Reference Conditions and Substructuring Techniques in Flexible Multibody System Dynamics

2018 ◽  
Vol 13 (4) ◽  
Author(s):  
James J. O'Shea ◽  
Paramsothy Jayakumar ◽  
Dave Mechergui ◽  
Ahmed A. Shabana ◽  
Liang Wang
Keyword(s):  
Degrees Of Freedom ◽  
Multibody System ◽  
Deformable Body ◽  
Reference Conditions ◽  
Deformation Analysis ◽  
Reduction Techniques ◽  
Problem Dimension ◽  
Definition Of ◽  
Deformation Modes ◽  
Substructuring Techniques

The floating frame of reference (FFR) formulation is widely used in multibody system (MBS) simulations for the deformation analysis. Nonetheless, the use of elastic degrees-of-freedom (DOF) in the deformation analysis can increase significantly the problem dimension. For this reason, modal reduction techniques have been proposed in order to define a proper set of assumed body deformation modes. Crucial to the proper definition of these modes when the finite element (FE) FFR formulation is used is the concept of the reference conditions, which define the nature of the deformable body coordinate system. Substructuring techniques, such as the Craig–Bampton (CB) method, on the other hand, have been proposed for developing efficient models using an assembly of their lower order substructure models. In this study, the appropriateness and generality of using the CB method in MBS algorithms are discussed. It is shown that, when a set of reference conditions are not applied, the CB transformation leads to the free–free deformation modes. Because a square CB transformation is equivalent to a similarity transformation that does not alter the problem to be solved, the motivation of using the CB method in MBS codes to improve the solution is examined. This paper demonstrates that free–free deformation modes cannot be used in all applications, shedding light on the importance of the concept of the FE/FFR reference conditions. It is demonstrated numerically that a unique model resonance frequency is achieved using different modes associated with different reference conditions if the shapes are similar.

Shape Dynamics and the Linking Theory

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Line Element ◽  
Hamiltonian Formulation ◽  
Operational Definition ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Problem Of Time ◽  
Definition Of ◽  
Matter Fields

This chapter explains in detail the current Hamiltonian formulation of SD, and the concept of Linking Theory of which (GR) and SD are two complementary gauge-fixings. The physical degrees of freedom of SD are identified, the simple way in which it solves the problem of time and the problem of observables in quantum gravity are explained, and the solution to the problem of constructing a spacetime slab from a solution of SD (and the related definition of physical rods and clocks) is described. Furthermore, the canonical way of coupling matter to SD is introduced, together with the operational definition of four-dimensional line element as an effective background for matter fields. The chapter concludes with two ‘structural’ results obtained in the attempt of finding a construction principle for SD: the concept of ‘symmetry doubling’, related to the BRST formulation of the theory, and the idea of ‘conformogeometrodynamics regained’, that is, to derive the theory as the unique one in the extended phase space of GR that realizes the symmetry doubling idea.

Influence of Clearances and Thermal Effects on the Dynamic Behavior of Gear-Hydrodynamic Journal Bearing Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
R. Fargère ◽  
P. Velex
Keyword(s):  
Degrees Of Freedom ◽  
Integration Scheme ◽  
Time Step ◽  
Specific Element ◽  
Normal Contact ◽  
Contact Algorithm ◽  
Gear Teeth ◽  
Proposed Model ◽  
Elastic Couplings ◽  
Definition Of

A global model of mechanical transmissions is introduced which deals with most of the possible interactions between gears, shafts, and hydrodynamic journal bearings. A specific element for wide-faced gears with nonlinear time-varying mesh stiffness and tooth shape deviations is combined with shaft finite elements, whereas the bearing contributions are introduced based on the direct solution of Reynolds' equation. Because of the large bearing clearances, particular attention has been paid to the definition of the degrees-of-freedom and their datum. Solutions are derived by combining a time step integration scheme, a Newton–Raphson method, and a normal contact algorithm in such a way that the contact conditions in the bearings and on the gear teeth are simultaneously dealt with. A series of comparisons with the experimental results obtained on a test rig are given which prove that the proposed model is sound. Finally, a number of results are presented which show that parameters often discarded in global models such as the location of the oil inlet area, the oil temperature in the bearings, the clearance/elastic couplings interactions, etc. can be influential on static and dynamic tooth loading.

