An optimized implementation of the Newmark/Newton‐Raphson algorithm for the time integration of non‐linear problems

The paper describes an optimized computational implementation of a basic ‘building block’ for non-linear structural dynamic analysis programs: the combination of the modified Newton-Raphson iterative technique with an implicit time integration operator (in this case a member of the Newmark family), working in an incremental--iterative formulation for the equations of motion. The objective of this implementation is to attain improved computational efficiency, regarding both CPU time and memory requirements. The basic formulation and derivation are presented, along with the implementation details; the positive aspects related to the computational optimization are highlighted.