Numerical Evaluation–Newmark-Beta Method

Implicit method, namely Newmark-Beta method is another numerical evaluation method besides central difference method. To derive for the equations compatible with this method, Taylor theorem needs to be deployed.

We have looked into an example for the implementation of Newmark-Beta method. It is advisable to construct a table to organize our calculation. During the analysis, we first calculate the displacement response at the future instance. Then, by using the result we solve for acceleration, and finally for velocity. The analysis is iterative in nature, similar to central difference method. Therefore, we are free to conduct our iterative calculation and end it at any time instance, regardless of the presence of external force. At the end, we have compared the displacement-time and hysteresis curves produced from both implicit and explicit methods.

The following shows the derivation and application of Newmark-Beta method. Watch the video above for full details.