On the generalized Bézier-based integration approach for co-simulation applications

References

• Aghdam, M. M., A. Fallah, and P. Haghi. 2015. Nonlinear initial value ordinary differential equations. In Nonlinear approaches in engineering applications: Applied mechanics, vibration control, and numerical analysis, ed. L. Dai and R. N. Jazar, 117–136. Cham: Springer International Publishing
   Google Scholar
• Andersson, H., P. Nordin, T. Borrvall, K. Simonsson, D. Hilding, M. Schill, P. Krus, and D. Leidermark. 2017. A co-simulation method for system-level simulation of fluid–structure couplings in hydraulic percussion units. Engineering with Computers 33 (2):317–33. doi: 10.1007/s00366-016-0476-8.
   Web of Science ®Google Scholar
• Antunes, P., J. Ambrósio, J. Pombo, and A. Facchinetti. 2020. A new methodology to study the pantograph–catenary dynamics in curved railway tracks. Vehicle System Dynamics 58 (3):425–52. doi: 10.1080/00423114.2019.1583348.
   Web of Science ®Google Scholar
• Antunes, P., H. Magalhães, J. Ambrósio, J. Pombo, and J. Costa. 2019. A co-simulation approach to the wheel–rail contact with flexible railway track. Multibody System Dynamics 45 (2):245–72. doi: 10.1007/s11044-018-09646-0.
   Web of Science ®Google Scholar
• Arnold, M. 2010. Stability of sequential modular time integration methods for coupled multibody system models. Journal of Computational and Nonlinear Dynamics 5 (3):031003. doi: 10.1115/1.4001389.
   Web of Science ®Google Scholar
• Baharudin, M. E., A. Rouvinen, P. Korkealaakso, and A. Mikkola. 2014. Real-time multibody application for tree harvester truck simulator. Proceedings of the Institution of Mechanical Engineers Part K 228 (2):182–98. doi: 10.1177/1464419314521182.
   Google Scholar
• Bayo, E., J. G. de Jalón, A. Avello, and J. Cuadrado. 1991. An efficient computational method for real time multibody dynamic simulation in fully cartesian coordinates. Computer Methods in Applied Mechanics and Engineering 92 (3):377–95. doi: 10.1016/0045-7825(91)90023-Y.
   Web of Science ®Google Scholar
• Bayo, E., J. Garcia De Jalon, and M. A. Serna. 1988. A modified lagrangian formulation for the dynamic analysis of constrained mechanical systems. Computer Methods in Applied Mechanics and Engineering 71 (2):183–95. doi: 10.1016/0045-7825(88)90085-0.
   Web of Science ®Google Scholar
• Benedikt, M., and A. Hofer. 2013. Guidelines for the application of a coupling method for non-iterative co-simulation. Paper presented at the 2013 8th EUROSIM Congress on Modelling and Simulation, IEEE, September 10–13.
   Google Scholar
• Benedikt, M., D. Watzenig, and A. Hofer. 2013. Modelling and analysis of the non-iterative coupling process for co-simulation. Mathematical and Computer Modelling of Dynamical Systems 19 (5):451–70. doi: 10.1080/13873954.2013.784340.
   Google Scholar
• Chen, W., S. Ran, C. Wu, and B. Jacobson. 2021. Explicit parallel co-simulation approach: Analysis and improved coupling method based on H-infinity synthesis. Multibody System Dynamics 52 (3):255–79. doi: 10.1007/s11044-021-09785-x.
   Web of Science ®Google Scholar
• Cuadrado, J., J. Cardenal, P. Morer, and E. Bayo. 2000. Intelligent simulation of multibody dynamics: space-state and descriptor methods in sequential and parallel computing environments. Multibody System Dynamics 4 (1):55–73. doi: 10.1023/A:1009824327480.
   Web of Science ®Google Scholar
• Dopico, D., A. Luaces, M. Gonzalez, and J. Cuadrado. 2011. Dealing with multiple contacts in a human-in-the-loop application. Multibody System Dynamics 25 (2):167–83. doi: 10.1007/s11044-010-9230-y.
