Applications of the element-free Galerkin method for singular stress analysis under strain gradient plasticity theories

2011 ◽  
Vol 78 (3) ◽  
pp. 452-461 ◽  
Author(s):  
Xiaofei Pan ◽  
Huang Yuan
Keyword(s):  
Galerkin Method ◽  
Stress Analysis ◽  
Strain Gradient ◽  
Strain Gradient Plasticity ◽  
Gradient Plasticity ◽  
Element Free Galerkin Method ◽  
Singular Stress ◽  
Element Free Galerkin ◽  
Element Free

scholarly journals Characterizing Flexoelectricity in Composite Material Using the Element-Free Galerkin Method

Energies ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 271 ◽  
Author(s):  
Bo He ◽  
Brahmanandam Javvaji ◽  
Xiaoying Zhuang
Keyword(s):  
Composite Material ◽  
Galerkin Method ◽  
Strain Gradient ◽  
Electromechanical Coupling ◽  
Mechanical Energy ◽  
Weight Functions ◽  
Gradient Term ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free

This study employs the Element-Free Galerkin method (EFG) to characterize flexoelectricity in a composite material. The presence of the strain gradient term in the Partial Differential Equations (PDEs) requires C 1 continuity to describe the electromechanical coupling. The use of quartic weight functions in the developed model fulfills this prerequisite. We report the generation of electric polarization in a non-piezoelectric composite material through the inclusion-induced strain gradient field. The level set technique associated with the model supervises the weak discontinuity between the inclusion and matrix. The increased area ratio between the inclusion and matrix is found to improve the conversion of mechanical energy to electrical energy. The electromechanical coupling is enhanced when using softer materials for the embedding inclusions.

Application of an Element-free Galerkin Method to Water Wave Propagation Problems

2014 ◽  
Vol 60 (1-4) ◽  
pp. 87-105 ◽  
Author(s):  
Ryszard Staroszczyk
Keyword(s):  
Wave Propagation ◽  
Galerkin Method ◽  
Present Model ◽  
Free Surface Elevation ◽  
Element Free Galerkin Method ◽  
Plane Flow ◽  
Element Free Galerkin ◽  
Proposed Model ◽  
Sloping Bed ◽  
Element Free

Abstract The paper is concerned with the problem of gravitational wave propagation in water of variable depth. The problem is solved numerically by applying an element-free Galerkin method. First, the proposed model is validated by comparing its predictions with experimental data for the plane flow in water of uniform depth. Then, as illustrations, results of numerical simulations performed for plane gravity waves propagating through a region with a sloping bed are presented. These results show the evolution of the free-surface elevation, displaying progressive steepening of the wave over the sloping bed, followed by its attenuation in a region of uniform depth. In addition, some of the results of the present model are compared with those obtained earlier by using the conventional finite element method.

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