I have made a matlab code for wave propagation the problem is as follows:
div[E grad(u)] = ro (d2u)
E=modulus of elasticity, ro = density, d2u = acceleration.
I applied two time integration schemes
1.Newmark (beta - gamma) [gamma = 0.5 and beta = 0.25]
2.Stormer-Verlet
The results are attached to the post. (I took print screen during the simulation)
The stormer-verlet is showing good enough results but there is a permanent deformation while applying Newmark on the 2nd and 2nd last node of the domain.
Can anyone please tell me the reason why this is happening and point out my mistake during application of Newmark time integration scheme?
Hi Abdullah, you could also try adding some numerical dissipation to the Newmark scheme in order to avoid instabilities. You cold modify the Newmark parameters to introduce dissipation (see Cardona) or change the time integration scheme to HHT or Generalized alpha.
Hi Abdullah, How are the boundary conditions imposed? Have they been fixed on both sides of the domain? When I was developing a FCT-FEM in Fortran 90, I remember I had similar problems which were due to a simple coding error. I don't know if it's also the case for you, but I guess it's worth to double-check.
Roberto Martini .. yes you got the point where I was making mistake. I have corrected the application of boundary conditions and now its working. Thank You
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