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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.

MSC:
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
Software:
RODAS
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[1] Alexander, R., Diagonally implicit Runge-Kutta methods for STIFF O.D.E.’s, SIAM J. numer. anal., 14, 6, 1006-1021, (1977) · Zbl 0374.65038
[2] Cash, J.R., Diagonally implicit Runge-Kutta formulae with error estimates, J. inst. math. applic., 24, 293-301, (1979) · Zbl 0419.65044
[3] Hilber, H.M.; Hughes, T.J.R.; Taylor, R.L., Improved numerical dissipation for time integration algorithms in structural dynamics, Earthquake engin. struct. dyn., 5, 283-292, (1977)
[4] Hughes, T.J.R., The finite element method, linear static and dynamic finite element analysis, (1987), Prentice Hall Englewood Cliffs, NJ
[5] Hairer, E.; Nørsett, S.P.; Wanner, G., Solving ordinary differential equation I, nonstiff problems, (1987), Springer Berlin · Zbl 0638.65058
[6] Hairer, E.; Wanner, G., Solving ordinary differential equations II, stiff and differential-algebraic problems, (1991), Springer Berlin · Zbl 0729.65051
[7] Mathisen, K.M., Large displacement analysis of flexible and rigid systems considering displacement-dependant loads and nonlinear constraints, ()
[8] Thomas, R.M., Phase properties of high order, almost P-stable formulae, Bit, 24, 225-238, (1984) · Zbl 0569.65052
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