Experiments with direct integration algorithms for ordinary differential equations in structural dynamics

Braekhus, Jon; Aasen, Jan Ole

doi:10.1016/0045-7949(81)90112-7

Cited by 9 publications

References 7 publications

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A test problem for structural systems with discontinuities

Brown

Borthwick²

1988

Earthq Engng Struct Dyn

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SUMMARYThe direct integration method for structural systems having force and/or stiffness discontinuities is known to present considerable numerical difficulties. A non-linear one-degree-of-freedom test problem having these characteristics is developed and its exact oscillation period determined. The effects on amplitude and phase of small perturbations of the switching point, such as are caused by fixed-step integration, have been studied. Artificial energy changes introduced at discontinuities by fixed-step explicit and implicit methods are investigated. For a number of commonly used algorithms orders of convergence in fixed-step integration of the test problem degrade from design value before, to 0 ( h ) after, the first discontinuity traversal. 0 ( h ) convergence is maintained for any number of discontinuity traversals thereafter, but design order can be recovered by locating the switching point sufficiently precisely.

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A test problem for structural systems with discontinuities

Brown

Borthwick²

1988

Earthq Engng Struct Dyn

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A new family of explicit time integration methods for linear and non‐linear structural dynamics

Chung

Lee

1994

Numerical Meth Engineering

143

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SUMMARYA new family of explicit single-step time integration methods with controllable high-frequency dissipation is presented for linear and non-linear structural dynamic analyses. The proposed methods are second-order accurate and completely explicit with a diagonal mass matrix, even when the damping matrix is not diagonal in the linear structural dynamics or the internal force vector is a function of velocities in the non-linear structural dynamics. Stability and accuracy of the new explicit methods are analysed for the linear undamped/damped cases. Furthermore, the new methods are compared with other explicit methods.

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Schwingungsmodelle mit mehreren Freiheitsgraden

Dresig¹,

Vulfson²

1989

Dynamik Der Mechanismen

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Experiments with direct integration algorithms for ordinary differential equations in structural dynamics

Cited by 9 publications

References 7 publications

A test problem for structural systems with discontinuities

A test problem for structural systems with discontinuities

A new family of explicit time integration methods for linear and non‐linear structural dynamics

Schwingungsmodelle mit mehreren Freiheitsgraden

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