Fractional calculus in solid mechanics: local versus non-local approach

2009 ◽  
Vol T136 ◽  
pp. 014003 ◽  
Author(s):  
Alberto Carpinteri ◽  
Pietro Cornetti ◽  
Alberto Sapora ◽  
Mario Di Paola ◽  
Massimiliano Zingales
Keyword(s):  
Fractional Calculus ◽  
Solid Mechanics ◽  
Local Approach ◽  
Non Local

Application of Fractional Calculus for Dynamic Problems of Solid Mechanics: Novel Trends and Recent Results

2009 ◽  
Vol 63 (1) ◽  
Author(s):  
Yuriy A. Rossikhin ◽  
Marina V. Shitikova
Keyword(s):  
Fractional Calculus ◽  
Degrees Of Freedom ◽  
Solid Mechanics ◽  
State Of The Art ◽  
Dynamic Problems ◽  
Engineering Problems ◽  
Multilayered Systems ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems

The present state-of-the-art article is devoted to the analysis of new trends and recent results carried out during the last 10years in the field of fractional calculus application to dynamic problems of solid mechanics. This review involves the papers dealing with study of dynamic behavior of linear and nonlinear 1DOF systems, systems with two and more DOFs, as well as linear and nonlinear systems with an infinite number of degrees of freedom: vibrations of rods, beams, plates, shells, suspension combined systems, and multilayered systems. Impact response of viscoelastic rods and plates is considered as well. The results obtained in the field are critically estimated in the light of the present view of the place and role of the fractional calculus in engineering problems and practice. This articles reviews 337 papers and involves 27 figures.

Rate Dependent Gradient Theory for Shear Band Analysis in Clayey Soils

2001 ◽  
Author(s):  
George Z. Voyiadjis ◽  
Chung R. Song
Keyword(s):  
Flow Characteristics ◽  
Gradient Theory ◽  
Clayey Soils ◽  
Local Behavior ◽  
Local Approach ◽  
Multi Scale ◽  
Viscosity Effect ◽  
Gradient Effect ◽  
Rate Dependent ◽  
Non Local

Abstract A rate dependent, non local approach is developed in this work for geo-materials. A multi-scale gradient theory is addressed for non local approach. Visco-plasticity is also incorporated for an additional regularization of the local behavior. The plastic spin is incorporated to separate the effect of micro-structural rotation from the gradient effect. The flow characteristics of the soil is also incorporated in order to separate the viscosity effect from the flow effect.

Application of variable-order fractional calculus in solid mechanics

2019 ◽  
pp. 207-224 ◽  
Author(s):  
Behrouz Parsa Moghaddam ◽  
Arman Dabiri ◽  
José António Tenreiro Machado
Keyword(s):  
Fractional Calculus ◽  
Solid Mechanics ◽  
Variable Order

scholarly journals Improving Signal-to-Noise Ratio in Susceptibility Weighted Imaging: A Novel Multicomponent Non-Local Approach

PLoS ONE ◽  
2015 ◽  
Vol 10 (6) ◽  
pp. e0126835 ◽  
Author(s):  
Pasquale Borrelli ◽  
Giuseppe Palma ◽  
Enrico Tedeschi ◽  
Sirio Cocozza ◽  
Marco Comerci ◽  
...  
Keyword(s):  
Signal To Noise Ratio ◽  
Susceptibility Weighted Imaging ◽  
Signal To Noise ◽  
Local Approach ◽  
Non Local ◽  
Noise Ratio
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