scholarly journals On the use of absolute interface coordinates in the floating frame of reference formulation for flexible multibody dynamics

2017 ◽  
Vol 43 (3) ◽  
pp. 193-208 ◽  
Author(s):  
Marcel Ellenbroek ◽  
Jurnan Schilder
Keyword(s):  
Multibody Dynamics ◽  
Flexible Multibody Dynamics ◽  
Frame Of Reference ◽  
Reference Formulation ◽  
Floating Frame Of Reference ◽  
Flexible Multibody ◽  
Floating Frame

Reduced-order thermomechanical modeling of multibody systems using floating frame of reference formulation

2018 ◽  
Vol 233 (3) ◽  
pp. 617-630
Author(s):  
Hiroki Yamashita ◽  
Rohit Arora ◽  
Hiroyuki Kanazawa ◽  
Hiroyuki Sugiyama
Keyword(s):  
Multibody Dynamics ◽  
Multibody Systems ◽  
Substantial Reduction ◽  
Frame Of Reference ◽  
Thermomechanical Coupling ◽  
Computational Time ◽  
Reference Formulation ◽  
Reduced Order ◽  
Floating Frame Of Reference ◽  
Floating Frame

In this study, a reduced-order thermomechanical coupling model, which accounts for the inertia coupling of the thermoelastic deformation and the large reference body motion, is proposed using the floating frame of reference formulation for the transient thermomechanical analysis of constrained multibody systems. In this approach, the reduced-order heat equations are fully embedded in the final form of the equations of motion. Accordingly, the transient thermal response as well as the resulting thermoelastic behavior of constrained multibody system can be predicted within the general multibody dynamics computer algorithm. It is demonstrated that appropriate selection of the thermal interface coordinates is crucial for describing the thermal modes (i.e. temperature distribution) induced by external heat sources using the Craig–Bampton component mode synthesis approach generalized for thermomechanical systems. Furthermore, a systematic procedure for imposing prescribed surface temperature given, for example, from thermal-fluid dynamics simulations is proposed for the thermomechanical floating frame of reference formulation. Using several numerical examples, simulation capabilities of the thermomechanical floating frame of reference formulation model are demonstrated for multibody dynamics applications. Numerical results show good agreement with the nonlinear thermomechanical finite element solutions considering the large rotational motion with substantial reduction in the model dimensionality and computational time.

scholarly journals Inertia forces and shape integrals in the floating frame of reference formulation

2017 ◽  
Vol 88 (3) ◽  
pp. 1953-1968 ◽  
Author(s):  
Grzegorz Orzechowski ◽  
Marko K. Matikainen ◽  
Aki M. Mikkola
Keyword(s):  
Frame Of Reference ◽  
Reference Formulation ◽  
Floating Frame Of Reference ◽  
Floating Frame ◽  
Inertia Forces

Consistent and Inertia-Shape-Integral-Free Invariants of the Floating Frame of Reference Formulation

2020 ◽  
Author(s):  
Andreas Zwölfer ◽  
Johannes Gerstmayr
Keyword(s):  
Continuum Mechanics ◽  
Equations Of Motion ◽  
Frame Of Reference ◽  
Reference Formulation ◽  
Lumped Mass ◽  
Floating Frame Of Reference ◽  
Mass Approximation ◽  
Floating Frame ◽  
Software Codes ◽  
Set Up

Abstract The conventional continuum-mechanics-based floating frame of reference formulation involves unhandy so-called inertia-shape-integrals in the equations of motion, which is why, commercial multibody software codes resort to a lumped mass approximation to avoid the evaluation of these integrals in their computer implementations. This paper recaps the conventional continuum mechanics floating frame of reference formulation and addresses its drawbacks by summarizing recent developments of the so-called nodal-based floating frame of reference formulation, which avoids inertia shape integrals ab initio, does not rely on a lumped mass approximation, and exhibits a way to calculate the so-called invariants, which are constant “ingredients” required to set up the equations of motion, in a consistent way.

scholarly journals A concise nodal-based derivation of the floating frame of reference formulation for displacement-based solid finite elements

2019 ◽  
Vol 49 (3) ◽  
pp. 291-313 ◽  
Author(s):  
Andreas Zwölfer ◽  
Johannes Gerstmayr
Keyword(s):  
Finite Element ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Frame Of Reference ◽  
Body Motion ◽  
Reference Formulation ◽  
Lumped Mass ◽  
Floating Frame Of Reference ◽  
Mass Approximation ◽  
Floating Frame

AbstractThe Floating Frame of Reference Formulation (FFRF) is one of the most widely used methods to analyze flexible multibody systems subjected to large rigid-body motion but small strains and deformations. The FFRF is conventionally derived via a continuum mechanics approach. This tedious and circuitous approach, which still attracts attention among researchers, yields so-called inertia shape integrals. These unhandy volume integrals, arising in the FFRF mass matrix and quadratic velocity vector, depend not only on the degrees of freedom, but also on the finite element shape functions. That is why conventional computer implementations of the FFRF are laborious and error prone; they require access to the algorithmic level of the underlying finite element code or are restricted to a lumped mass approximation. This contribution presents a nodal-based treatment of the FFRF to bypass these integrals. Each flexible body is considered in its spatially discretized state ab initio, wherefore the integrals are replaced by multiplications by a constant finite element mass matrix. Besides that, this approach leads to a simpler and concise but rigorous derivation of the equations of motion. The steps to obtain the inertia-integral-free equations of motion (in 2D and 3D spaces) are presented in a clear and comprehensive way; the final result provides ready-to-implement equations of motion without a lumped mass approximation, in contrast to the conventional formulation.

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