Steps Towards Non-Smooth Multibody Dynamics

2021 ◽  
Author(s):  
Friedrich Pfeiffer
Keyword(s):  
System Theory ◽  
Multibody Dynamics ◽  
Multibody System ◽  
Local Development ◽  
Impact Behavior ◽  
Unilateral Constraints ◽  
The Past ◽  
Bilateral Constraints ◽  
Large Systems ◽  
Contact And Impact

Abstract Before the background of many thoughts about contact and impact behavior with and without friction in the past centuries a comprehensive theory appeared not before the second half of the last century, mainly connected with the names of Moreau in Montpellier and Panagiotopoulos in Thessaloniki. My former Institute has been part of this evolution focusing on non-smooth multibody dynamics and on large systems. The local development from simple impact to complex contact systems including all possible contact details will be subject of the paper, considering also the necessary mathematical evolution from classical multibody system theory with bilateral constraints and single-valued forces to non-smooth multibody system theory with unilateral constraints and set-valued forces. Paper will be illustrated by practical examples.

Instantaneous impulses in multibody dynamics

2015 ◽  
Vol 22 (4) ◽  
pp. 581-635
Author(s):  
P Lidström
Keyword(s):  
Multibody Dynamics ◽  
Virtual Work ◽  
Mass Matrix ◽  
Full Rank ◽  
Rigid Bodies ◽  
Unilateral Constraints ◽  
Lagrange’S Equations ◽  
Bilateral Constraints ◽  
The Impact ◽  
Lagrange's Equations

This paper considers instantaneous impulses in multibody dynamics. Instantaneous impulses may act on the multibody from its exterior or they may appear in its interior as a consequence of two of its parts interacting by an impact imposed by a unilateral constraint. The theory is based on the Euler laws of instantaneous impulses, which may be seen as a complement to the Euler laws for regular motions. Based on these laws, and specific continuum properties of the quantities involved, local balance laws for momentum and moment of momentum, involving instantaneous impulses and introducing the Cauchy impulse tensor, are derived. Thermodynamical restrictions on the impulse tensor are formulated based on the dissipation inequality. By stating a principle of virtual work for instantaneous impulses, and demonstrating its equivalence to Euler’s laws, Lagrange’s equations are derived. Lagrange’s equations are convenient to use in the case of multibody dynamics containing rigid as well as flexible parts. A central theme of this paper is the discussion of the interaction between parts of the multibody and their relation to geometrical and kinematical constraints. This interaction is severely affected by the presence of friction, which is notoriously difficult to handle. In a preparation for this discussion we first consider the one-point impact between two rigid bodies. The importance of the so-called impact tensor for this problem is demonstrated. In order to be able to handle the impact laws of Poisson and Stonge, an impact process, governed by a system of ordinary differential equations, is defined. Within this model phenomena, such as slip stop, slip start and slip direction reversal, may be handled. For a multibody with an arbitrary number of parts and multiple impacts, the situation is much more complicated and certain simplifications have to be introduced. Equations of motion for a multibody, consisting of rigid parts and in the presence of ideal bilateral constraints and unilateral constraints involving friction, are formulated. Unique solutions are obtained, granted that the mass matrix of the multibody system is non-singular, the constraint matrices satisfy specific full rank conditions and that the friction is not too high.

The Political Economy of Local Governance in Yemen

2020 ◽  
Vol 13 (4) ◽  
pp. 45-69
Author(s):  
Benoit Challand ◽  
Joshua Rogers
Keyword(s):  
Political Economy ◽  
Political Culture ◽  
Local Governance ◽  
Local Development ◽  
The Political ◽  
The Past ◽  
Strong State ◽  
Self Help ◽  
Local Initiatives ◽  
Self Rule

This paper provides an historical exploration of local governance in Yemen across the past sixty years. It highlights the presence of a strong tradition of local self-rule, self-help, and participation “from below” as well as the presence of a rival, official, political culture upheld by central elites that celebrates centralization and the strong state. Shifts in the predominance of one or the other tendency have coincided with shifts in the political economy of the Yemeni state(s). When it favored the local, central rulers were compelled to give space to local initiatives and Yemen experienced moments of political participation and local development.

