Journal
OCEAN ENGINEERING
Volume 109, Issue -, Pages 145-160Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.oceaneng.2015.08.050
Keywords
Discrete Euler-Lagrange equation; Multibody dynamics; Floating crane; Constraint-based wire rope; Joint constraint
Funding
- Industrial Strategic Technology Development Program - Ministry of Knowledge Economy of the Republic of Korea [10035331]
- BK21 Plus, Education & Research Center for Offshore Plant Engineers (COPE) of Seoul National University, Republic of Korea
- Engineering Research Institute of Seoul National University, Republic of Korea
- Research Institute of Marine Systems Engineering of Seoul National University, Republic of Korea
- Korea Evaluation Institute of Industrial Technology (KEIT) [10035331] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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In this study, we derived a Discrete Euler-Lagrange (DEL) equation to represent the motion of a multi-body system, in which many bodies are connected physically by joints or wire ropes. By discretizing and re-formulating the traditional Euler-Lagrange equation, we obtained a discrete time integrator, called the Stomer-Verlet method. Similarly, we discretized the equations of constraints of joints and wire ropes by the midpoint rule. Then, we adapted regularization and stabilization methods, to overcome numerical instability and the stiffness problem. The DEL equation can be formulated automatically, by defining the equations of joint constraints and their derivatives. In addition, the stretching of the wire rope is mathematically modeled as constraints for stability. To apply the DEL equation to a floating vessel, hydrostatic and hydrodynamic forces are considered as external forces. We applied the DEL equation to a mass-spring system with the large spring coefficient. And we tested a spring pendulum modeled by a constraint-based wire rope. Despite the large spring coefficient, the DEL equation with the constraint-based wire rope shows relatively stable motion. We tested the automatic formulation by three-dimensional multiple pendulums. Finally, we simulated a floating crane and a heavy load connected by constraint-based wire rope, based on set of regular waves with different wave heights, directions and periods. (C) 2015 Elsevier Ltd. All rights reserved.
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