Modeling Contact/Impact in Hybrid Parameter Multiple Body Mechanical Systems: Extensions for Higher Order Continuum Models

1995 ◽  
Author(s):  
Alan A. Barhorst
Keyword(s):  
Mechanical Systems ◽  
Higher Order ◽  
Continuum Models ◽  
Timoshenko Beams ◽  
Constrained Motion ◽  
Contact Impact ◽  
Systematic Formulation ◽  
Impact Motion ◽  
Hybrid Differential Equations ◽  
The Continuum

Abstract In recent work the author presented a systematic formulation of hybrid parameter multiple body mechanical systems undergoing contact/impact motion. The method rigorously modeled all motion regimes of hybrid multiple body systems (i.e. free motion, contact/impact motion, and constrained motion), utilizing minimal sets of hybrid differential equations. The contact/impact regime was modeled via the idea of instantaneous non-holonomic constraint application. The technique previously presented did not include the possibility of continuum assumptions along the lines of Timoshenko beams, higher order plate theories, or rational theories considering intrinsic spin-inertia. In this paper, the above mentioned method is extended to include the higher order continuum assumptions which eliminates some of the continuum shortfalls from the previous work.

Contact/Impact in Hybrid Parameter Multiple Body Mechanical Systems—Extensions for Higher-Order Continuum Models

1998 ◽  
Vol 120 (1) ◽  
pp. 142-144 ◽  
Author(s):  
Alan A. Barhorst
Keyword(s):  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Higher Order ◽  
Constrained Motion ◽  
Momentum Exchange ◽  
Contact Impact ◽  
Systematic Formulation ◽  
Impact Motion ◽  
Boundary Equations ◽  
Hybrid Differential Equations

In recent work the author presented a systematic formulation of hybrid parameter multiple body mechanical systems (HPMBS) undergoing contact/impact motion. The method rigorously models all motion regimes of hybrid multiple body systems (i.e., free motion, contact/impact motion, and constrained motion), utilizing minimal sets of hybrid differential equations; Lagrange multipliers are not required. The contact/impact regime was modeled via the idea of instantaneously applied nonholonomic constraints. The technique previously presented did not include the possibility of continuum assumptions along the lines of Timoshenko beams, higher order plate theories, or rational theories considering intrinsic spin-inertia. In this technical brief, the above-mentioned method is extended to include the higher-order continuum assumptions which eliminates the continuum shortfalls from the previous work. The main contributions of this work include: 1) the previous work is rigorously extended, and 2) the fact that coefficients of restitution are not required for modeling the momentum exchange between motion regimes of HPMBS. The field and boundary equations provide the needed extra equations that are used to supply post-collision pointwise relationships for the generalized velocities and velocity fields.

New Formulations on Acceleration Energies in Analytical Dynamics

2016 ◽  
Vol 823 ◽  
pp. 43-48
Author(s):  
Iuliu Negrean ◽  
Kalman Kacso ◽  
Claudiu Schonstein ◽  
Adina Duca ◽  
Florina Rusu ◽  
...  
Keyword(s):  
Dynamic Behavior ◽  
Fast Moving ◽  
Mechanical Systems ◽  
Higher Order ◽  
Dynamic Study ◽  
Final Part ◽  
Transient Phase ◽  
Dynamic Aspect ◽  
Analytical Dynamics ◽  
Time Variations

This paper presents new formulations on the higher order motion energies that are applied in the dynamic study of multibody mechanical systems in keeping with the researches of the main author. The analysis performed in this paper highlights the importance of motion energies of higher order in the study of dynamic behavior of fast moving mechanical systems, as well as in transient phase of motion. In these situations, are developed higher order time variations of the linear and angular accelerations. As a result, in the final part of this paper is presented an application that emphasizes this essential dynamic aspect regarding the higher order acceleration energies.

scholarly journals Anisotropic damage for higher order continuum models

PAMM ◽  
2005 ◽  
Vol 5 (1) ◽  
pp. 331-332 ◽  
Author(s):  
Tobias Ebinger ◽  
Holger Steeb ◽  
Stefan Diebels
Keyword(s):  
Higher Order ◽  
Continuum Models ◽  
Anisotropic Damage

scholarly journals Murray’s law for discrete and continuum models of biological networks