A Two-Dimensional Linear Assumed Strain Triangular Element for Finite Deformation Analysis

2005 ◽  
Vol 73 (6) ◽  
pp. 970-976 ◽  
Author(s):  
Fernando G. Flores
Keyword(s):  
Finite Deformation ◽  
Degrees Of Freedom ◽  
Yield Function ◽  
Triangular Element ◽  
Deformation Analysis ◽  
Elastic Model ◽  
Stress Strain ◽  
Metric Tensor ◽  
Assumed Strain ◽  
Non Linear

An assumed strain approach for a linear triangular element able to handle finite deformation problems is presented in this paper. The element is based on a total Lagrangian formulation and its geometry is defined by three nodes with only translational degrees of freedom. The strains are computed from the metric tensor, which is interpolated linearly from the values obtained at the mid-side points of the element. The evaluation of the gradient at each side of the triangle is made resorting to the geometry of the adjacent elements, leading to a four element patch. The approach is then nonconforming, nevertheless the element passes the patch test. To deal with plasticity at finite deformations a logarithmic stress-strain pair is used where an additive decomposition of elastic and plastic strains is adopted. A hyper-elastic model for the elastic linear stress-strain relation and an isotropic quadratic yield function (Mises) for the plastic part are considered. The element has been implemented in two finite element codes: an implicit static/dynamic program for moderately non-linear problems and an explicit dynamic code for problems with strong nonlinearities. Several examples are shown to assess the behavior of the present element in linear plane stress states and non-linear plane strain states as well as in axi-symmetric problems.

Interface Reduction in Craig-Bampton Component Mode Synthesis by Orthogonal Polynomial Series

2017 ◽  
Author(s):  
Luigi Carassale ◽  
Mirko Maurici
Keyword(s):  
Degrees Of Freedom ◽  
Axial Compressor ◽  
Component Mode Synthesis ◽  
Reduction Techniques ◽  
Interface Reduction ◽  
Reduction Methods ◽  
Interface Displacement ◽  
Polynomial Series ◽  
Efficient Representation

The component mode synthesis based on the Craig-Bampton method has two strong limitations that appear when the number of the interface degrees of freedom is large. First, the reduced-order model obtained is overweighed by many unnecessary degrees of freedom. Second, the reduction step may become extremely time consuming. Several interface reduction techniques addressed successfully the former problem, while the latter remains open. In this paper we tackle this latter problem through a simple interface-reduction technique based on an a-priory choice of the interface modes. An efficient representation of the interface displacement field is achieved adopting a set of orthogonal basis functions determined by the interface geometry. The proposed method is compared with other existing interface reduction methods on a case study regarding a rotor blade of an axial compressor.

A Light Weight Compliant Hand Mechanism With High Degrees of Freedom

2005 ◽  
Vol 127 (6) ◽  
pp. 934-945 ◽  
Author(s):  
Jason Potratz ◽  
Jingzhou Yang ◽  
Karim Abdel-Malek ◽  
Esteban Peña Pitarch ◽  
Nicole Grosland
Keyword(s):  
Degrees Of Freedom ◽  
Static Load ◽  
Current Control ◽  
Deformation Analysis ◽  
Dimensional Model ◽  
3 Dimensional ◽  
Wrist Flexor ◽  
Compression Spring ◽  
Extensor Muscles ◽  
Control Scheme

This paper presents the design and prototyping of an inherently compliant lightweight hand mechanism. The hand mechanism itself has 15 degrees of freedom and five fingers. Although the degrees of freedom in each finger are coupled, reducing the number of independent degrees of freedom to 5, the 15 degrees of freedom of the hand could potentially be individually actuated. Each joint consists of a novel flexing mechanism that is based on the loading of a compression spring in the axial and transverse direction via a cable and conduit system. Currently, a bench top version of the prototype is being developed; the three joints of each finger are coupled together to simplify the control system. The current control scheme under investigation simulates a control scheme where myoelectric signals in the wrist flexor and extensor muscles are converted in to x and y coordinates on a control scheme chart. Static load-deformation analysis of finger segments is studied based on a 3-dimensional model without taking the stiffener into account, and the experiment validates the simulation.

Analytical Model for Rockfall Protection Galleries - a Blind Prediction of Test Results and Conclusion

2011 ◽  
Vol 82 ◽  
pp. 722-727 ◽  
Author(s):  
Kristian Schellenberg ◽  
Norimitsu Kishi ◽  
Hisashi Kon-No
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Test Results ◽  
Blind Prediction ◽  
Proposed Model ◽  
Input Parameters ◽  
Scale Test ◽  
Definition Of ◽  
Protective Structures ◽  
Cushion Layer

A system of multiple degrees of freedom composed out of three masses and three springs has been presented in 2008 for analyzing rockfall impacts on protective structures covered by a cushion layer. The model has then been used for a blind prediction of a large-scale test carried out in Sapporo, Japan, in November 2009. The test results showed substantial deviations from the blind predictions, which led to a deeper evaluation of the model input parameters showing a significant influence of the modeling properties for the cushion layer on the overall results. The cushion properties include also assumptions for the loading geometry and the definition of the parameters can be challenging. This paper introduces the test setup and the selected parameters in the proposed model for the blind prediction. After comparison with the test results, adjustments in the input parameters in order to match the test results have been evaluated. Conclusions for the application of the model as well as for further model improvements are drawn.