   Web of Science ®Google Scholar
• Dopico, D., F. González, J. Cuadrado, and J. Kövecses. 2014. Determination of holonomic and nonholonomic constraint reactions in an index-3 augmented lagrangian formulation with velocity and acceleration projections. Journal of Computational and Nonlinear Dynamics 9 (4):041006. doi: 10.1115/1.4027671.
   Web of Science ®Google Scholar
• D'Silva, S., P. Sundaram, and J. G. D'Ambrosio. 2006. Co-simulation platform for diagnostic development of a controlled chassis system. SAE Transactions 115:498–507.
   Google Scholar
• Gomes, C., C. Thule, D. Broman, P. G. Larsen, and H. Vangheluwe. 2019. Co-simulation: A survey. ACM Computing Surveys 51 (3):1–33. doi: 10.1145/3179993.
   Web of Science ®Google Scholar
• González, F., A. Luaces, U. Lugrís, and M. González. 2009. Non-intrusive parallelization of multibody system dynamic simulations. Computational Mechanics 44 (4):493–504. doi: 10.1007/s00466-009-0386-3.
   Web of Science ®Google Scholar
• González, F., D. Dopico, R. Pastorino, and J. Cuadrado. 2016. Behaviour of augmented Lagrangian and Hamiltonian methods for multibody dynamics in the proximity of singular configurations. Nonlinear Dynamics 85 (3):1491–508. doi: 10.1007/s11071-016-2774-5.
   Web of Science ®Google Scholar
• González, F., M. Á. Naya, A. Luaces, and M. González. 2011. On the effect of multirate co-simulation techniques in the efficiency and accuracy of multibody system dynamics. Multibody System Dynamics 25 (4):461–83. doi: 10.1007/s11044-010-9234-7.
   Web of Science ®Google Scholar
• González, F., M. González, and A. Mikkola. 2010. Efficient coupling of multibody software with numerical computing environments and block diagram simulators. Multibody System Dynamics 24 (3):237–53. doi: 10.1007/s11044-010-9199-6.
   Web of Science ®Google Scholar
• González, F., S. Arbatani, A. Mohtat, and J. Kövecses. 2019. Energy-leak monitoring and correction to enhance stability in the co-simulation of mechanical systems. Mechanism and Machine Theory 131:172–88. doi: 10.1016/j.mechmachtheory.2018.09.007.
   Web of Science ®Google Scholar
• González, M., F. González, A. Luaces, and J. Cuadrado. 2007. Interoperability and neutral data formats in multibody system simulation. Multibody System Dynamics 18 (1):59–72. doi: 10.1007/s11044-007-9060-8.
   Web of Science ®Google Scholar
• Gu, B., and H. H. Asada. 2004. Co-simulation of algebraically coupled dynamic subsystems without disclosure of proprietary subsystem models. Journal of Dynamic Systems, Measurement, and Control 126 (1):1–13. doi: 10.1115/1.1648307.
   Web of Science ®Google Scholar
• Heydarpour, Y., and M. M. Aghdam. 2016a. A hybrid Bézier based multi-step method and differential quadrature for 3D transient response of variable stiffness composite plates. Composite Structures 154:344–59. doi: 10.1016/j.compstruct.2016.07.060.
   Web of Science ®Google Scholar
• Heydarpour, Y., and M. M. Aghdam. 2016b. A novel hybrid Bézier based multi-step and differential quadrature method for analysis of rotating FG conical shells under thermal shock. Composites Part B Engineering 97:120–40. doi: 10.1016/j.compositesb.2016.04.055.
   Web of Science ®Google Scholar
• Heydarpour, Y., and M. M. Aghdam. 2017. A coupled integral–differential quadrature and B-spline-based multi-step technique for transient analysis of VSCL plates. Acta Mechanica 228 (9):2965–86. doi: 10.1007/s00707-017-1850-3.
   Web of Science ®Google Scholar
• Hollari, R. N., A. Taghvaeipour, M. M. Aghdam, and F. González. 2022. Novel co-simulation technique in the flexible analysis of a parallel robot. Paper presented at the 2022 10th RSI International Conference on Robotics and Mechatronics (ICRoM), November 22–24. doi: 10.1109/ICRoM57054.2022.10025339.