Flexible Multibody Dynamics Formulation by Hamilton’s Equations

2010 ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Multibody Dynamics ◽  
Multibody System ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Flexible Multibody Dynamics ◽  
Flexible Body ◽  
Flexible Multibody System ◽  
Generalized Coordinates ◽  
Flexible Multibody ◽  
The Matrix

Numerical solution of the dynamics equations of a flexible multibody system as represented by Hamilton’s canonical equations requires that its generalized velocities q˙ be solved from the generalized momenta p. The relation between them is p = J(q)q˙, where J is the system mass matrix and q is the generalized coordinates. This paper presents the dynamics equations for a generic flexible multibody system as represented by p˙ and gives emphasis to a systematic way of constructing the matrix J for solving q˙. The mass matrix is shown to be separable into four submatrices Jrr, Jrf, Jfr and Jff relating the joint momenta and flexible body mementa to the joint coordinate rates and the flexible body deformation coordinate rates. Explicit formulas are given for these submatrices. The equations of motion presented here lend insight to the structure of the flexible multibody dynamics equations. They are also a versatile alternative to the acceleration-based dynamics equations for modeling mechanical systems.

A Model for Sustaining Evidence-Based Practices in a Statewide System

2017 ◽  
Vol 98 (1) ◽  
pp. 18-26 ◽  
Author(s):  
Jason M. Lang ◽  
Kellie G. Randall ◽  
Michelle Delaney ◽  
Jeffrey J. Vanderploeg
Keyword(s):  
Public Health ◽  
Cognitive Behavioral Therapy ◽  
Quality Indicators ◽  
Behavioral Therapy ◽  
Health Impact ◽  
Evidence Based ◽  
Evidence Based Practices ◽  
The Public ◽  
The Past ◽  
Large Systems

Over the past 20 years, efforts have been made to broadly disseminate evidence-based practices (EBPs). However, the public health impact of EBPs has yet to be realized and most EBPs are not sustained. Few structured models exist for disseminating and sustaining EBPs across large systems. This article describes the EBP Dissemination and Support Center (DSC) model and how it was used to sustain trauma-focused cognitive behavioral therapy (TF-CBT) across Connecticut. More than 600 clinicians at 35 agencies have been trained and nearly all agencies have sustained TF-CBT for up to 9 years. More than 6,200 children have received TF-CBT and have shown improvements in outcomes and quality indicators. Recommendations are made for using or adapting the DSC model.

scholarly journals Evolution of management of local development processes (on the example of Bagrationovsky district of the Kaliningrad region)

2018 ◽  
Vol 170 ◽  
pp. 01132
Author(s):  
Andrey Gorokhov ◽  
Alexey Ignatyev ◽  
Vitaly Smirnov
Keyword(s):  
Pharmaceutical Company ◽  
Local Development ◽  
Living Environment ◽  
Positive Experience ◽  
Potential Mechanism ◽  
Federal Programs ◽  
Urban Settlement ◽  
The Past ◽  
Development Processes ◽  
Kaliningrad Region

The purpose of the study is to develop a potential mechanism for monitoring and motivating municipal authorities, based on the evolution of management of development processes. The paper describes the positive experience of management of local development processes on the example of the Bagrationovsky urban settlement, whose administration actively interacted with the pharmaceutical company “Infamed-K” located in Bagrationovsk. As a result, it was possible not only to ensure the participation of the settlement in various regional and federal programs on co-financing terms, fully pay off the past due debt that has occurred earlier, but also create a favorable living environment and solve many problems of the residents.

scholarly journals The Embeddedness of Social Sciences and Economics in Research on Resources

Resources ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 15
Author(s):  
Juan Uribe-Toril ◽  
José Luis Ruiz-Real ◽  
Jaime de Pablo Valenciano
Keyword(s):  
Social Sciences ◽  
State Of The Art ◽  
Local Development ◽  
The State ◽  
Special Issue ◽  
Continuous Review ◽  
The Past ◽  
Research Fields ◽  
Wide Range ◽  
Knowledge Area

Sustainability, local development, and ecology are keywords that cover a wide range of research fields in both experimental and social sciences. The transversal nature of this knowledge area creates synergies but also divergences, making a continuous review of the existing literature necessary in order to facilitate research. There has been an increasing number of articles that have analyzed trends in the literature and the state-of-the-art in many subjects. In this Special Issue of Resources, the most prestigious researchers analyzed the past and future of Social Sciences in Resources from an economic, social, and environmental perspective.