2019 ◽  
Vol 29 (12) ◽  
pp. 2359-2376
Author(s):  
Jan Haskovec ◽  
Peter Markowich ◽  
Giulia Pilli
Keyword(s):  
Biological Networks ◽  
Discrete Model ◽  
Continuum Model ◽  
Transportation Network ◽  
Continuum Models ◽  
Scaling Relation ◽  
Murray's Law ◽  
Murray’S Law ◽  
Rectangular Mesh ◽  
The Continuum

We demonstrate the validity of Murray’s law, which represents a scaling relation for branch conductivities in a transportation network, for discrete and continuum models of biological networks. We first consider discrete networks with general metabolic coefficient and multiple branching nodes and derive a generalization of the classical 3/4-law. Next we prove an analogue of the discrete Murray’s law for the continuum system obtained in the continuum limit of the discrete model on a rectangular mesh. Finally, we consider a continuum model derived from phenomenological considerations and show the validity of the Murray’s law for its linearly stable steady states.

Dynamics of Mechanical Systems and the Generalized Free-Body Diagram—Part I: General Formulation

2008 ◽  
Vol 75 (6) ◽  
Author(s):  
József Kövecses
Keyword(s):  
Configuration Space ◽  
Dynamic Equilibrium ◽  
Mechanical Systems ◽  
Constrained Systems ◽  
Dynamic Equations ◽  
Analytical Mechanics ◽  
Constrained Motion ◽  
Equilibrium Equations ◽  
Free Body Diagram ◽  
Free Body

In this paper, we generalize the idea of the free-body diagram for analytical mechanics for representations of mechanical systems in configuration space. The configuration space is characterized locally by an Euclidean tangent space. A key element in this work relies on the relaxation of constraint conditions. A new set of steps is proposed to treat constrained systems. According to this, the analysis should be broken down to two levels: (1) the specification of a transformation via the relaxation of the constraints; this defines a subspace, the space of constrained motion; and (2) specification of conditions on the motion in the space of constrained motion. The formulation and analysis associated with the first step can be seen as the generalization of the idea of the free-body diagram. This formulation is worked out in detail in this paper. The complement of the space of constrained motion is the space of admissible motion. The parametrization of this second subspace is generally the task of the analyst. If the two subspaces are orthogonal then useful decoupling can be achieved in the dynamics formulation. Conditions are developed for this orthogonality. Based on this, the dynamic equations are developed for constrained and admissible motions. These are the dynamic equilibrium equations associated with the generalized free-body diagram. They are valid for a broad range of constrained systems, which can include, for example, bilaterally constrained systems, redundantly constrained systems, unilaterally constrained systems, and nonideal constraint realization.

scholarly journals Higher order continuum models for cellular materials including damage

PAMM ◽  
2004 ◽  
Vol 4 (1) ◽  
pp. 276-277
Author(s):  
Tobias Ebinger ◽  
Holger Steeb ◽  
Stefan Diebels
Keyword(s):  
Cellular Materials ◽  
Higher Order ◽  
Continuum Models

Atomically Informed Continuum Models for the Elastic Contact Properties of Hollow and Coated Rigid Cylinders at the Nanoscale

2017 ◽  
Vol 84 (3) ◽  
Author(s):  
Leon Gorelik ◽  
Dan Mordehai
Keyword(s):  
Contact Stiffness ◽  
Md Simulations ◽  
Atomic Scale ◽  
Continuum Models ◽  
Elastic Contact ◽  
Pressure Profiles ◽  
Hollow Cylinders ◽  
Coated Surfaces ◽  
The One ◽  
The Continuum

Understanding the mechanical properties of contacts at the nanoscale is key to controlling the strength of coated surfaces. In this work, we explore to which extent existing continuum models describing elastic contacts with coated surfaces can be extended to the nanoscale. Molecular dynamics (MD) simulations of hollow cylinders or coated rigid cylinders under compression are performed and compared with models at the continuum level, as two representative extreme cases of coating which is substantially harder or softer than the substrate, respectively. We show here that the geometry of the atomic-scale contact is essential to capture the contact stiffness, especially for hollow cylinders with high relative thicknesses and for coated rigid cylinders. The contact pressure profiles in atomic-scale contacts are substantially different than the one proposed in the continuum models for rounded contacts. On the basis of these results, we formulate models whose solution can be computed analytically for the contact stiffness in the two extreme cases, and show how to bridge between the atomic and continuum scales with atomically informed geometry of the contact.

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