Analysis of an arbitrarily oriented crack in a functionally graded plane using a non-local approach

2016 ◽  
Vol 85 ◽  
pp. 387-397 ◽  
Author(s):  
N. Jamia ◽  
S. El-Borgi ◽  
R. Fernandes ◽  
V. Vegamoor
Keyword(s):  
Functionally Graded ◽  
Local Approach ◽  
Non Local ◽  
Arbitrarily Oriented Crack

scholarly journals Non-Local Buckling Analysis of Functionally Graded Nanoporous Metal Foam Nanoplates

Coatings ◽  
2018 ◽  
Vol 8 (11) ◽  
pp. 389 ◽  
Author(s):  
Yanqing Wang ◽  
Zhiyuan Zhang
Keyword(s):  
Metal Foam ◽  
Plate Theory ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Local Buckling ◽  
Functionally Graded ◽  
Small Scale ◽  
Refined Plate Theory ◽  
Nanoporous Metal ◽  
Non Local

In this study, the buckling of functionally graded (FG) nanoporous metal foam nanoplates is investigated by combining the refined plate theory with the non-local elasticity theory. The refined plate theory takes into account transverse shear strains which vary quadratically through the thickness without considering the shear correction factor. Based on Eringen’s non-local differential constitutive relations, the equations of motion are derived from Hamilton’s principle. The analytical solutions for the buckling of FG nanoporous metal foam nanoplates are obtained via Navier’s method. Moreover, the effects of porosity distributions, porosity coefficient, small scale parameter, axial compression ratio, mode number, aspect ratio and length-to-thickness ratio on the buckling loads are discussed. In order to verify the validity of present analysis, the analytical results have been compared with other previous studies.

scholarly journals Exact Mechanical Hierarchy of Non-Linear Fractional-Order Hereditariness

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 673
Author(s):  
Gioacchino Alotta ◽  
Emanuela Bologna ◽  
Massimiliano Zingales
Keyword(s):  
Functionally Graded ◽  
State Variable ◽  
Linear Approach ◽  
Power Law Decay ◽  
Separable Kernel ◽  
Proposed Model ◽  
Non Linear ◽  
Linear Transform ◽  
Single Integral ◽  
Non Local

Non-local time evolution of material stress/strain is often referred to as material hereditariness. In this paper, the widely used non-linear approach to single integral time non-local mechanics named quasi-linear approach is proposed in the context of fractional differential calculus. The non-linear model of the springpot is defined in terms of a single integral with separable kernel endowed with a non-linear transform of the state variable that allows for the use of Boltzmann superposition. The model represents a self-similar hierarchy that allows for a time-invariance as the result of the application of the conservation laws at any resolution scale. It is shown that the non-linear springpot possess an equivalent mechanical hierarchy in terms of a functionally-graded elastic column resting on viscous dashpots with power-law decay of the material properties. Some numerical applications are reported to show the capabilities of the proposed model.

scholarly journals Static and Dynamic Solutions of Functionally Graded Micro/Nanobeams under External Loads Using Non-Local Theory

Vibration ◽  
2020 ◽  
Vol 3 (2) ◽  
pp. 51-69
Author(s):  
Reza Moheimani ◽  
Hamid Dalir
Keyword(s):  
Power Index ◽  
Linear Equations ◽  
Local Effect ◽  
Functionally Graded ◽  
Local Theory ◽  
Classical Elasticity ◽  
Graded Materials ◽  
Nano Scale ◽  
Non Local ◽  
External Loads

Functionally graded materials (FGMs) have wide applications in different branches of engineering such as aerospace, mechanics, and biomechanics. Investigation of the mechanical behaviors of structures made of these materials has been performed widely using classical elasticity theories in micro/nano scale. In this research, static, dynamic and vibrational behaviors of functional micro and nanobeams were investigated using non-local theory. Governing linear equations of the problem were driven using non-local theory and solved using an analytical method for different boundary conditions. Effects of the axial load, the non-local parameter and the power index on the natural frequency of different boundary condition are assessed. Then, the obtained results were compared with those obtained from classical theory. These results showed that a non-local effect could greatly affect the behaviors of these beams, especially at nano scale.

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
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