Damping perturbation based time integration asymptotic method for structural dynamics

TL;DR

This paper introduces a novel explicit time integration method for structural dynamics that artificially perturbs damping, providing high accuracy and efficiency with well-defined convergence conditions.

Contribution

A new numerical scheme based on damping perturbation is developed, offering explicit iteration, convergence analysis, and improved computational performance in structural dynamics simulations.

Findings

High accuracy in numerical examples

Stable and efficient iterative scheme

Defined maximum time step for convergence

Abstract

The light damping hypothesis is usually assumed in structural dynamics since dissipative forces are in general weak with respect to inertial and elastic forces. In this paper a novel numerical method of time integration based on the artificial perturbation of damping is proposed. The asymptotic expansion of the transient response results in an infinite series which can be summed, leading to a well-defined explicit iterative step-by-step scheme. Conditions for convergence are rigorously analyzed, enabling the determination of the methodology boundaries in form of maximum time step. The numerical properties of the iterative scheme, i.e. stability, accuracy and computational effort are also studied in detail. The approach is validated with two numerical examples, showing a high accuracy and computational efficiency relative to other methods.