Time Integration

Explicit time integration based on Newmark method is conditionally stable. The Courant condition also takes into account the flow of material through the elements gives the stability condition as:(1)

$$\text{Δ}t\le S_f*\frac{\text{Δ}l}{c+v-w}$$

(2)

$$v-w=\sqrt{\frac{1}{N}{\displaystyle \sum _{i=1}^3{\displaystyle \sum _{l=1}^N{\left(v_i^l-w_i^l\right)}^2}}}$$

Where,

$N$

Number of nodes for considered elements