   Google Scholar
• Kabir, H., and M. M. Aghdam. 2019. A robust Bézier based solution for nonlinear vibration and post-buckling of random checkerboard graphene nano-platelets reinforced composite beams. Composite Structures 212:184–98. doi: 10.1016/j.compstruct.2019.01.041.
   Web of Science ®Google Scholar
• Kübler, R., and W. Schiehlen. 2000. Modular simulation in multibody system dynamics. Multibody System Dynamics 4 (2/3):107–27. doi: 10.1023/A:1009810318420.
   Web of Science ®Google Scholar
• LeVeque, R. J. 2007. Finite difference methods for ordinary and partial differential equations: Steady-state and time-dependent problems. Philadelphia: SIAM.
   Google Scholar
• Li, P., Q. Yuan, D. Lu, T. Meyer, and B. Schweizer. 2020. Improved explicit co-simulation methods incorporating relaxation techniques. Archive of Applied Mechanics 90 (1):17–46. doi: 10.1007/s00419-019-01597-y.
   Web of Science ®Google Scholar
• Malczyk, P., J. Frączek, F. González, and J. Cuadrado. 2019. Index-3 divide-and-conquer algorithm for efficient multibody system dynamics simulations: Theory and parallel implementation. Nonlinear Dynamics 95 (1):727–47. doi: 10.1007/s11071-018-4593-3.
   Web of Science ®Google Scholar
• Michaud, F., U. Lugrís, and J. Cuadrado. 2017. A co-integration approach for the forward-dynamics based solution of the muscle recruitment problem. 7º Congresso Nacional de Biomecânica, Guimaraes (CNB2017).
   Google Scholar
• Naya, M. A., J. Cuadrado, D. Dopico, and U. Lugris. 2011. An efficient unified method for the combined simulation of multibody and hydraulic dynamics: Comparison with simplified and co-integration approaches. Archive of Mechanical Engineering 58 (2):223–243. doi: 10.2478/v10180-011-0016-4.
   Google Scholar
• Peiret, A., F. González, J. Kövecses, and M. Teichmann. 2018. Multibody system dynamics interface modelling for stable multirate co-simulation of multiphysics systems. Mechanism and Machine Theory 127:52–72. doi: 10.1016/j.mechmachtheory.2018.04.016.
   Web of Science ®Google Scholar
• Peiret, A., F. González, J. Kövecses, and M. Teichmann. 2020. Co-simulation of multibody systems with contact using reduced interface models. Journal of Computational and Nonlinear Dynamics 15 (4):041001. doi: 10.1115/1.4046052.
   Web of Science ®Google Scholar
• Peiret, A., J. Kövecses, F. González, and M. Teichmann. 2019. Interface Models for Multirate Co-Simulation of Nonsmooth Multibody Systems. Paper presented at the ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. doi: 10.1115/DETC2019-98098.
   Google Scholar
• Rahikainen, J., A. Mikkola, J. Sopanen, and J. Gerstmayr. 2018. Combined semi-recursive formulation and lumped fluid method for monolithic simulation of multibody and hydraulic dynamics. Multibody System Dynamics 44 (3):293–311. doi: 10.1007/s11044-018-9631-x.
   Web of Science ®Google Scholar
• Rahikainen, J., F. González, and M. Á. Naya. 2020. An automated methodology to select functional co-simulation configurations. Multibody System Dynamics 48 (1):79–103. doi: 10.1007/s11044-019-09696-y.
   Web of Science ®Google Scholar
• Rahikainen, J., F. González, M. Á. Naya, J. Sopanen, and A. Mikkola. 2020. On the cosimulation of multibody systems and hydraulic dynamics. Multibody System Dynamics 50 (2):143–67. doi: 10.1007/s11044-020-09727-z.
   Web of Science ®Google Scholar
• Rahikainen, J., M. Kiani, J. Sopanen, P. Jalali, and A. Mikkola. 2018. Computationally efficient approach for simulation of multibody and hydraulic dynamics. Mechanism and Machine Theory 130:435–46. doi: 10.1016/j.mechmachtheory.2018.08.023.
   Web of Science ®Google Scholar
• Raoofian, A., A. Peiret, J. Kövecses, and M. Teichmann. 2022. Non-smooth unilateral reduced models for co-simulation of mechanical systems. Mechanism and Machine Theory 173:104829. doi: 10.1016/j.mechmachtheory.2022.104829.
