An efficient weighted residual time integration family. (English) Zbl 1535.70055
Summary: A new family of time integration methods is formulated. The recommended technique is useful and robust for the loads with large variations and the systems with nonlinear damping behavior. It is also applicable for the structures with lots of degrees of freedom, and can handle general nonlinear dynamic systems. By comparing the presented scheme with the fourth-order Runge-Kutta and the Newmark algorithms, it is concluded that the new strategy is more stable. The authors’ formulations have good results on amplitude decay and dispersion error analyses. Moreover, the family orders of accuracy are \(m+2\) and \(m+3\) for even and odd values of \(m\), respectively. Findings demonstrate the superiority of the new family compared to explicit and implicit methods and dissipative and non-dissipative algorithms.
MSC:
| 70H06 | Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics |
Keywords:
time integration; high order of accuracy; weighted residual method; general nonlinear dynamic systems; robust for high variation loads; computational efficiencyReferences:
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