Combined Discrete-Continuum Analysis for Ballasted Rail Tracks

2021 ◽  
pp. 266-273
Author(s):  
T. Ngo ◽  
Buddhima Indraratna ◽  
C. Rujikiatkamjorn
Keyword(s):  
Continuum Analysis

scholarly journals Compactness by Coarse-Graining in Long-Range Lattice Systems

2020 ◽  
Vol 20 (4) ◽  
pp. 783-794
Author(s):  
Andrea Braides ◽  
Margherita Solci
Keyword(s):  
Long Range ◽  
Coarse Graining ◽  
Interaction Energies ◽  
Lattice Systems ◽  
Range Interaction ◽  
Surface Energies ◽  
Continuum Analysis ◽  
Long Range Interaction ◽  
Typical Range ◽  
Limit Energy

AbstractWe consider energies on a periodic set {\mathcal{L}} of the form {\sum_{i,j\in\mathcal{L}}a^{\varepsilon}_{ij}\lvert u_{i}-u_{j}\rvert}, defined on spin functions {u_{i}\in\{0,1\}}, and we suppose that the typical range of the interactions is {R_{\varepsilon}} with {R_{\varepsilon}\to+\infty}, i.e., if {\lvert i-j\rvert\leq R_{\varepsilon}}, then {a^{\varepsilon}_{ij}\geq c>0}. In a discrete-to-continuum analysis, we prove that the overall behavior as {\varepsilon\to 0} of such functionals is that of an interfacial energy. The proof is performed using a coarse-graining procedure which associates to scaled functions defined on {\varepsilon\mathcal{L}} with equibounded energy a family of sets with equibounded perimeter. This agrees with the case of equibounded {R_{\varepsilon}} and can be seen as an extension of coerciveness result for short-range interactions, but is different from that of other long-range interaction energies, whose limit exits the class of surface energies. A computation of the limit energy is performed in the case {\mathcal{L}=\mathbb{Z}^{d}}.

Continuum Analysis Approach for Rocking Core-Moment Frames

2018 ◽  
Vol 144 (3) ◽  
pp. 04018006 ◽  
Author(s):  
Nima Rahgozar ◽  
Abdolreza S. Moghadam ◽  
Armin Aziminejad
Keyword(s):  
Analysis Approach ◽  
Moment Frames ◽  
Continuum Analysis

Multi-continuum analysis of thermally induced matrix cracking

2005 ◽  
Vol 72 (12) ◽  
pp. 1993-2008 ◽  
Author(s):  
Seth Nickerson ◽  
J. Steven Mayes ◽  
Jeffry S. Welsh
Keyword(s):  
Matrix Cracking ◽  
Thermally Induced ◽  
Continuum Analysis
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