Development of Plate Infinite Element Method for Stress Analysis of Elastic Bodies with Singularities

2013 ◽  
Vol 29 (3) ◽  
pp. 481-492 ◽  
Author(s):  
D. S. Liu ◽  
K. L. Cheng ◽  
Z. W. Zhuang
Keyword(s):  
Stress Analysis ◽  
Simulation Analysis ◽  
Computational Domain ◽  
Computationally Efficient ◽  
Infinite Element ◽  
Cracked Plates ◽  
Elastic Bodies ◽  
Infinite Element Method ◽  
Bending Problems ◽  
Element Method

AbstractA Plate Infinite Element Method (PIEM) formulation based on Reissner-Mindlin theory is proposed for the stress analysis of cracked plates under bending and tension. The validity of the proposed formulation is demonstrated by comparing the results obtained for the normalized Stress Intensity Factor (SIF) under various loading conditions with the solutions presented in the literature. Importantly, the proposed formulation enables the effects of different crack lengths to be analyzed without the need to re-mesh the computational domain for each simulation/analysis. Overall, the PIEM formulation provides an accurate and computationally-efficient means of analyzing a wide variety of plate bending problems.

scholarly journals Development of High-Order Infinite Element Method for Bending Analysis of Mindlin–Reissner Plates

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
D. S. Liu ◽  
Y. W. Chen ◽  
C. J. Lu
Keyword(s):  
Plate Theory ◽  
Reduction Process ◽  
High Order ◽  
Plate Bending ◽  
Computational Domain ◽  
Infinite Element ◽  
Infinite Element Method ◽  
Bending Problems ◽  
Complicated Geometries ◽  
Element Method

An approach is presented for solving plate bending problems using a high-order infinite element method (IEM) based on Mindlin–Reissner plate theory. In the proposed approach, the computational domain is partitioned into multiple layers of geometrically similar virtual elements which use only the data of the boundary nodes. Based on the similarity, a reduction process is developed to eliminate virtual elements and overcome the problem that the conventional reduction process cannot be directly applied. Several examples of plate bending problems with complicated geometries are reported to illustrate the applicability of the proposed approach and the results are compared with those obtained using ABAQUS software. Finally, the bending behavior of a rectangular plate with a central crack is analyzed to demonstrate that the stress intensity factor (SIF) obtained using the high-order PIEM converges faster and closer than low-order PIEM to the analytical solution.

Analysis of Structural and Non-Structural Problems by Coupling of Finite and Infinite Elements

2014 ◽  
Vol 578-579 ◽  
pp. 445-455
Author(s):  
Mustapha Demidem ◽  
Remdane Boutemeur ◽  
Abderrahim Bali ◽  
El-Hadi Benyoussef
Keyword(s):  
Numerical Technique ◽  
Near Field ◽  
Main Idea ◽  
Far Field ◽  
Mining Operations ◽  
Infinite Element ◽  
Infinite Elements ◽  
Structural Problems ◽  
Infinite Element Method ◽  
Element Method

The main idea of this paper is to present a smart numerical technique to solve structural and non-structural problems in which the domain of interest extends to large distance in one or more directions. The concerned typical problems may be the underground excavation (tunneling or mining operations) and some heat transfer problems (energy flow rate for construction panels). The proposed numerical technique is based on the coupling between the finite element method (M.E.F.) and the infinite element method (I.E.M.) in an attractive manner taking into consideration the advantages that both methods offer with respect to the near field and the far field (good accuracy and sensible reduction of equations to be solved). In this work, it should be noticed that the using of this numerical coupling technique, based on the infinite element ascent formulation, has introduced a more realistic and economic way to solve unbounded problems for which modeling and efficiency have been elegantly improved. The types of the iso-parametric finite elements used are respectively the eight-nodes (Q8) and the four-nodes (Q4) for the near field. However, for the far field the iso-parametric infinite elements used are the eight-nodes (Q8I) and the six-nodes (Q6I).

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