The TR-BDF2 method for second order problems in structural mechanics

TL;DR

This paper demonstrates that the TR-BDF2 method, when reformulated for second order structural mechanics problems, offers improved accuracy and efficiency over traditional methods like Newmark, through analysis and benchmark testing.

Contribution

The paper introduces a reformulation of the TR-BDF2 method that reduces computational complexity and enhances performance for structural mechanics applications.

Findings

TR-BDF2 outperforms Newmark in accuracy and efficiency

Reformulation reduces algebraic system size to displacement degrees of freedom

Numerical experiments confirm superior performance

Abstract

The application of the TR-BDF2 method to second order problems typical of structural mechanics and seismic engineering is discussed. A reformulation of this method is presented, that only requires the solution of algebraic systems of size equal to the number of displacement degrees of freedom. A linear analysis and numerical experiments on relevant benchmarks show that the TR-BDF2 method is superior in terms of accuracy and efficiency to the classical Newmark method and to its generalizations.