suggestions! 

2. I tried to implement the time integration scheme proposed by Combescure et. al (An energy-conserving scheme for dynamic crack growth using the extended finite element method). But I am not sure about some of the strategies they are following in that paper. Anyone can clarify some of the questions I have?

 

Time integration scheme for Dynamic Crack Propagation in XFEM?

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.

 

Why two different heaviside enrichment functions used in XFEM?

I have been looking at XFEM literature for a while and wondering why do we need 2 different heaviside enrichment functions in XFEM? In paper titled "A finite element method for crack growth without remeshing" by Nicolas Moes et al.(1999), they use the following function for heaviside enrichment:

 H(x,y)={1, for y>0

             -1,for y<0}

 While, in paper titled "A review of extended/generalized finite element methods for material modeling" by Ted Belytschko et al.(2009), they use the following function for heaviside enrichment:

Matlab source code for XFEM implementation (2D dynamic crack propagation problem)

Hello everyone,

 

I was looking for a Matlab source code for implementing XFEM to solve a dynamic problem (specifically dynamic crack propagation problem). I found several source codes which only solve static problems (they don't calculate mass matrix and they don't do the time integration). 

 

My research goal is to remove the oscillations from stress intensity factors  for a dynmic crack propagation problem. I will really appreciate any kind of help/suggestions.

 

With respectfully

Bhuiyan, A B M Abdul Ali

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