On the Dynamic Isotropy of Mechanisms With Two Degrees of Freedom

2005 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Closed Curves ◽  
Special Cases ◽  
Dynamic Performances ◽  
Definition Of ◽  
Geometric Locus

The comparison of mechanisms with different topology or with different geometry, but with the same topology, is a necessary operation during the design of a machine sized for a given task. Therefore, tools that evaluate the dynamic performances of a mechanism are welcomed. This paper deals with the dynamic isotropy of 2-dof mechanisms starting from the definition introduced in a previous paper. In particular, starting from the condition that identifies the dynamically isotropic configurations, it shows that, provided some special cases are not considered, 2-dof mechanisms have at most a finite number of isotropic configurations. Moreover, it shows that, provided the dynamically isotropic configurations are excluded, the geometric locus of the configuration space that collects the points associated to configurations with the same dynamic isotropy is constituted by closed curves. This results will allow the classification of 2-dof mechanisms from the dynamic-isotropy point of view, and the definition of some methodologies for the characterization of the dynamic isotropy of these mechanisms. Finally, examples of applications of the obtained results will be given.

scholarly journals Integration of Nonlinear Models of Flexible Body Deformation in Multibody System Dynamics

2013 ◽  
Vol 9 (1) ◽  
Author(s):  
Martin Schulze ◽  
Stefan Dietz ◽  
Bernhard Burgermeister ◽  
Andrey Tuganov ◽  
Holger Lang ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Multibody System ◽  
Nonlinear Models ◽  
Equations Of Motion ◽  
Flexible Structures ◽  
General Purpose ◽  
Cosserat Rod ◽  
Rod Model ◽  
Flexible Deformation ◽  
Run Up

Current challenges in industrial multibody system simulation are often beyond the classical range of application of existing industrial simulation tools. The present paper describes an extension of a recursive order-n multibody system (MBS) formulation to nonlinear models of flexible deformation that are of particular interest in the dynamical simulation of wind turbines. The floating frame of reference representation of flexible bodies is generalized to nonlinear structural models by a straightforward transformation of the equations of motion (EoM). The approach is discussed in detail for the integration of a recently developed discrete Cosserat rod model representing beamlike flexible structures into a general purpose MBS software package. For an efficient static and dynamic simulation, the solvers of the MBS software are adapted to the resulting class of MBS models that are characterized by a large number of degrees of freedom, stiffness, and high frequency components. As a practical example, the run-up of a simplified three-bladed wind turbine is studied where the dynamic deformations of the three blades are calculated by the Cosserat rod model.

Updating of Finite Element Models Based on a Double Condensation Procedure Using Frequency Response Functions Data

1995 ◽  
Author(s):  
Rémi Berriet ◽  
René Fillod ◽  
Noureddine Bouhaddi
Keyword(s):  
Frequency Response ◽  
Degrees Of Freedom ◽  
Noise Pollution ◽  
Test Case ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Measured Frequency ◽  
Modal Damping ◽  
Applied Forces ◽  
Definition Of

Abstract In order to take into account information from test data, not only at the resonances, but also in the other parts of the measured frequency spectrum, it is of interest to use directly measured Frequency Response Functions (FRF) instead of modal data. We also avoid by this way an experimental modal analysis. In return we have to introduce damping terms into the analytical model, we have to weight the FRF data in a systematic manner and to compute simultaneously a large amount of data. The presented procedure analyses overall these three aspects: definition of modal damping parameters, definition of weighted FRF data and condensation of the problem. This last notion is particularly pointed out. The condensation is performed in two steps : a static condensation of the model on the degrees of freedom corresponding to the location of the sensors, and a simultaneous condensation of experimental and analytical FRF data by a common transformation matrix. The first applications are performed on a simulated test case with large stiffness, mass and modal damping perturbations introduced in the initial model as well as strong noise pollution of measured responses and applied forces.

The DDA Method

2016 ◽  
pp. 90-102
Author(s):  
Katalin Bagi
Keyword(s):  
Numerical Integration ◽  
Displacement Field ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Short Overview ◽  
Abrupt Changes ◽  
Discontinuous Deformation ◽  
Iteration Technique

“DDA” stands for “Discontinuous Deformation Analysis”, suggesting that the displacement field of the analyzed domain shows abrupt changes on the element boundaries in the model. This chapter introduces the theoretical fundaments of DDA: mechanical characteristics of the elements together with the basic degrees of freedom, contact behavior, the equations of motion and their numerical integration with the help of Newmark's beta-method taking into account contact creation, loss and sliding with the help of an open-close iteration technique. Finally, a short overview on practical and scientific applications for masonry structures is given.

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