Early computer simulations of earthquakes suffered from mathematical rounding errors that caused virtual buildings to blow up on screen; Nathan Newmark developed an unconditionally stable numerical formula that marches through time with absolute accuracy. Published in 1959, the Newmark-beta method is the numerical integration engine powering every modern earthquake simulation, crash test, and explosion defense model engineered today.

In civil and structural engineering, designing high-rise buildings and nuclear power plants to survive violent earthquakes requires calculating how every floor vibrates during seconds of violent ground shaking. Early computer simulations were mathematically unstable: tiny numerical rounding errors compounded rapidly, causing simulated buildings to explode into infinite values on computers.
University of Illinois civil engineer Nathan Newmark formulated an unconditionally stable time integration method. Acting like a mathematically perfect digital time machine, the Newmark-beta equation calculates acceleration, velocity, and displacement step-by-step through an earthquake without ever blowing up or drifting out of control.
Newmark’s equation is embedded in every structural dynamics simulation package on Earth. By safeguarding nuclear power plants against catastrophic earthquakes, by protecting towering skyscrapers from hurricane wind gusts, and by saving thousands of lives during major seismic disasters, Newmark time-integration protects global infrastructure.
A Method of Computation for Structural Dynamics
Method is capable of application to structures of any degree of complication, with any relationship between force and displacement, from linear elastic behavior through various degrees of inelastic behavior or plastic response, up to failure; any type of dynamic loading, due to shock or impact, vibration, earthquake, or nuclear blast can be considered; use of high-speed digital computers.
Ask this paper your own questions, or keep browsing the verified research catalogue.