J-estimation formulas for nonlinear crack problems

1994 ◽  
Vol 68 (1) ◽  
pp. R15-R18 ◽  
Author(s):  
Yury G. Matvienko
Keyword(s):  
Crack Problems ◽  
Nonlinear Crack ◽  
J Estimation

Studies of the Line-Spring Model for Nonlinear Crack Problems

1985 ◽  
Vol 107 (4) ◽  
pp. 412-420 ◽  
Author(s):  
V. Kumar ◽  
M. D. German
Keyword(s):  
Finite Element ◽  
Deformation Theory ◽  
Crack Tip ◽  
Surface Cracks ◽  
Spring Model ◽  
Crack Problems ◽  
Line Spring Model ◽  
Nonlinear Crack ◽  
Shell Finite Element ◽  
The Continuum

This paper presents an investigation of the line-spring model (LSM) of Rice and Levy as applied to nonlinear crack problems. A J2 deformation theory of plasticity formulation of a LSM for obtaining the fully plastic crack solutions is first described in the framework of a shell finite element method. Results are obtained for 2-D axial and circumferential cracks in cylinders and are compared against those developed by detailed finite element crack tip analyses. Discrepancies are found in the case of axially cracked cylinders under internal pressure. To overcome this problem a modified approach, termed the continuum-LSM, is presented, and its finite element implementation is described in some detail. It is shown that in contrast to the shell-LSM, the results obtained by the continuum-LSM for internally pressurized axially cracked cylinders are in close agreement with detailed finite element crack-tip calculations. Lastly, a discussion on the fully plastic analysis of surface cracks by the LSM is also given.

Wavelet Finite Element Method Analysis of Bending Plate Based on Hermite Interpolation

2013 ◽  
Vol 389 ◽  
pp. 267-272 ◽  
Author(s):  
Peng Shen ◽  
Yu Min He ◽  
Zhi Shan Duan ◽  
Zhong Bin Wei ◽  
Pan Gao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Thin Plate ◽  
Hermite Interpolation ◽  
Energy Functional ◽  
Field Function ◽  
Wavelet Finite Element Method ◽  
Wavelet Finite Element ◽  
Crack Problems ◽  
Element Method

In this paper, a new kind of finite element method (FEM) is proposed, which use the two-dimensional Hermite interpolation scaling function constructed by tensor product as the basis interpolation function of field function, and then combine with the energy functional with related mechanics and variational principle, the wavelet finite element equations for solving elastic thin plate unit that constructed in this paper are derived. Then the bending problem of thin plate is solved very quickly and availably through the matlab program. The numerical example in this paper indicates the correctness and validity of this method, and has high calculation precision and convergence speed. Moreover, it also provides a reliable method to solve the free vibration problem of thin plate and the pipe crack problems.

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