An advanced boundary element method for solving 2D and 3D static problems in Mindlin's strain-gradient theory of elasticity

2010 ◽  
Vol 83 (11) ◽  
pp. 1407-1427 ◽  
Author(s):  
G. F. Karlis ◽  
A. Charalambopoulos ◽  
D. Polyzos
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Strain Gradient ◽  
Theory Of Elasticity ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Mindlin’S Strain Gradient Theory ◽  
2D And 3D ◽  
Element Method

Nonlinear Forced Vibration Analysis of FG Cylindrical Nanopanels Based on Mindlin’s Strain Gradient Theory and 3D Elasticity

2020 ◽  
Vol 21 (6) ◽  
pp. 523-537 ◽  
Author(s):  
Y. Gholami ◽  
R. Ansari ◽  
R. Gholami ◽  
H. Rouhi
Keyword(s):  
Strain Gradient ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Solution Technique ◽  
Geometrical Parameters ◽  
Gradient Theory ◽  
Harmonic Load ◽  
Response Curves ◽  
Mindlin’S Strain Gradient Theory ◽  
3D Elasticity

AbstractA numerical approach is used herein to study the primary resonant dynamics of functionally graded (FG) cylindrical nanoscale panels taking the strain gradient effects into consideration. The basic relations of the paper are written based upon Mindlin’s strain gradient theory (SGT) and three-dimensional (3D) elasticity. Since the formulation is developed using Mindlin’s SGT, it is possible to reduce it to simpler size-dependent theories including modified forms of couple stress and strain gradient theories (MCST & MSGT). The governing equations is derived and directly discretized via the variational differential quadrature technique. Then, a numerical solution technique is employed to study the nonlinear resonance response of nanopanels with various edge conditions under a harmonic load. The impacts of length scale parameter, material and geometrical parameters on the frequency–response curves of nanopanels are investigated. In addition, comparisons are provided between the predictions of MSGT, MCST and the classical elasticity theory.

scholarly journals Thermo-electro-mechanical behaviour of Nano-sized structures

2020 ◽  
Vol 310 ◽  
pp. 00060
Author(s):  
Miroslav Repka ◽  
Ladislav Sator
Keyword(s):  
Size Effect ◽  
Mechanical Behaviour ◽  
Strain Gradient ◽  
Mechanical Response ◽  
Scale Parameter ◽  
Theory Of Elasticity ◽  
Strain Gradient Theory ◽  
Length Scale Parameter ◽  
Gradient Theory ◽  
Length Scale

Thermo-electro-mechanical behaviour of the nano-sized structures is analysed by the finite element method (FEM). The mechanical response of the nano-sized structures cannot be modelled with classical continuum theories due to the size effect phenomenon. The strain gradient theory with one length scale parameter has been applied to study size effect phenomenon. The coupled theory of thermo-electricity has been used together with strain gradient theory of elasticity. The governing equations have been derived and incorporated into the commercial software Comsol via weak form module. The influence of the length scale parameter on mechanical response of the structures is investigated by some numerical examples.

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