Lagrangian Bond Graphs for Solid Continuum Dynamics Modeling

1994 ◽  
Vol 116 (2) ◽  
pp. 178-192 ◽  
Author(s):  
E. P. Fahrenthold ◽  
J. D. Wargo
Keyword(s):  
Finite Element ◽  
Bond Graph ◽  
Dynamics Modeling ◽  
Bond Graphs ◽  
Element Discretization ◽  
Large Order ◽  
Wide Range ◽  
Bond Graph Modeling ◽  
Continuum Dynamics ◽  
Fixed Bond

The limitations of existing continuum bond graph modeling techniques have effectively precluded their use in large order problems, where nonrepetitive graph structures and causal patterns are normally present. As a result, despite extensive publication of bond graph models for continuous systems simulations, bond graph methods have not offered a viable alternative to finite element analysis for the vast majority of practical problems. However, a new modeling approach combining Lagrangian (mass fixed) bond graphs with a selected finite element discretization scheme allows for direct simulation of a wide range of large order solid continuum dynamics problems. With appropriate modifications, including the use of Eulerian (space fixed) bond graphs, the method may be extended to include fluid dynamics modeling.

System Dynamics Modeling of Porous Media

1997 ◽  
Vol 119 (2) ◽  
pp. 251-259 ◽  
Author(s):  
E. P. Fahrenthold ◽  
M. Venkataraman
Keyword(s):  
Porous Media ◽  
Reference Frames ◽  
Numerical Models ◽  
Bond Graph ◽  
Dynamics Modeling ◽  
Element Discretization ◽  
Highly Nonlinear ◽  
Wide Range ◽  
Engineering Problems ◽  
Bond Graph Theory

A wide range of engineering problems involve porous media modeling. General porous media models are highly nonlinear, geometrically complex, and must account for energy transfer between fluid and solid constituents normally modeled in distinct Lagrangian and Eulerian reference frames. Combining finite element discretization techniques with bond graph methods greatly simplifies the model formulation process, as compared to alternative schemes based on weighted residual solutions of the governing partial differential equations. The result generalizes existing numerical models of porous media and current network thermodynamics/bond graph theory.

Some Key Issues in Using Bond Graphs and Genetic Programming for Mechatronic System Design

2001 ◽  
Author(s):  
R. C. Rosenberg ◽  
E. D. Goodman ◽  
Kisung Seo
Keyword(s):  
Genetic Programming ◽  
System Design ◽  
Design Space ◽  
Bond Graph ◽  
Mechatronic System ◽  
Bond Graphs ◽  
Mechatronic Systems ◽  
Energy Behavior ◽  
Key Issues ◽  
Bond Graph Modeling

Abstract Mechatronic system design differs from design of single-domain systems, such as electronic circuits, mechanisms, and fluid power systems, in part because of the need to integrate the several distinct domain characteristics in predicting system behavior. The goal of our work is to develop an automated procedure that can explore mechatronic design space in a topologically open-ended manner, yet still find appropriate configurations efficiently enough to be useful. Our approach combines bond graphs for model representation with genetic programming for generating suitable design candidates as a means of exploring the design space. Bond graphs allow us to capture the common energy behavior underlying the several physical domains of mechatronic systems in a uniform notation. Genetic programming is an effective way to generate design candidates in an open-ended, but statistically structured, manner. Our initial goal is to identify the key issues in merging the bond graph modeling tool with genetic programming for searching. The first design problem we chose is that of finding a model that has a specified set of eigenvalues. The problem can be studied using a restricted set of bond graph elements to represent suitable topologies. We present the initial results of our studies and identify key issues in advancing the approach toward becoming an effective and efficient open-ended design tool for mechatronic systems.

scholarly journals Bond graph modelling of the cardiac action potential: implications for drift and non-unique steady states

