Model reduction of contact dynamics simulation using a modified Lyapunov balancing method

2011 ◽  
Vol 6 (4) ◽  
pp. 383-391 ◽  
Author(s):  
Jianxun Liang ◽  
Ou Ma ◽  
Caishan Liu
Author(s):  
Jianxun Liang ◽  
Ou Ma ◽  
Caishan Liu

Finite element methods are widely used for simulations of contact dynamics of flexible multibody systems. Such a simulation is computationally very inefficient because the system’s dimension is usually very large and the simulation time step has to be very small in order to ensure numerical stability. A potential solution to the problem is to apply a model reduction method in the simulation. Although many model reduction techniques have been developed, most of them cannot be readily applied due to the high nonlinearity of the involved contact dynamics model. This paper presents a solution to the problem. The approach is based on a modified Lyapunov balanced truncation method. A numerical example is presented to demonstrate that, by applying the proposed model reduction method, the simulation process can be significantly speeded up while the resulting error caused by the model reduction is still within an acceptable level.


Author(s):  
Jianxun Liang ◽  
Ou Ma

Finite element models can accurately simulate impact-contact dynamics response of a multibody dynamical system. However, such a simulation remains very inefficient because very small integration time step must be used when solving the involved differential equations. Although many model reduction techniques can be used to improve the efficiency of finite element based simulations, most of these techniques cannot be readily applied to contact dynamics simulations due to the high nonlinearity of the contact dynamics model. This paper presents a model reduction approach for finite-element based multibody contact dynamics simulation, based on a modified Lyapunov balanced truncation method. An example is presented to demonstrate that, by applying the model reduction the simulation process is significantly speeded up and the resulting error is bounded within an acceptable level. The performance of the method with respect to some influential factors such as element size, shape and contact stiffness is also investigated.


2020 ◽  
Vol 117 (35) ◽  
pp. 21336-21345 ◽  
Author(s):  
Wonmuk Hwang ◽  
Robert J. Mallis ◽  
Matthew J. Lang ◽  
Ellis L. Reinherz

EachαβT cell receptor (TCR) functions as a mechanosensor. The TCR is comprised of a clonotypic TCRαβligand-binding heterodimer and the noncovalently associated CD3 signaling subunits. When bound by ligand, an antigenic peptide arrayed by a major histocompatibility complex molecule (pMHC), the TCRαβhas a longer bond lifetime under piconewton-level loads. The atomistic mechanism of this “catch bond” behavior is unknown. Here, we perform molecular dynamics simulation of a TCRαβ-pMHC complex and its variants under physiologic loads to identify this mechanism and any attendant TCRαβdomain allostery. The TCRαβ-pMHC interface is dynamically maintained by contacts with a spectrum of occupancies, introducing a level of control via relative motion between Vα and Vβ variable domains containing the pMHC-binding complementarity-determining region (CDR) loops. Without adequate load, the interfacial contacts are unstable, whereas applying sufficient load suppresses Vα-Vβ motion, stabilizing the interface. A second level of control is exerted by Cα and Cβ constant domains, especially Cβ and its protruding FG-loop, that create mismatching interfaces among the four TCRαβdomains and with a pMHC ligand. Applied load enhances fit through deformation of the TCRαβmolecule. Thus, the catch bond involves the entire TCRαβconformation, interdomain motion, and interfacial contact dynamics, collectively. This multilayered architecture of the machinery fosters fine-tuning of cellular response to load and pMHC recognition. Since the germline-derived TCRαβectodomain is structurally conserved, the proposed mechanism can be universally adopted to operate under load during immune surveillance by diverseαβTCRs constituting the T cell repertoire.


Author(s):  
Thomas A. Brain ◽  
Erik B. Kovel ◽  
John R. MacLean ◽  
Leslie J. Quiocho

Pong is a new software tool developed at the NASA Johnson Space Center that advances interference-based geometric contact dynamics based on 3D graphics models. The Pong software consists of three parts: a set of scripts to extract geometric data from 3D graphics models, a contact dynamics engine that provides collision detection and force calculations based on the extracted geometric data, and a set of scripts for visualizing the dynamics response with the 3D graphics models. The contact dynamics engine can be linked with an external multibody dynamics engine to provide an integrated multibody contact dynamics simulation. This paper provides a detailed overview of Pong including the overall approach, modeling capabilities, which encompasses force generation to computational performance, and example applications.


Author(s):  
James H. Little ◽  
Jeffrey L. Kauffman ◽  
Matthias Huels

Predicting the energy dissipation associated with contact of underplatform dampers remains a critical challenge in turbomachinery blade and friction damper design. Typical turbomachinery blade forced vibration response analyses rely on reduced order models and simplified nonlinear codes to predict blade vibration characteristics in a computationally tractable manner. Recent research has focused on both the model reduction process and simulation of the contact dynamics. This paper proposes two academic turbine blade geometries with coupled underplatform dampers as vehicles by which these model reduction and forced response simulation techniques may be compared. The blades correspond to two types of freestanding turbine blades and demonstrate the same qualitative behavior as more complex industry geometries. The blade geometries are fully described here and analyzed using the same procedure as used for an industry-specific blade. Standard results are presented in terms of resonance frequency, amplitude, and damping across a range of aerodynamic excitation. In addition, the predicted blade vibration characteristics are examined under variations in the contact interface: friction coefficient, damper / platform surface roughness, and damper mass, with relative sensitivities to each term generated. Finally, the effect of the number of modes retained in the reduced order model is studied to uncover patterns of convergence as well as to provide additional sets of standard data for comparison with other model reduction and forced response simulation methods.


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