Sensitivity Analysis of Dynamic Equilibrium Positions in Multibody Systems Undergoing Prescribed Rotational Motions

2007 ◽  
Author(s):  
Dong Hwan Choi ◽  
Hong Hee Yoo ◽  
Jonathan A. Wickert
Keyword(s):  
Finite Difference ◽  
Multibody Systems ◽  
Present Method ◽  
Dynamic Equilibrium ◽  
Step Size ◽  
Sensors And Actuators ◽  
Design Variables ◽  
Dynamic Equilibrium State ◽  
Rotational Motions ◽  
Engineered Systems

Multibody systems that undergo a prescribed rotational motion arise in such engineered systems as robots, spacecraft, propulsion and power generation systems, and certain sensors and actuators. The sensitivity of the system’s response to changes in the design variables is important for optimization and trade-off studies, as well as for understanding the implications of manufacturing tolerances. A general formulation is developed for analytically calculating the first-order design sensitivities of coordinate values for a multibody system’s dynamic equilibrium state during prescribed rotational motions. The method is based upon the use of relative coordinates, and a velocity transformation technique, and it is applicable to multibody systems having open or closed loop configurations. To illustrate effectiveness, accuracy, and computational efficiency, the present method is applied in three examples, and the sensitivities obtained analytically are compared with those obtained by the standard finite difference method. The finite difference approach is particularly sensitive to the choice of step size near a critical speed, and its implementation is generally more costly that the present method. In particular, there is a zero-sensitivity point at which the equilibrium configuration is insensitive to small perturbations in the design parameter’s value. That condition can be a useful design point to the extent that manufacturing tolerance and variation in design parameter’s values have no effect on dynamic equilibrium positions.

Efficient Sensitivity Analysis for Multibody Dynamics Systems Using an Iterative Steps Method With Application in Topology Optimization

2011 ◽  
Author(s):  
Guang Dong ◽  
Zheng-Dong Ma ◽  
Gregory Hulbert ◽  
Noboru Kikuchi ◽  
Sudhakar Arepally ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Multibody Dynamics ◽  
Optimization Problem ◽  
Finite Difference Methods ◽  
Analysis Method ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Sensitivity Analysis Method ◽  
Rotational Motions

Efficient and reliable sensitivity analyses are critical for topology optimization, especially for multibody dynamics systems, because of the large number of design variables and the complexities and expense in solving the state equations. This research addresses a general and efficient sensitivity analysis method for topology optimization with design objectives associated with time dependent dynamics responses of multibody dynamics systems that include nonlinear geometric effects associated with large translational and rotational motions. An iterative sensitivity analysis relation is proposed, based on typical finite difference methods for the differential algebraic equations (DAEs). These iterative equations can be simplified for specific cases to obtain more efficient sensitivity analysis methods. Since finite difference methods are general and widely used, the iterative sensitivity analysis is also applicable to various numerical solution approaches. The proposed sensitivity analysis method is demonstrated using a truss structure topology optimization problem with consideration of the dynamic response including large translational and rotational motions. The topology optimization problem of the general truss structure is formulated using the SIMP (Simply Isotropic Material with Penalization) assumption for the design variables associated with each truss member. It is shown that the proposed iterative steps sensitivity analysis method is both reliable and efficient.

A Strategy to Accelerate the Numerical Integration in the Dynamic Simulation of Multibody Systems

1997 ◽  
Author(s):  
Jesús Cardenal ◽  
Javier Cuadrado ◽  
Eduardo Bayo
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Stiff Systems ◽  
Step Size ◽  
Step Method ◽  
Integral Of Motion ◽  
Time Step ◽  
Time Step Size ◽  
Variable Time ◽  
Numerical Integrator

Abstract This paper presents a multi-index variable time step method for the integration of the equations of motion of constrained multibody systems in descriptor form. The basis of the method is the augmented Lagrangian formulation with projections in index-3 and index-1. The method takes advantage of the better performance of the index-3 formulation for large time steps and of the stability of the index-1 for low time steps, and automatically switches from one method to the other depending on the required accuracy and values of the time step. The variable time stepping is accomplished through the use of an integral of motion, which in the case of conservative systems becomes the total energy. The error introduced by the numerical integrator in the integral of motion during consecutive time steps provides a good measure of the local integration error, and permits a simple and reliable strategy for varying the time step. Overall, the method is efficient and powerful; it is suitable for stiff and non-stiff systems, robust for all time step sizes, and it works for singular configurations, redundant constraints and topology changes. Also, the constraints in positions, velocities and accelerations are satisfied during the simulation process. The method is robust in the sense that becomes more accurate as the time step size decreases.

