A computational procedure for interaction of high-speed vehicles on flexible structures without assuming known vehicle nominal motion.

*(English)*Zbl 0687.73073Summary: An efficient and reliable computational procedure is proposed for the analysis of interaction between high-speed vehicles and flexible structures. In contrast to traditional approaches, the vehicle nominal motion is considered here as an unknown of the problem. The equations encountered, for vehicle motion (after elimination of algebraic constraints) and for structural motion, form a set of nonlinear, coupled differential equations. In spatially-discrete form, these equations do not have the form of explicit ODEs. Predictor/corrector algorithms, which combine Runge-Kutta methods and linear multistep methods with an unconditionally stable algorithm for structural dynamics, are proposed to solve the partitioned DAEs of the interaction problem. The proposed algorithms carry special features pertaining to our formulation of vehicle/structure interaction, and yield accurate results which satisfy the essential system energy balance. The present approach effectively resolves the Timoshenko paradox in moving load problems. Several illustrative examples are presented.

Reviewer: Reviewer (Berlin)

##### MSC:

74S30 | Other numerical methods in solid mechanics (MSC2010) |

65F30 | Other matrix algorithms (MSC2010) |

##### Keywords:

partitioned differential algebraic equations; subalgorithms; set of nonlinear, coupled differential equations; Predictor/corrector algorithms; Runge-Kutta methods; linear multistep methods; unconditionally stable algorithm; structural dynamics; Timoshenko paradox; moving load problems##### Software:

DASSL
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\textit{L. Vu-Quoc} and \textit{M. Olsson}, Comput. Methods Appl. Mech. Eng. 76, No. 3, 207--244 (1989; Zbl 0687.73073)

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