   Web of Science ®Google Scholar
• Raoofian, A., A. Taghvaeipour, and A. Kamali E. 2022. Elastodynamic analysis of multibody systems and parametric mass matrix derivation. Mechanics Based Design of Structures and Machines 50 (10):3626–48. doi: 10.1080/15397734.2020.1815211.
   Web of Science ®Google Scholar
• Sadjina, S., and E. Pedersen. 2020. Energy conservation and coupling error reduction in non-iterative co-simulations. Engineering with Computers 36 (4):1579–87. doi: 10.1007/s00366-019-00783-4.
   Web of Science ®Google Scholar
• Sadjina, S., L. T. Kyllingstad, S. Skjong, and E. Pedersen. 2017. Energy conservation and power bonds in co-simulations: Non-iterative adaptive step size control and error estimation. Engineering with Computers 33 (3):607–20. doi: 10.1007/s00366-016-0492-8.
   Web of Science ®Google Scholar
• Samin, J. C., O. Brüls, J. F. Collard, L. Sass, and P. Fisette. 2007. Multiphysics modeling and optimization of mechatronic multibody systems. Multibody System Dynamics 18 (3):345–73. doi: 10.1007/s11044-007-9076-0.
   Web of Science ®Google Scholar
• Schierz, T., and M. Arnold. 2012. Stabilized overlapping modular time integration of coupled differential-algebraic equations. Applied Numerical Mathematics 62 (10):1491–502. doi: 10.1016/j.apnum.2012.06.020.
   Web of Science ®Google Scholar
• Schweizer, B., and D. Lu. 2014. Semi-implicit co-simulation approach for solver coupling. Archive of Applied Mechanics 84 (12):1739–69. doi: 10.1007/s00419-014-0883-5.
   Web of Science ®Google Scholar
• Schweizer, B., and D. Lu. 2015. Predictor/corrector co-simulation approaches for solver coupling with algebraic constraints. Journal of Applied Mathematics and Mechanics 95 (9):911–38. doi: 10.1002/zamm.201300191.
   Google Scholar
• Schweizer, B., D. Lu, and P. Li. 2016. Co-simulation method for solver coupling with algebraic constraints incorporating relaxation techniques. Multibody System Dynamics 36 (1):1–36. doi: 10.1007/s11044-015-9464-9.
   Web of Science ®Google Scholar
• Schweizer, B., P. Li, and D. Lu. 2015. Explicit and implicit cosimulation methods: Stability and convergence analysis for different solver coupling approaches. Journal of Computational and Nonlinear Dynamics 10 (5):051007. doi: 10.1115/1.4028503.
   Web of Science ®Google Scholar
• Tsai, F.-F., and E. J. Haug. 1991. Real-time multibody system dynamic simulation: Part II. A parallel algorithm and numerical results. Mechanics of Structures and Machines 19 (2):129–62. doi: 10.1080/08905459108905140.
   Web of Science ®Google Scholar
• Wojtyra, M. 2003. Multibody simulation model of human walking. Mechanics Based Design of Structures and Machines 31 (3):357–79. doi: 10.1081/SME-120022855.
   Web of Science ®Google Scholar
• Yoo, W.-S., K.-N. Kim, H.-W. Kim, and J.-H. Sohn. 2007. Developments of multibody system dynamics: Computer simulations and experiments. Multibody System Dynamics 18 (1):35–58. doi: 10.1007/s11044-007-9062-6.
   Web of Science ®Google Scholar
• Yusufoğlu, E. 2006. Numerical solution of duffing equation by the laplace decomposition algorithm. Applied Mathematics and Computation 177 (2):572–80. doi: 10.1016/j.amc.2005.07.072.
   Web of Science ®Google Scholar
• Zhang, R., H. Zhang, A. Zanoni, Q. Wang, and P. Masarati. 2021. A tight coupling scheme for smooth/non-smooth multibody co-simulation of a particle damper. Mechanism and Machine Theory 161:104181. doi: 10.1016/j.mechmachtheory.2020.104181.
   Web of Science ®Google Scholar