Simulating the anchor lifting maneuver of ships using contact detection techniques and continuous contact force models

  • Daniel DopicoEmail author
  • Alberto Luaces
  • Mariano Saura
  • Javier Cuadrado
  • David Vilela


Designing the geometry of a ship’s hull to guarantee a correct anchor maneuver is not an easy task. The engineer responsible for the design has to make sure that the anchor does not jam up during the lifting process and the position adopted by the anchor on the hull is acceptable when it is completely stowed. Some years ago, the design process was based on wooden scale models of the hull, anchor and chain links, which are expensive, their building process is time consuming and they do not offer the required precision. As a result of this research, a computational tool to simulate the anchor maneuver of generic ships given by CAD models was developed, and it is proving to be very helpful for the naval engineers.

In this work, all the theory developed to simulate anchor maneuvers is thoroughly described, taking into account both the behavior of the anchor and the chain. To consider the contact forces between all the elements involved in the maneuver, a general contact algorithm for rigid bodies of arbitrary shapes and a particular contact algorithm for the chain links have been developed. In addition to the contact problem, aspects like the dynamic formulation of the equations of motion or the static equilibrium position problem are also covered in this work. To test the theory, a simulation of the anchor lifting maneuver of a ship is included as a case study.

In spite of the motivation to develop the theory, the algorithms derived in this work are general and usable in any other multibody simulation with contacts, under the scope of validity of the models proposed. To illustrate this, the simulation of a valve rocker arm and cam system is accomplished, too.

The computational and contact detection algorithms derived have been implemented in MBSLIM, a library for the dynamic simulation of multibody systems, and MBS model, a library for the contact detection and 3D rendering of multibody systems.


Multibody dynamics Contact detection Contact forces Simulation Anchor maneuver Ship 



The support of the Spanish Ministry of Economy and Competitiveness (MINECO) under project DPI2016-81005-P is greatly acknowledged. The authors want to acknowledge the support of the Spanish company Navantia in this research as well.


