R-function method in problems of elastoplastic bending of plates of arbitrary shape

1999 ◽  
Vol 35 (1) ◽  
pp. 76-80
Author(s):  
L. V. Kurpa ◽  
A. V. Arkhipov
Keyword(s):  
Arbitrary Shape ◽  
Function Method ◽  
Elastoplastic Bending

scholarly journals Calculation of Stress Intensity Factors for Elliptical Cracks in Finite Bodies by Using the Boundary Weight Function Method

1999 ◽  
Vol 121 (2) ◽  
pp. 181-187 ◽  
Author(s):  
C.-C. Ma ◽  
I-K. Shen
Keyword(s):  
Stress Intensity ◽  
Weight Function ◽  
Stress Intensity Factors ◽  
Arbitrary Shape ◽  
Function Method ◽  
Weight Functions ◽  
Mode I ◽  
Intensity Factors ◽  
Weight Function Method ◽  
Arbitrary Loading

In this study, mode I stress intensity factors for a three-dimensional finite cracked body with arbitrary shape and subjected to arbitrary loading is presented by using the boundary weight function method. The weight function is a universal function for a given cracked body and can be obtained from any arbitrary loading system. A numerical finite element method for the determination of weight function relevant to cracked bodies with finite dimensions is used. Explicit boundary weight functions are successfully demonstrated by using the least-squares fitting procedure for elliptical quarter-corner crack and embedded elliptical crack in parallelepipedic finite bodies. If the stress distribution of a cut-out parallelepipedic cracked body from any arbitrary shape of cracked body subjected to arbitrary loading is determined, the mode I stress intensity factors for the cracked body can be obtained from the predetermined boundary weight functions by a simple surface integration. Comparison of the calculated results with some available solutions in the published literature confirms the efficiency and accuracy of the proposed boundary weight function method.

scholarly journals Green's Function Method for an Axisymmetric Void Between Parallel Walls

2007 ◽  
Vol 5 (2) ◽  
Author(s):  
Gautam Sudhir Chandekar ◽  
Joseph D. Richardson ◽  
Yuri A. Melnikov ◽  
Sally J. Pardue
Keyword(s):  
Finite Element ◽  
Green’S Function ◽  
Green's Function ◽  
Arbitrary Shape ◽  
Function Method ◽  
Numerical Solutions ◽  
Numerical Implementation ◽  
Finite Element Code ◽  
Present Formulation ◽  
Function Formulation

The Green's function for potential theory is developed for an axisymmetric void of arbitrary shape located between two parallel walls. Numerical results are given to demonstrate the accuracy in the Green's function formulation by comparison with numerical solutions obtained using a commercial finite element code. The present formulation is attractive since numerical implementation only involves unknowns on the surface of the void.

scholarly journals Boundary Weight Functions for Cracks in Three-Dimensional Finite Bodies

1999 ◽  
Vol 15 (1) ◽  
pp. 17-26
Author(s):  
Chien-Ching Ma ◽  
I-Kuang Shen
Keyword(s):  
Stress Intensity ◽  
Weight Function ◽  
Stress Intensity Factors ◽  
Arbitrary Shape ◽  
Function Method ◽  
Three Dimensional ◽  
Weight Functions ◽  
Mode I ◽  
Intensity Factors ◽  
Arbitrary Loading

ABSTRACTAn efficient boundary weight function method for the determination of mode I stress intensity factors in a three-dimensional cracked body with arbitrary shape and subjected to arbitrary loading is presented in this study. The functional form of the boundary weight functions are successfully demonstrated by using the least squares fitting procedure. Explicit boundary weight functions are presented for through cracks in rectangular finite bodies. If the stress distribution of a cut out rectangular cracked body from any arbitrary shape of cracked body subjected to arbitrary loading is determined, the mode I stress intensity factors for the cracked body can be obtained from the predetermined boundary weight functions by a simple integration. Comparison of the calculated results with some solutions by other workers from the literature confirms the efficiency and accuracy of the proposed boundary weight function method.

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