Dear all mechanicians,

I modeled a disk with outer diameter of 48 mm and inner diameter of 24 mm. The material is defined as isotropic; in this case, it's glass-ceramics (E = 90GPa, v = 0.24). The inner diameter is constrained to transverse directions, while it is subjected to half-sine wave impulse of 500G (G = 9.81 m/s^2) within 2 ms. The disk moved up under this loading, and I extracted the vertical displacement at the tip with respect to time (time-history analysis). The time step was 1e-6 second, and the duration was 4 ms. The disk was made of 8-node hexahedron element, with one element in the thickness. Three formulations were tested: (1) reduced integration [RI], (2) selectively-reduced integration [SRI] and (3) full integration [FI].

After conducting convergence study (starting from a very coarse mesh model to a very fine model), the conclusion is this: the model with FI is converged faster. It means that when I was comparing maximum displacement, coarse-mesh model will give similar value to the fine-mesh model. Whilst for SRI and RI, coarse mesh will give lower value, and after mesh refinement, it will give similar value to the FI results.  

I did simulation with explicit solver (LSDYNA). The conclusion is the same.

What could be the cause of the slow convergency of RI and SRI? Can anyone refer me to the literatures on this dynamic problem?

Thank you!