  1. 1.
    Flores, P., Lankarani, H.M.: Contact Force Models for Multibody Dynamics. Solid Mechanics and Its Applications. Springer, Cham (2016) CrossRefzbMATHGoogle Scholar
  2. 2.
    Narwal, A.K., Vaz, A., Gupta, K.: Bond graph modeling of dynamics of soft contact interaction of a non-circular rigid body rolling on a soft material. Mech. Mach. Theory 86, 265–280 (2015) CrossRefGoogle Scholar
  3. 3.
    Banerjee, A., Chanda, A., Das, R.: Historical origin and recent development on normal directional impact models for rigid body contact simulation: a critical review. Arch. Comput. Methods Eng. 24, 397–422 (2017) MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Gilardi, G., Sharf, I.: Literature survey of contact dynamics modelling. Mech. Mach. Theory 37(10), 1213–1239 (2002) MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Greenwood, D.T.: Principles of Dynamics. Prentice-Hall, New York (1965) Google Scholar
  6. 6.
    Wehage, R.A., Haug, E.J.: Generalized coordinate partitioning in dynamic analysis of mechanical systems. Tech. rep., University of Iowa (1981) Google Scholar
  7. 7.
    Khulief, Y.A., Shabana, A.A.: Dynamic analysis of constrained system of rigid and flexible bodies with intermittent motion. J. Mech. Transm. Autom. Des. (1984). Google Scholar
  8. 8.
    Lankarani, H., Nikravesh, P.: Contact force model with hysteresis damping for impact analysis of multibody systems. J. Mech. Des. 112(3), 369–376 (1990) CrossRefGoogle Scholar
  9. 9.
    Flores, P., Ambrosio, J.: On the contact detection for contact–impact analysis in multibody systems. Multibody Syst. Dyn. 24, 103–122 (2010) MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Machado, M., Moreira, P., Flores, P., Lankarani, H.: Compliant contact force models in multibody dynamics: evolution of the Hertz contact theory. Mech. Mach. Theory 53, 99–121 (2012) CrossRefGoogle Scholar
  11. 11.
    Pfeiffer, F., Glocker, C.: Multibody Dynamics with Unilateral Contacts. Springer, Vienna (2000). CISM International Centre for Mechanical Sciences zbMATHGoogle Scholar
  12. 12.
    Brogliato, B.: Nonsmooth Mechanics: Models, Dynamics and Control, 3rd edn. Springer, Berlin (2016) CrossRefzbMATHGoogle Scholar
  13. 13.
    Flores, P., Leine, R., Glocker, C.: Application of the nonsmooth dynamics approach to model and analysis of the contact-impact events in cam-follower systems. Nonlinear Dyn. 69(4), 2117–2133 (2012) MathSciNetCrossRefGoogle Scholar
  14. 14.
    Dopico, D., Luaces, A., Gonzalez, M., Cuadrado, J.: Dealing with multiple contacts in a human-in-the-loop application. Multibody Syst. Dyn. 25(2), 167–183 (2011) MathSciNetCrossRefGoogle Scholar
  15. 15.
    Lopes, D., Silva, M., Ambrosio, J., Flores, P.: A mathematical framework for rigid contact detection between quadric and superquadric surfaces. Multibody Syst. Dyn. 24, 255–280 (2010). MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Bedah, A.A., Uicker, J.: Contact prediction between moving objects bounded by curved surfaces. J. Comput. Inf. Sci. Eng. 12(1), 011003 (2011). CrossRefGoogle Scholar
  17. 17.
    Choi, J., Ryu, H.S., Kim, C.W., Choi, J.H.: An efficient and robust contact algorithm for a compliant contact force model between bodies of complex geometry. Multibody Syst. Dyn. 23, 99–120 (2010) CrossRefzbMATHGoogle Scholar
  18. 18.
    Gonthier, Y., Lange, C., McPhee, J.: A volumetric contact model implemented using polynomial geometry. In: ECCOMAS Thematic Conference Multibody Dynamics 2009, Warsaw, Poland, pp. 144–145 (2009), no. CD, paper 223 Google Scholar
  19. 19.
    Garcia de Jalon, J., Bayo, E.: Kinematic and Dynamic Simulation of Multibody Systems: The Real-Time Challenge. Springer, New York (1994) CrossRefGoogle Scholar
  20. 20.
    Bayo, E., García de Jalon, J., Serna, M.: A modified Lagrangian formulation for the dynamic analysis of constrained mechanical systems. Comput. Methods Appl. Mech. Eng. 71, 183–195 (1988) MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Cuadrado, J., Gutierrez, R., Naya, M., Morer, P.: A comparison in terms of accuracy and efficiency between a MBS dynamic formulation with stress analysis and a non-linear FEA code. Int. J. Numer. Methods Eng. 51, 1033–1052 (2001) CrossRefzbMATHGoogle Scholar
  22. 22.
