On the influence of model reduction techniques in topology optimization of flexible multibody systems using the floating frame of reference approach

2015 ◽  
Vol 53 (1) ◽  
pp. 67-80 ◽  
Author(s):  
Alexander Held ◽  
Christine Nowakowski ◽  
Ali Moghadasi ◽  
Robert Seifried ◽  
Peter Eberhard
Keyword(s):  
Topology Optimization ◽  
Model Reduction ◽  
Multibody Systems ◽  
Frame Of Reference ◽  
Flexible Multibody Systems ◽  
Floating Frame Of Reference ◽  
Reduction Techniques ◽  
Flexible Multibody ◽  
Floating Frame

Development of Reduced Order Thermomechanical Model Using Floating Frame of Reference Formulation

2017 ◽  
Author(s):  
Hiroki Yamashita ◽  
Rohit Arora ◽  
Hiroyuki Kanazawa ◽  
Hiroyuki Sugiyama
Keyword(s):  
Multibody Systems ◽  
Thermal Deformation ◽  
Frame Of Reference ◽  
Flexible Multibody Systems ◽  
Flexible Body ◽  
Reference Formulation ◽  
Thermomechanical Model ◽  
Reduced Order ◽  
Floating Frame Of Reference ◽  
Floating Frame

In this paper, a reduced order thermomechanical model based on the Craig-Bampton component mode synthesis method is extended to the floating frame of reference formulation for the thermomechanical analysis of flexible multibody systems. To this end, coupled structural and thermal equations of finite element models are partitioned in terms of the internal and interface coordinates, each of which consists of the structural and thermal coordinates. Both deformation including the thermal effect and temperature in the internal region are then defined by a linear combination of the thermomechanical fixed-interface normal modes and thermomechanical constraint modes to account for structural and thermal modes associated with external forces and heat sources applied to the system. The final form of equations include equations of motion associated with a flexible body that incorporates thermal deformation and the reduced order heat equations that describe the transient change in the temperature over the flexible body. For this reason, the inertia coupling of the reference motion and the thermal deformation is automatically considered using the floating frame of reference formulation. Both equations are integrated forward in time simultaneously using general multibody dynamics computer algorithms to account for the coupled structural and thermal behavior of flexible multibody systems. Several numerical examples are presented to demonstrate the use of the numerical procedure developed in this study.

System-Level Modal Representation of Flexible Multibody Systems

2009 ◽  
Author(s):  
Gert H. K. Heirman ◽  
Wim Desmet
Keyword(s):  
Model Reduction ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Flexible Multibody Systems ◽  
System Level ◽  
Algebraic Equations ◽  
Flexible Multibody ◽  
Simulation Results ◽  
Model Equations ◽  
Model Reduction Technique

The presence of both differential and algebraic equations in the model equations, as well as the number of degrees of freedom needed to accurately represent flexibility, prohibit fast simulation of flexible multibody systems (e.g. real-time). In this research, Global Modal Parametrization, a model reduction technique for flexible multibody systems is further developed to speed up simulation of flexible multibody systems. The reduction of the model is achieved by projection on a curvilinear subspace instead of a fixed vector space, requiring significantly less degrees of freedom to represent the system dynamics with the same level of accuracy. The complexity of simulation of the reduced model equations is estimated. In a numerical experiment, simulation results for the original model equations are compared with simulation results for the model equations obtained after model reduction, showing a good match. The dominant sources of error of the proposed methodology are illustrated and explained.

Modeling of Revolute Joints in Topology Optimization of Flexible Multibody Systems

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Ali Moghadasi ◽  
Alexander Held ◽  
Robert Seifried
Keyword(s):  
Topology Optimization ◽  
Multibody Systems ◽  
Multibody System ◽  
Order Reduction ◽  
Flexible Multibody Systems ◽  
Hertzian Contact ◽  
Revolute Joints ◽  
Nonlinear Finite Elements ◽  
Flexible Multibody ◽  
Hertzian Contact Law

In recent years, topology optimization has been used for optimizing members of flexible multibody systems to enhance their performance. Here, an extension to existing topology optimization schemes for flexible multibody systems is presented in which a more accurate model of revolute joints and bearing domains is included. This extension is of special interest since a connection between flexible members in a multibody system using revolute joints is seen in many applications. Moreover, the modeling accuracy of the bearing area is shown to be influential on the shape of the optimized structure. In this work, the flexible bodies are incorporated in the multibody simulation using the floating frame of reference formulation, and their elastic deformation is approximated using global shape functions calculated in the model order reduction analysis. The modeling of revolute joints using Hertzian contact law is incorporated in this framework by introducing a corrector load in the bearing model. Furthermore, an application example of a flexible multibody system with revolute joints is optimized for minimum value of compliance, and a comparative study of the optimization result is performed with an equivalent system which is modeled with nonlinear finite elements.

A Novel Approach to Real-Time Flexible Multibody Simulation: Sub-System Global Modal Parameterization

2011 ◽  
Author(s):  
Frank Naets ◽  
Gert H. K. Heirman ◽  
Wim Desmet
Keyword(s):  
Model Reduction ◽  
Real Time ◽  
Relative Motion ◽  
Multibody Systems ◽  
Differential Algebraic Equations ◽  
Flexible Multibody Systems ◽  
System Level ◽  
Algebraic Equations ◽  
Global Modal Parameterization ◽  
Flexible Multibody

This paper introduces a novel model reduction technique, namely Sub-System Global Modal Parameterization (SS-GMP), for real-time simulation of flexible multibody systems. In the past, other system-level model reduction techniques have been proposed for this purpose, but these were limited in applicability due to the large storage requirements for systems with many rigid degrees-of-freedom (DOFs). However, in the SS-GMP approach, the motion of a mechanism is split up into a global motion and a relative motion of the (sub-)system. The relative motion is then reduced according to the Global Modal Parameterization, which is a model reduction procedure suitable for closed chain flexible multibody systems. In combination with suitable explicit solvers, the SS-GMP approach enables (hard) real-time simulations due to the strong reduction in the number of DOFs and the conversion of a system of differential-algebraic equations into a system of ordinary differential equations. The proposed approach is validated numerically with a quarter-car model. This fully flexible mechanism is simulated faster than real-time on a regular PC with the SS-GMP approach while providing accurate results.

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