Stiffness and Mass Matrices of FEM-Applicable Dynamic Infinite Element with Unified Shape Basis

2009 ◽  
Author(s):  
Konstantin Kazakov ◽  
Alexander Korsunsky
Keyword(s):  
Infinite Element ◽  
Mass Matrices

An Integration Technique in Burnett Infinite Element

2003 ◽  
Author(s):  
L.-X. Li ◽  
J.-S. Sun ◽  
H. Sakamoto
Keyword(s):  
Finite Geometry ◽  
Weighting Factor ◽  
Point Of View ◽  
Infinite Element ◽  
Transient Problems ◽  
Infinite Point ◽  
Mass Matrices ◽  
Local Coordinates ◽  
Infinite Element Method ◽  
Potential Disadvantage

Burnett element [1] has been regarded as the most important contribution to infinite element method. It comprises two principal features: one is the use of confocal ellipsoidal coordinate system; another is the exact multi-pole expansion in the newly defined “radial” direction. The former leads in effect to a quasi one-dimensional problem from the infinite point of view, and thereby makes the latter be possibly carried out. However, in evaluating the system matrices, undefined integrals are involved. Hence, the resulting “stiffness”, “damping” and “mass” matrices don’t have definite physical significance. The potential disadvantage is that this efficient element cannot be directly used to solve transient problems. In this paper, presentation of the theory of multi-pole expansion used in Burnett element is changed in form and the shape functions are subsequently expressed in terms of local coordinates by using the infinite-to-finite geometry mapping. In addition to the use of Astley type weighting functions [2] and to the modification of the weighting factor, the system matrices of Burnett infinite element are eventually bounded and integrated term by term using Gauss rules.

Structure of quark mass matrices in the rishon model

1983 ◽  
Vol 121 (5) ◽  
pp. 326-330 ◽  
Author(s):  
G. Ecker
Keyword(s):  
Quark Mass ◽  
Mass Matrices

Fermionic mass matrices with large neutrino mixing in a GUT scenario

1990 ◽  
Vol 331 (1) ◽  
pp. 213-243 ◽  
Author(s):  
Yoav Achiman ◽  
Jens Erler ◽  
Wolfgang Kalau
Keyword(s):  
Neutrino Mixing ◽  
Mass Matrices

scholarly journals Infinite Element Static-Dynamic Unified Artificial Boundary

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Zhiqiang Song ◽  
Fei Wang ◽  
Yujie Liu ◽  
Chenhui Su
Keyword(s):  
Reaction Force ◽  
Tangential Direction ◽  
Dynamic Effects ◽  
Artificial Boundary ◽  
Infinite Element ◽  
Dynamic Synthesis ◽  
Dynamic Boundary ◽  
Static Calculation ◽  
Force Calculation ◽  
External Wave

The method, which obtains a static-dynamic comprehensive effect from superposing static and dynamic effects, is inapplicable to large deformation and nonlinear elastic problems under strong earthquake action. The static and dynamic effects must be analyzed in a unified way. These effects involve a static-dynamic boundary transformation problem or a static-dynamic boundary unified problem. The static-dynamic boundary conversion method is tedious. If the node restraint reaction force caused by a static boundary condition is not applied, then the model is not balanced at zero moment, and the calculation result is distorted. The static numerical solution error is large when the structure possesses tangential static force in a viscoelastic static-dynamic unified boundary. This paper proposed a new static-dynamic unified artificial boundary based on an infinite element in ABAQUS to solve static-dynamic synthesis effects conveniently and accurately. The static and dynamic mapping theories of infinite elements were introduced. The characteristic of the infinite element, which has zero displacement at faraway infinity, was discussed in theory. The equivalent nodal force calculation formula of infinite element unified boundary was deduced from an external wave input. A calculation and application program of equivalent nodal forces was developed using the Python language to complete external wave inputting. This new method does not require a static and dynamic boundary transformation and import of stress field and constraint counterforce of boundary nodes. The static calculation precision of the infinite element unified boundary is more improved than the viscoelastic static-dynamic unified boundary, especially when the static load is in the tangential direction. In addition, the foundation simulation range of finite field can be significantly reduced given the utilization of the infinite element static dynamic unified boundary. The preciseness of static calculation and dynamic calculation and static-dynamic comprehensive analysis are unaffected.

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