    Cuadrado, J., Gutierrez, R., Naya, M., Gonzalez, M.: Experimental validation of a flexible mbs dynamic formulation through comparison between measured and calculated stresses on a prototype car. Multibody Syst. Dyn. 11, 147–166 (2004) CrossRefzbMATHGoogle Scholar
  23. 23.
    Dopico, D., González, F., Cuadrado, J., Kovecses, J.: Determination of holonomic and nonholonomic constraint reactions in an index-3 augmented Lagrangian formulation with velocity and acceleration projections. J. Comput. Nonlinear Dyn. 9, 041006 (2014) CrossRefGoogle Scholar
  24. 24.
    Bayo, E., Ledesma, R.: Augmented Lagrangian and mass-orthogonal projection methods for constrained multibody dynamics. Nonlinear Dyn. 9, 113–130 (1996) MathSciNetCrossRefGoogle Scholar
  25. 25.
    Chung, J., Hulbert, G.: A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-alpha method. J. Appl. Mech. 60, 371–375 (1993) MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Géradin, M., Cardona, A.: Flexible Multibody Dynamics. A Finite Element Approach. Wiley, Chichester (2001) Google Scholar
  27. 27.
    Cuadrado, J., Dopico, D., Naya, M., Gonzalez, M.: Penalty, semi-recursive and hybrid methods for MBS real-time dynamics in the context of structural integrators. Multibody Syst. Dyn. 12(2), 117–132 (2004) CrossRefzbMATHGoogle Scholar
  28. 28.
    Cuadrado, J., Cardenal, J., Morer, P., Bayo, E.: Intelligent simulation of multibody dynamics: space-state and descriptor methods in sequential and parallel computing environments. Multibody Syst. Dyn. 4, 55–73 (2000) CrossRefzbMATHGoogle Scholar
  29. 29.
    Newmark, N.: A method of computation for structural dynamics. J. Eng. Mech. Div. 85(3), 67–94 (1959) Google Scholar
  30. 30.
    Garcia Orden, J., Dopico, D.: On the stabilizing properties of energy-momentum integrators and coordinate projections for constrained mechanical systems. In: Multibody Dynamics: Computational Methods and Applications, pp. 49–68. Springer, Dordrecht (2007) CrossRefGoogle Scholar
  31. 31.
    Hunt, K., Crossley, F.: Coefficient of restitution interpreted as damping in vibroimpact. J. Appl. Mech. 42(2), 440–445 (1975) CrossRefGoogle Scholar
  32. 32.
    Flores, P., Machado, M., Silva, M., Martins, J.: On the continuous contact force models for soft materials in multibody dynamics. Multibody Syst. Dyn. 25, 357–375 (2011). CrossRefzbMATHGoogle Scholar
  33. 33.
    Lankarani, H., Nikravesh, P.: Continuous contact force models for impact analysis in multibody systems. Nonlinear Dyn. 5(2), 193–207 (1994) Google Scholar
  34. 34.
    Herbert, R., McWhannell, D.: Shape and frequency composition of pulses from an impact pair. J. Eng. Ind. 99(3), 513–518 (1977) CrossRefGoogle Scholar
  35. 35.
    Lee, T.W., Wang, A.: On the dynamics of intermittent-motion mechanisms. Part 1: dynamic model and response. Part 2: Geneva mechanisms, ratchets, and escapements. J. Mech. Transm. Autom. Des. 105(3), 534–551 (1983) CrossRefGoogle Scholar
  36. 36.
    Gonthier, Y., McPhee, J., Lange, C., Piedboeuf, J.-C.: A regularized contact model with asymmetric damping and dwell-time dependent friction. Multibody Syst. Dyn. 11(3), 209–233 (2004) CrossRefzbMATHGoogle Scholar
  37. 37.
    Goldsmith, W.: Impact, the Theory and Physical Behaviour of Colliding Solids. Edward Arnold Ltd., London (1960) zbMATHGoogle Scholar
  38. 38.
    Van Den Bergen, G.: Collision Detection in Interactive 3D Environments. Elsevier, Amsterdam (2004) zbMATHGoogle Scholar
  39. 39.
    Ericson, C.: Real-Time Collision Detection. Elsevier, Amsterdam (2005) Google Scholar
  40. 40.
    Nocedal, J., Wright, S.: Numerical Optimization. Springer Series in Operations Research. Springer, New York (1999) CrossRefzbMATHGoogle Scholar
  41. 41.
    Blumentals, A., Brogliato, B., Bertails-Descoubes, F.: The contact problem in Lagrangian systems subject to bilateral and unilateral constraints, with or without sliding Coulomb’s friction: a tutorial. Multibody Syst. Dyn. 38, 43–76 (2016) MathSciNetCrossRefzbMATHGoogle Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Laboratorio de Ingeniería MecánicaUniversidade da CoruñaFerrolSpain
  2. 2.Departamento de Ingeniería MecánicaUniversidad Politécnica de CartagenaCartagenaSpain

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