A family of unconditionally stable explicit algorithms for structural dynamics

GUO Haoxin1,WU Chunli2

Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (12) : 48-56.

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Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (12) : 48-56.

A family of unconditionally stable explicit algorithms for structural dynamics

  • GUO Haoxin1,WU Chunli2
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Abstract

The implicit dissipative HHT-  method is analyzed using discrete control theory, a one-parameter family of explicit structural dynamics algorithms with controllable numerical energy dissipation, referred to as the explicit HHT-  method, is developed for linear and nonlinear structural dynamic numerical analysis applications. New algorithm adopts the recursive formula of velocity and displacement of explicit algorithm. Accuracy stability, numerical dispersion, and energy dissipation characteristics of the proposed algorithms are studied. It is shown that the algorithms are unconditionally stable for linear elastic and stiffness softening-type nonlinear systems. The amount of numerical damping is controlled by a single parameter, for a specific value of this parameter, the resulting algorithm is shown to produce no numerical energy dissipation. It is further shown that the numerical dispersion and energy dissipation characteristics of the proposed explicit algorithms are the same as that of the implicit HHT-  method. A numerical example is presented to verify the correctness of theoretical analysis.

Key words

direct integration algorithm / explicit / unconditional stability / numerical energy dissipation / dynamic analysis / discrete transfer function

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GUO Haoxin1,WU Chunli2. A family of unconditionally stable explicit algorithms for structural dynamics[J]. Journal of Vibration and Shock, 2020, 39(12): 48-56

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