Smoothed Galerkin methods using cell-wise strain smoothing technique

2012 ◽  
Vol 36 (5) ◽  
pp. 825-835 ◽  
Author(s):  
X.Y. Cui ◽  
G.Y. Li
Keyword(s):  
Galerkin Methods ◽  
Smoothing Technique ◽  
Strain Smoothing Technique ◽  
Strain Smoothing

scholarly journals Free Vibration Analysis of Functionally Graded Shells Using an Edge-Based Smoothed Finite Element Method

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 684 ◽  
Author(s):  
Tien Dat Pham ◽  
Quoc Hoa Pham ◽  
Van Duc Phan ◽  
Hoang Nam Nguyen ◽  
Van Thom Do
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Smoothing Technique ◽  
Strain Smoothing ◽  
Smoothed Finite Element Method ◽  
Edge Based

An edge-based smoothed finite element method (ES-FEM) combined with the mixed interpolation of tensorial components technique for triangular shell element (MITC3), called ES-MITC3, for free vibration analysis of functionally graded shells is investigated in this work. In the formulation of the ES-MITC3, the stiffness matrices are obtained by using the strain-smoothing technique over the smoothing domains that are formed by two adjacent MITC3 triangular shell elements sharing an edge. The strain-smoothing technique can improve significantly the accuracy and convergence of the original MITC3. The material properties of functionally graded shells are assumed to vary through the thickness direction by a power–rule distribution of volume fractions of the constituents. The numerical examples demonstrated that the present ES-MITC3method is free of shear locking and achieves the high accuracy compared to the reference solutions in the literature.

Development of the Smoothed Natural Neighbor Petrov-Galerkin Method

2012 ◽  
Vol 201-202 ◽  
pp. 198-201
Author(s):  
Kai Wang ◽  
Shen Jie Zhou ◽  
Zhi Feng Nie
Keyword(s):  
Boundary Condition ◽  
Galerkin Method ◽  
Accurate Result ◽  
Computational Cost ◽  
Smoothing Technique ◽  
Essential Boundary Condition ◽  
Natural Neighbor ◽  
Strain Smoothing ◽  
Mlpg Method ◽  
Domain Integration

The strain smoothing technique is employed in the natural neighbor Petrov-Galerkin method (NNPG), and the so-called smoothed natural neighbor Petrov-Galerkin method is proposed and studied. This method inherits the advantages of the generalized MLPG method and possesses the easy imposition of essential boundary condition and the domain integration is completely avoided. In comparison with the traditional NNPG, the smoothed natural neighbor Petrov-Galerkin method can obtained more stable and accurate result without increasing the computational cost.

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