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Alternative integration methods for problems in structural dynamics. (English) Zbl 0851.73076
Summary: Runge-Kutta methods for the time integration of the equations of motion in structural dynamics are presented. The methods belong to a class called singly-diagonally-implicit Runge-Kutta methods. The computational cost needed per step is comparable to Newmark methods with \(\alpha\) damping. The methods proposed are \(L\)-stable which means that they instantly damp out the higher modes in the solution. The numerical dissipation can be controlled by a parameter. Both second and third order methods are presented. Some characteristics of the methods are compared with the Newmark method with \(\alpha\) damping.

74S20 Finite difference methods applied to problems in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
70-08 Computational methods for problems pertaining to mechanics of particles and systems
Full Text: DOI
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