2018 ◽  
Vol 474 (2214) ◽  
pp. 20180106 ◽  
Author(s):  
Michael Pan ◽  
Peter J. Gawthrop ◽  
Kenneth Tran ◽  
Joseph Cursons ◽  
Edmund J. Crampin
Keyword(s):  
Action Potential ◽  
Conservation Laws ◽  
Cardiac Electrophysiology ◽  
Bond Graph ◽  
Steady States ◽  
Cardiac Action Potential ◽  
Bond Graphs ◽  
Charge Conservation ◽  
Cardiac Action ◽  
Wide Range

Mathematical models of cardiac action potentials have become increasingly important in the study of heart disease and pharmacology, but concerns linger over their robustness during long periods of simulation, in particular due to issues such as model drift and non-unique steady states. Previous studies have linked these to violation of conservation laws, but only explored those issues with respect to charge conservation in specific models. Here, we propose a general and systematic method of identifying conservation laws hidden in models of cardiac electrophysiology by using bond graphs, and develop a bond graph model of the cardiac action potential to study long-term behaviour. Bond graphs provide an explicit energy-based framework for modelling physical systems, which makes them well suited for examining conservation within electrophysiological models. We find that the charge conservation laws derived in previous studies are examples of the more general concept of a ‘conserved moiety’. Conserved moieties explain model drift and non-unique steady states, generalizing the results from previous studies. The bond graph approach provides a rigorous method to check for drift and non-unique steady states in a wide range of cardiac action potential models, and can be extended to examine behaviours of other excitable systems.

Eulerian Bond Graphs for Fluid Continuum Dynamics Modeling

1996 ◽  
Vol 118 (1) ◽  
pp. 48-57 ◽  
Author(s):  
E. P. Fahrenthold ◽  
M. Venkataraman
Keyword(s):  
Compressible Flows ◽  
System Modeling ◽  
General Purpose ◽  
Dynamics Modeling ◽  
Modeling Tools ◽  
Element Discretization ◽  
Inertia Effects ◽  
Flow Geometry ◽  
Viscous Compressible Flows ◽  
Continuum Dynamics

The development of high resolution, general purpose models of viscous, compressible flows is extremely difficult with existing system dynamics modeling tools. Published work admits to significant limitations, with regards to the treatment of flow geometry, inertia effects, or mass and energy convection. Combining a finite element discretization scheme with a bond graph based model formulation procedure provides a very general purpose tool for continuum fluid system modeling.

scholarly journals Simultaneous Kinematic and Contact Force Modeling of a Human Finger Tendon System Using Bond Graphs and Robotic Validation

2019 ◽  
Vol 142 (3) ◽  
Author(s):  
James A. Tigue ◽  
Raymond J. King ◽  
Stephen A. Mascaro
Keyword(s):  
Bond Graph ◽  
Contact Forces ◽  
Free Motion ◽  
Force Transmission ◽  
Bond Graphs ◽  
Moment Arms ◽  
Static Contact ◽  
Surface Contact ◽  
Bond Graph Modeling ◽  
Contact Experiments

Abstract This paper aims to use bond graph modeling to create the most comprehensive finger tendon model and simulation to date. Current models are limited to either free motion without external contact or fixed finger force transmission between tendons and fingertip. The forward dynamics model, presented in this work, simultaneously simulates the kinematics of tendon-finger motion and contact forces of a central finger given finger tendon inputs. The model equations derived from bond graphs are accompanied by nonlinear relationships modeling the anatomical complexities of moment arms, tendon slacking, and joint range of motion (ROM). The structure of the model is validated using a robotic testbed, Utah's Anatomically correct Robotic Testbed (UART) finger. Experimental motion of the UART finger during free motion (no external contact) and surface contact are simulated using the bond graph model. The contact forces during the surface contact experiments are also simulated. On average, the model was able to predict the steady-state pose of the finger with joint angle errors less than 6 deg across both free motion and surface contact experiments. The static contact forces were accurately predicted with an average of 11.5% force magnitude error and average direction error of 12 deg.

