An Eigenfunction Expansion Method in the Stress Concentration Analysis

2012 ◽  
Vol 204-208 ◽  
pp. 4406-4409
Author(s):  
Yang Bai ◽  
Li Chen
Keyword(s):  
Stress Concentration ◽  
Boundary Conditions ◽  
Linear Combination ◽  
Eigenfunction Expansion ◽  
Original Problem ◽  
Expansion Method ◽  
Numerical Results ◽  
Eigenfunction Expansion Method ◽  
Completeness Property

This paper deals with the traditional stress concentration problems based on the eigenfunction expansion approach. Due to the completeness property of the eigenfunction space obtained by the previous researches, the solution of an arbitrary problem can be expressed by their linear combination. Thus the original problem is transformed into finding the combination of these eigenfuctions satisfying boundary conditions. By applying adjoint symplectic relationships of the ortho-normalization, the combination can be obtained numerically. Numerical results in tensional problems show that stress concentration appears when one of the ends of the solid is clamped. The concentration is seriously confined near the boundary of the fixed, and decrease rapidly with the distance of the boundarys.

The Quasi-Static Analysis for Two-Dimensional Thin Plates

2011 ◽  
Vol 255-260 ◽  
pp. 166-169
Author(s):  
Li Chen ◽  
Yang Bai
Keyword(s):  
Boundary Conditions ◽  
Eigenfunction Expansion ◽  
Solution Space ◽  
Expansion Method ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Elastic Plates ◽  
Various Boundary Conditions ◽  
Eigenfunction Expansion Method ◽  
Concentration Phenomena

The eigenfunction expansion method is introduced into the numerical calculations of elastic plates. Based on the variational method, all the fundamental solutions of the governing equations are obtained directly. Using eigenfunction expansion method, various boundary conditions can be conveniently described by the combination of the eigenfunctions due to the completeness of the solution space. The coefficients of the combination are determined by the boundary conditions. In the numerical example, the stress concentration phenomena produced by the restriction of displacement conditions is discussed in detail.

The Bending Singularity at the Apex of V-Notch in an Anisotropic Thick Plate

2017 ◽  
Vol 735 ◽  
pp. 95-99
Author(s):  
Chung De Chen
Keyword(s):  
Eigenfunction Expansion ◽  
Thick Plate ◽  
Plate Theory ◽  
Expansion Method ◽  
Numerical Results ◽  
The Other ◽  
Mindlin Plate ◽  
Eigenfunction Expansion Method ◽  
Singularity Order ◽  
Mindlin Plate Theory

In this paper, the bending singularity at the apex of V-notch in an anisotropic thick plate is investigated. The Stroh-like formalism is used to model the anisotropy of the material. Based on the Ressiner-Mindlin plate theory and the eigenfunction expansion method, the characteristic equation for bending singularity order is derived and the order can be determined numerically. The numerical results show that the singularity orders strongly depend on the plate angle a. In addition, the singularity orders also depend on the principal orientation of the anisotropic material. The singularity orders for the case of are stronger than for that of. In the case of, to reduce the anisotropy is helpful to release the singularity at the notch tip. For the other case of, it is preferable to increase the anisotropy to reduce the singularity. The disappearance conditions of the bending singularity can be found based on the numerical results.

3-D Eddy Currents Analysis in Orthotropic Materials Using Truncated Region Eigenfunction Expansion Method

2012 ◽  
Vol 239-240 ◽  
pp. 258-263 ◽  
Author(s):  
Yu Jie Bai ◽  
Xiao Zhang Zhang ◽  
Lei Jiang ◽  
Chang Liang Tang
Keyword(s):  
Eigenfunction Expansion ◽  
Eddy Currents ◽  
Separation Of Variables ◽  
Expansion Method ◽  
Orthotropic Materials ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Eigenfunction Expansion Method ◽  
Vector Differential Equation ◽  
Good Agreement

A model for 3-D eddy currents analysis in orthotropic materials such as CFRPs is proposed. With artificial magnetic insulation boundary conditions, we solved a vector differential equation which describes the magnetic vector potential in the CFRPs materials with a delta coil near it using the method of separation of variables. As a result of the truncated region eigenfunction expansion method, a series solution was obtained, from which we got the eddy currents distribution. The distribution shows a good agreement with the work by others.

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