Design Sensitivity Analysis of Nonlinear Multidisciplinary Multibody Systems in the MIXEDMODELS Platform

2007 ◽  
Author(s):  
Shilpa A. Vaze ◽  
Prakash Krishnaswami ◽  
James DeVault
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Systems ◽  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
The State ◽  
Design Sensitivity Analysis ◽  
Design Parameters ◽  
State Variables ◽  
Sensitivity Coefficients ◽  
Design Variables

Most state-of-the-art multibody systems are multidisciplinary and encompass a wide range of components from various domains such as electrical, mechanical, hydraulic, pneumatic, etc. The design considerations and design parameters of the system can come from any of these domains or from a combination of these domains. In order to perform analytical design sensitivity analysis on a multidisciplinary system (MDS), we first need a uniform modeling approach for this class of systems to obtain a unified mathematical model of the system. Based on this model, we can derive a unified formulation for design sensitivity analysis. In this paper, we present a modeling and design sensitivity formulation for MDS that has been successfully implemented in the MIXEDMODELS (Multidisciplinary Integrated eXtensible Engine for Driving Metamodeling, Optimization and DEsign of Large-scale Systems) platform. MIXEDMODELS is a unified analysis and design tool for MDS that is based on a procedural, symbolic-numeric architecture. This architecture allows any engineer to add components in his/her domain of expertise to the platform in a modular fashion. The symbolic engine in the MIXEDMODELS platform synthesizes the system governing equations as a unified set of non-linear differential-algebraic equations (DAE’s). These equations can then be differentiated with respect to design to obtain an additional set of DAE’s in the sensitivity coefficients of the system state variables with respect to the system’s design variables. This combined set of DAE’s can be solved numerically to obtain the solution for the state variables and state sensitivity coefficients of the system. Finally, knowing the system performance functions, we can calculate the design sensitivity coefficients of these performance functions by using the values of the state variables and state sensitivity coefficients obtained from the DAE’s. In this work we use the direct differentiation approach for sensitivity analysis, as opposed to the adjoint variable approach, for ease in error control and software implementation. The capabilities and performance of the proposed design sensitivity analysis formulation are demonstrated through a numerical example consisting of an AC rectified DC power supply driving a slider crank mechanism. In this case, the performance functions and design variables come from both electrical and mechanical domains. The results obtained were verified by perturbation analysis, and the method was shown to be very accurate and computationally viable.

On the Solution of the Diffusion Equations by Numerical Methods

1966 ◽  
Vol 88 (4) ◽  
pp. 421-427 ◽  
Author(s):  
H. Z. Barakat ◽  
J. A. Clark
Keyword(s):  
Exact Solution ◽  
Finite Difference ◽  
Present Method ◽  
Finite Difference Methods ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Approximation Procedure ◽  
Implicit Methods ◽  
Difference Methods ◽  
Explicit Finite Difference

An explicit-finite difference approximation procedure which is unconditionally stable for the solution of the general multidimensional, nonhomogeneous diffusion equation is presented. This method possesses the advantages of the implicit methods, i.e., no severe limitation on the size of the time increment. Also it has the simplicity of the explicit methods and employs the same “marching” type technique of solution. Results obtained by this method for several different problems are compared with the exact solution and with those obtained by other finite-difference methods. For the examples solved the numerical results obtained by the present method are in closer agreement with the exact solution than are those obtained by the other methods.

A highly stable explicit scheme for a fourth-order nonlinear diffusion filter

2020 ◽  
Vol 11 (04) ◽  
pp. 2050030
Author(s):  
Mahipal Jetta
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Fourth Order ◽  
Nonlinear Diffusion ◽  
Splitting Scheme ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Diffusion Filter ◽  
Spatial Derivatives

The standard finite difference scheme (forward difference approximation for time derivative and central difference approximations for spatial derivatives) for fourth-order nonlinear diffusion filter allows very small time-step size to obtain stable results. The alternating directional implicit (ADI) splitting scheme such as Douglas method is highly stable but compromises accuracy for a relatively larger time-step size. In this paper, we develop [Formula: see text] stencils for the approximation of second-order spatial derivatives based on the finite pointset method. We then make use of these stencils for approximating the fourth-order partial differential equation. We show that the proposed scheme allows relatively bigger time-step size than the standard finite difference scheme, without compromising on the quality of the filtered image. Further, we demonstrate through numerical simulations that the proposed scheme is more efficient, in obtaining quality filtered image, than an ADI splitting scheme.

scholarly journals Geosystems‘ Pathways to the Future of Sustainability

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Mihai Voda ◽  
Shadrack Kithiia ◽  
Edward Jackiewicz ◽  
Qingyun Du ◽  
Constantin Adrian Sarpe
Keyword(s):  
Dynamic Equilibrium ◽  
Objective Assessment ◽  
Google Earth ◽  
Integrative Approach ◽  
Positioning Systems ◽  
Technological Advances ◽  
Identification Evaluation ◽  
Global Positioning ◽  
Dynamic Equilibrium State ◽  
Societal Changes

