Optimized Gauss-Legendre-Hermite 2-point (O-GLH-2P) method for nonlinear time-history analysis of structures. (English) Zbl 07830933
Meccanica 59, No. 3, 305-332 (2024); correction ibid. 59, No. 4, 681 (2024).
Summary: An efficient time-integration method is developed for nonlinear dynamic analysis (NDA) of single-degree-of-freedom (SDOF) structural systems. The main novelty of the new method is to couple Gauss-Legendre integrator with particular forms of Hermite interpolator to solve the vibration equation under earthquake excitation. Accordingly, the simplest Gauss-Legendre quadrature is adopted from numerical analysis while Hermite interpolators are separately constructed for the given task of evaluating the internal points, so-called stages. Then, using swarm intelligence, a greatly constructive modification is made in the body of the Gauss-Legendre integrator to strengthen it for dealing with high-frequency NDA problems. So, an additional part is included in the integrator and it is tuned by calibration factor (CF) which is introduced in this work. The modern evolutionary optimizer is used to obtain the optimal calibration factor (OCF) formula. The resulted method is called optimized Gauss-Legendre-Hermite 2-point (O-GLH-2P) method because it is basically founded on the 2-point Gauss-Legendre formula which is optimized in an evolutionary procedure. O-GLH-2P provides a completely general implicit NDA algorithm for linear and nonlinear analyses of structural systems undergoing earthquake excitation. The advantages of the proposed algorithm against conventional ones are as follows: 1) It works more precisely than the conventional methods such as Newmark-\(\beta\) and Wilson-\(\theta\) methods, 2) Very simple relations and basic formulas are used in the main body of the O-GLH-2P algorithm, 3) It runs appropriately fast; however, it still cannot work as fast as the Newmark-\(\beta\) method, 4) It robustly analyzes high-frequency systems with \(T_n \leq 0.12\)s. These systems can be difficultly analyzed by the others unless very fine mesh is employed, and 5) O-GLH-2P conducts a more precise analysis for conservative and near-conservative systems which have small damping ratio, i.e., \(\zeta \leq 0.01\). In brief, the extreme simplicity and high precision of the proposed method make it stand higher than its counterparts. Numerical studies clearly verify the superiority of O-GLH-2P against the others.
MSC:
| 74S20 | Finite difference methods applied to problems in solid mechanics |
| 74L10 | Soil and rock mechanics |
| 74L05 | Geophysical solid mechanics |
| 86A15 | Seismology (including tsunami modeling), earthquakes |
Keywords:
seismic response; mass-spring system; earthquake excitation; Runge-Kutta time integration schemeReferences:
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