An Energy-Minimization Finite-Element Approach for the Frank--Oseen Model of Nematic Liquid Crystals

2015 ◽  
Vol 53 (5) ◽  
pp. 2226-2254 ◽  
Author(s):  
J. H. Adler ◽  
T. J. Atherton ◽  
D. B. Emerson ◽  
S. P. MacLachlan
Keyword(s):  
Finite Element ◽  
Liquid Crystals ◽  
Energy Minimization ◽  
Nematic Liquid Crystals ◽  
Finite Element Approach ◽  
Element Approach ◽  
Oseen Model

A Finite Element Approach to the Transient Dynamics of Rolling Tires with Emphasis on Rolling Noise Simulation4

2007 ◽  
Vol 35 (3) ◽  
pp. 165-182 ◽  
Author(s):  
Maik Brinkmeier ◽  
Udo Nackenhorst ◽  
Heiner Volk
Keyword(s):  
Finite Element ◽  
Traffic Noise ◽  
Complex Eigenvalue ◽  
Arbitrary Lagrangian Eulerian ◽  
Finite Element Approach ◽  
Road Systems ◽  
Element Approach ◽  
Road Surface Roughness ◽  
Complex Eigenvalue Analysis ◽  
Rolling Noise

Abstract The sound radiating from rolling tires is the most important source of traffic noise in urban regions. In this contribution a detailed finite element approach for the dynamics of tire/road systems is presented with emphasis on rolling noise prediction. The analysis is split into sequential steps, namely, the nonlinear analysis of the stationary rolling problem within an arbitrary Lagrangian Eulerian framework, and a subsequent analysis of the transient dynamic response due to the excitation caused by road surface roughness. Here, a modal superposition approach is employed using complex eigenvalue analysis. Finally, the sound radiation analysis of the rolling tire/road system is performed.

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