Abstract The world’s future development depends on effective human-computer linkages. From local to global, the virtual illustrations of a geographical place have to emphasize in an integrative approach peoples‘ key position in the Geosystem. Human values and social networks are now empowered by the unlimited creativity of smartphone applications. Our Geosystem grounded theory envisions that the sustainable management of natural resources is a lifelong learning environment where the poor communities have access to the new technological advances. This paper will attempt to show the effectiveness of Geomedia techniques in the Geosystems identification, evaluation, and valorization processes for the benefit of local inhabitants. This present research methodology uses smartphone apps, Google Earth environmental datasets, Global Positioning Systems, and WebGIS for a geographical investigation and objective assessment of regions throughout the world. The results demonstrate that self-sustainable Geosystems will always be capable to regulate, control and assess progress towards their dynamic equilibrium state, continuously adapting to environmental and societal changes.

scholarly journals Limiting the development of riparian vegetation in the Isère River: A physical modelling study

2018 ◽  
Vol 40 ◽  
pp. 02015
Author(s):  
Nicolas Claude ◽  
Clément Leroux ◽  
Marion Duclercq ◽  
Pablo Tassi ◽  
Kamal El Kadi Abderrezzak
Keyword(s):  
Plant Development ◽  
Dynamic Equilibrium ◽  
Initial Conditions ◽  
Physical Modelling ◽  
Sand Mixture ◽  
Dynamic Equilibrium State ◽  
Actual Configuration ◽  
Vegetation Encroachment ◽  
Movable Bed ◽  
Riparian Plant

Physical modelling experiments are conducted to investigate if a modification of the Isère River (French Alps) hydrology by changing dams management is able to foster riverbed morphodynamic and, thus limiting riparian plant development. The experimental setup is a 1:35 scale, undistorted movable bed designed to ensure the Froude number similarity and initial conditions for sediment particle motion. The physical model is 35 m long, 2.6 m wide, with a sand mixture composed of three grain size classes. Two runs with different flow and bed load conditions are simulated. Preliminary results show an intense riverbed activity when the system reaches a dynamic equilibrium state. Under these conditions, bar mobility is strong enough to limit vegetation encroachment only when water discharges are higher than the discharge of a 5-years flood during more than 10 days. These results indicate that the hydrological characteristics of the Isère River and the actual configuration of the hydropower structures could be not able to release annually the flow conditions needed to control riparian plant development.

A Robust Semi-Analytical Method for Calculating the Response Sensitivity of a Time Delay System

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Mohammad H. Kurdi ◽  
Raphael T. Haftka ◽  
Tony L. Schmitz ◽  
Brian P. Mann
Keyword(s):  
Time Delay ◽  
Finite Difference ◽  
Stability Boundary ◽  
Delay System ◽  
Milling Process ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Step Size ◽  
Input Variables ◽  
Delay Differential

It is often necessary to establish the sensitivity of an engineering system’s response to variations in the process/control parameters. Applications of the calculated sensitivity include gradient-based optimization and uncertainty quantification, which generally require an efficient and robust sensitivity calculation method. In this paper, the sensitivity of the milling process, which can be modeled by a set of time delay differential equations, to variations in the input parameters is calculated. The semi-analytical derivative of the maximum eigenvalue provides the necessary information for determining the sensitivity of the process stability to input variables. Comparison with the central finite difference derivative of the stability boundary shows that the semi-analytical approach is more efficient and robust with respect to step size and numerical accuracy of the response. An investigation of the source of inaccuracy of the finite difference approximation found that it is caused by discontinuities associated with the iterative process of root finding using the bisection method.

Dynamic Equilibrium Configurations of Multibody Systems

2014 ◽  
Vol 619 ◽  
pp. 8-12
Author(s):  
Ju Seok Kang
Keyword(s):  
Iteration Method ◽  
Multibody Systems ◽  
Equilibrium Configuration ◽  
Dynamic Equilibrium ◽  
Mechanical Systems ◽  
Railway Vehicle ◽  
Algebraic Form ◽  
Constrained Mechanical Systems ◽  
Speed Governor ◽  
Equilibrium Configurations

It is difficult to calculate dynamic equilibrium configuration in the mechanical systems, especially with the constraint conditions. In this paper, a method to calculate the dynamic equilibrium positions in the constrained mechanical systems is proposed. The accelerations of independent coordinates are derived in the algebraic form so that the numerical solution is easily obtained by the iteration method. The proposed method has been applied to calculate the dynamic equilibrium configuration for speed governor and the wheelset of railway vehicle.

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