Solution of Mathematical Adjoint Equation for a Higher Order Nodal Expansion Method

1996 ◽  
Vol 123 (3) ◽  
pp. 381-391 ◽  
Author(s):  
Taek Kyum Kim ◽  
Chang Hyo Kim
Keyword(s):  
Adjoint Equation ◽  
Expansion Method ◽  
Higher Order ◽  
Nodal Expansion Method

Improved nodal expansion method for solving neutron diffusion equation in cylindrical geometry

2010 ◽  
Vol 240 (8) ◽  
pp. 1997-2004 ◽  
Author(s):  
Dengying Wang ◽  
Fu Li ◽  
Jiong Guo ◽  
Jinfeng Wei ◽  
Jingyu Zhang ◽  
...  
Keyword(s):  
Diffusion Equation ◽  
Expansion Method ◽  
Cylindrical Geometry ◽  
Neutron Diffusion ◽  
Nodal Expansion Method ◽  
Neutron Diffusion Equation

The Higher Order Crack Tip Fields of Exponential Gradient FGMs Plates with Reissner’s Effect

2013 ◽  
Vol 278-280 ◽  
pp. 491-494
Author(s):  
Yao Dai ◽  
Xiao Chong
Keyword(s):  
Asymptotic Expansion ◽  
Crack Tip ◽  
Expansion Method ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Shear Deformation ◽  
Plate Bending ◽  
Graded Materials ◽  
Fundamental Significance ◽  
Asymptotic Expansion Method

The Reissner’s plate bending theory with consideration of transverse shear deformation effects is adopted to study the fundamental fracture problem in functionally graded materials (FGMs) plates for a crack perpendicular to material gradient. The crack-tip higher order asymptotic fields of FGMs plates are obtained by the asymptotic expansion method. This study has fundamental significance as Williams’ solution.

Development of Three-Dimensional Neutron Kinetics Code Based on High Order Nodal Expansion Method in Hexagonal-Z Geometry

2018 ◽  
Author(s):  
Guo Chao ◽  
Liu Yu ◽  
He Hangxing ◽  
Liu Luguo ◽  
Wang Xiaoyu ◽  
...  
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Expansion Method ◽  
High Order ◽  
Benchmark Problems ◽  
Weighting Method ◽  
Control Rod ◽  
Order Polynomial ◽  
Runge Kutta ◽  
Nodal Expansion Method

To solve three-dimensional kinetics problems, a high order nodal expansion method for hexagonal-z geometry (HONEM) and a Runge-Kutta (RK) method are respectively adopted to deal with the spatial and temporal problem. In the HONEM, 1D partially-integrated flux are approximated by using four order polynomial. The two order polynomial is adopted to the approximation of partially-integrated leakages. The Runge-Kutta method is adopted as a tool for dispersing the time term of 3D kinetics equation. A flux weighting method (FWM) is used for obtaining homogenized cross sections of mix node. The three-dimensional hexagonal kinetics code has been developed based on this method and tested with two benchmark problems of VVER which are the control rod ejection without any feedback and with simple adiabatic Doppler feedback. The results calculated by this code agree well with the reference results and the code is validated.

The Higher Order Axis-Directional Crack-Tip Field for Reissner's FGMs Cylindrical Shell

2013 ◽  
Vol 791-793 ◽  
pp. 746-749
Author(s):  
Yao Dai ◽  
Lei Zhang ◽  
Xiao Chong ◽  
Chun Fang Xue
Keyword(s):  
Cylindrical Shell ◽  
Asymptotic Expansion ◽  
Crack Problem ◽  
Crack Tip ◽  
Expansion Method ◽  
Higher Order ◽  
Crack Tip Field ◽  
Engineering Structures ◽  
Crack Tip Fields ◽  
Asymptotic Expansion Method

Reissners theory for cylindrical shell is adopted to analyze the axis-directional crack problem for FGMs cylindrical shell by using the asymptotic expansion method. The eigen-solution of the crack-tip fields for the cylindrical shell is obtained. The results are similar to Williams solution for the plane problems in homogeneous materials, and will be applied widely to engineering structures.

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