Discrete methods of solution for dynamic linear and nonlinear problems

Abstract

Based on the recursive explicit form of Newmark γ-β method developed by Zienkiewicz for displacements, similar recursive expressions for velocities and accelerations are developed. The general solution of dynamic linear and nonlinear problems using the developed relations is discussed first. Reutilizing the same explicit relations, two more approaches for analysis of general dynamics problems are introduced. The first one is a nonrecursive state matrix approach. The second is a first-order reduction of the original second-order form. Algorithms for the solution of both linear and nonlinear problems are outlined and applied to simple dynamic systems. The developed methods present a unifying, algorithmic and consistent approach for the discrete solution of dynamics problems.