A General Purpose Formulation for Nonsmooth Dynamics With Finite Rotations: Application to the Woodpecker Toy

2020 ◽  
Vol 16 (3) ◽  
Author(s):  
Alejandro Cosimo ◽  
Federico J. Cavalieri ◽  
Javier Galvez ◽  
Alberto Cardona ◽  
Olivier Brüls
Keyword(s):  
Finite Element ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Horizontal Displacement ◽  
General Purpose ◽  
Nonsmooth Dynamics ◽  
Unilateral Constraints ◽  
Simulation Code ◽  
Frictional Contacts ◽  
Large Rotations

Abstract The aim of this work is to extend the finite element multibody dynamics approach to problems involving frictional contacts and impacts. The nonsmooth generalized-α (NSGA) scheme is adopted, which imposes bilateral and unilateral constraints both at position and velocity levels avoiding drift phenomena. This scheme can be implemented in a general purpose simulation code with limited modifications of pre-existing elements. The study of the woodpecker toy dynamics sets up a good example to show the capabilities of the NSGA scheme within the context of a general finite element framework. This example has already been studied by many authors who generally adopted a model with a minimal set of coordinates and small rotations. It is shown that good results are obtained using a general purpose finite element code for multibody dynamics, in which the equations of motion are assembled automatically and large rotations are easily taken into account. In addition, comparing results between different models of the woodpecker toy, the importance of modeling large rotations and the horizontal displacement of the woodpecker's sleeve is emphasized.

A Multibody System Model for Meshing Gears

2010 ◽  
Vol 44-47 ◽  
pp. 1273-1278 ◽  
Author(s):  
Liu Lei
Keyword(s):  
Multibody Dynamics ◽  
Multibody System ◽  
Gear Wheel ◽  
Numerical Approach ◽  
Computational Effort ◽  
Rigid Bodies ◽  
The Body ◽  
System Model ◽  
New Approach ◽  
Elastic Elements

As a type of numerical approach to dynamics of gears, multibody dynamics method can handle realistic cases of contact modeling with acceptable accuracy and considerably less computational effort. The ability to simulate contact between teeth has become an essential topic in multibody dynamics. Fully rigid method is not suited for a high quality of the analysis to take into account some elasticity in the model of meshing gear wheels. In our new approach the circumferentially rotatable rigid teeth and elastic elements composed of rotational spring-damper combinations are hereby put forward. The teeth and the body of each gear wheel are still regarded as rigid bodies, but they are connected with each other by elastic elements. Besides, Lankarani & Nikravesh Contact Model is utilized, which counts energy dissipation by means of viscous damping. Both large motions with revolutions and important elasticity are considered in this teeth-wheel multibody system model. Two examples are provided in which the simulation results of completely rigid method, the approach in [10], our new approach and finite element methods are compared. Comparisons indicate that our newly developed approach is more suitable for modeling multibody geared systems.

Kinematics for unilateral constraints in multibody dynamics

2016 ◽  
Vol 22 (8) ◽  
pp. 1654-1687
Author(s):  
P Lidström
Keyword(s):  
Multibody Dynamics ◽  
Distance Function ◽  
Contact Surface ◽  
Equations Of Motion ◽  
Time Derivative ◽  
Unilateral Constraint ◽  
Contact Forces ◽  
Unilateral Constraints ◽  
Constraint Forces ◽  
Friction Forces

This paper is concerned with the kinematics of unilateral constraints in multibody dynamics. These constraints are related to the contact between parts and the principle of impenetrability of matter and have the property that they may be active, in which case they give rise to constraint forces, or passive, in which case they do not give rise to constraint forces. In order to check whether the constraint is active or passive a distance function between parts of the multibody is required. The paper gives a rigorous definition of the distance function and derives certain of its properties. The unilateral constraint may then be expressed in terms of this distance function. The paper analyses the transitions from passive constraints to active and vice versa. Sufficient regularity of the transplacements of the parts and their boundary surfaces will lead to specific properties of the time derivative of the distance function. When the unilateral constraint is active then the parts are geometrically in contact and there is a certain contact surface that, in specific cases, may degenerate into a point. If the parts are in mechanical contact over the contact surface then there will be an interaction between the parts given by contact forces, such as normal and friction forces. Parts in contact may be at rest relative to one another, over the contact surface, or they may be in relative sliding motion. The transition from non-sliding contact to sliding and from sliding to non-sliding is discussed and necessary conditions on the relative velocity and the traction vector are derived. Appropriate complementary conditions are then formulated. These are instrumental when the technique of linear complementarity is used in order to find solutions to the equations of motion.

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