Bond Graph Modeling and Simulating of 3 RPR Planar Parallel Manipulator

2014 ◽  
Author(s):  
Cheng Yin ◽  
Shengqi Jian ◽  
Md. Hassan Faghih ◽  
Md. Toufiqul Islam ◽  
Luc Rolland
Keyword(s):  
Parallel Manipulator ◽  
High Speed ◽  
Reference Frames ◽  
Bond Graph ◽  
Dynamics Simulation ◽  
Bond Graphs ◽  
End Effector ◽  
Planar Parallel Manipulator ◽  
Bond Graph Modeling ◽  
Graph System

A 3-RPR planar parallel robot is a kind of planar mechanisms, which can work at high speed, with high accuracy and high rigidity. In this paper, a multi-body bond graph system will be built for the 3-RPR planar parallel manipulator (PPM), along with 3 PID controllers which give commands to 3 DC motors respectively. The advantage of bond graphs is that they can integrate different types of dynamics systems, the manipulator, the control and the motor can be modelled and simulated altogether in the same process. Bond graph will be established for each rigid body with body-fixed coordinate’s reference frames, which are connected with parasitic elements (damping and compliance) to each other. The PID set-point signals are generated by the explicit inverse kinematic equations. The 3 prismatic lengths constitute the measured feedback signals. In order to make the end-effector reach the ideal position with target orientation, the three links should reach the target lengths simultaneously. In this study, the dynamics simulation of 3-RPR PPM is conducted after building the bond graph system. As the 3 motors are working simultaneously and independently, the end-effector will arrive to the expected position. Finally, the bond graph and control system are validated with the compiled results and 3D animation. Force plot and torque plot will be generated as dynamics performance. Moreover, kinematics of manipulators are also calculated using bond graph. Eventually, bond graphs are shown to be effective in solving not only dynamic but also kinematic problems.

Finite element implementation of the eigenfunction series solution for transient heat conduction problems with low Biot number

2011 ◽  
Vol 226 (6) ◽  
pp. 1579-1588 ◽  
Author(s):  
A Al-Shabibi ◽  
J R Barber
Keyword(s):  
Finite Element ◽  
Heat Conduction ◽  
Heat Loss ◽  
Biot Number ◽  
Transient Heat Conduction ◽  
Attractive Alternative ◽  
Small Subset ◽  
Element Discretization ◽  
Transient Heat Conduction Problem ◽  
Wide Range

Analytical solutions to transient heat conduction problems are often obtained by superposition of a particular solution (often the steady-state solution) and an eigenfunction series, representing the terms that decay exponentially with time. Here, a finite element realization of this method is presented in which conventional finite element discretization is used for the spatial distribution of temperature and analytical methods for the time dependence. This leads to a linear eigenvalue problem whose solution then enables a general numerical model of the transient system to be created. The method is an attractive alternative to conventional time-marching schemes, particularly in cases where it is desired to explore the effect of a wide range of operating parameters. The method can be applied to any transient heat conduction problem, but particular attention is paid to the case where the Biot number is small compared with unity and where the evolution of the system is very close to that with zero heat loss from the exposed surfaces. This situation arises commonly in machines such as brakes and clutches which experience occasional short periods of intense heating. Numerical examples show that with typical parameter values, the simpler zero heat loss solution provides very good accuracy. One also shows that good approximations can be achieved using a relatively small subset of the eigenvectors of the problem.

Dynamical Models for Multidimensional Structures Using Bond Graphs

1980 ◽  
Vol 102 (3) ◽  
pp. 180-187 ◽  
Author(s):  
D. L. Margolis
Keyword(s):  
Finite Element ◽  
Dynamic System ◽  
Finite Element Methods ◽  
Bond Graph ◽  
Dynamical Models ◽  
Bond Graphs ◽  
Long Wavelength ◽  
Lawrence Livermore Laboratory

Bond graphs are used to construct finite mode, long wavelength models of multidimensional structures. These structures are, in some cases, either too large or constructed from so many physical pieces that complete modeling using finite element methods is prohibited. Bond graph development for this type of dynamic system is given. The technique is demonstrated for the Lawrence Livermore Laboratory Shiva-Nova laser spaceframe.

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