A coupled IEM/FEM approach for solving elastic problems with multiple cracks

A 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.

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“…Accordingly, the present study adopts the PIE-FE coupling method technique proposed in [21]. As Fig.…”

Section: Pie-fe Coupling Methodsmentioning

confidence: 99%

“…Liu and Chiou [21][22][23] utilized IEM formulations to solve a variety of elasticity and singularity problems. In addition, the authors proposed a convergence criterion for the IEM formulation which extended the imaginary "infinity layer" concept to practical applications and ensured the convergence of the overall IE stiffness matrix.…”

Section: Introductionmentioning

confidence: 99%

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

2013

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“…Due to the similarity property of the isoparametric elements, the stiffness of the lower-level isoparametric element in Fig. 1 is equal to that of the element in the layer above (9)…”

Section: Similarity Of Nine-node Isoparametric Elementsmentioning

confidence: 99%

Development of High-Order Infinite Element Method for Stress Analysis of Elastic Bodies with Singularities

Liu

Cheng

Zhuang

2010

JMMP

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Structural analysis problems are traditionally solved using the Finite Element Method (FEM). However, when the structure of interest contains discontinuities such as cracks or re-entrant corners, a large number of elements are required to accurately reproduce the stress characteristics in the region of the discontinuities. As a result, the FEM method requires a large storage space and has a slow convergence speed. It has been shown that the Infinite Element Method (IEM) overcomes these limitations and provides a feasible means of solving various types of elasticity and singularity problems. Previous studies have generally focused on the use of IEM formulations based on low-order elements (2×2). By contrast, this study develops a high-order (3×3) IEM formulation. The solutions obtained using the proposed IEM method for various 2D elasto-static problems are compared with the results obtained using the traditional low-order IEM method and the analytical solutions presented in the literature. It is shown that the results obtained using the proposed method are more accurate than those obtained using the low-order IEM method and are in excellent agreement with the analytical solutions. 1132heterogeneous properties, those with inhomogeneous behaviors pose a far greater challenge. Various researchers have suggested that the limitations of the FEM and BEM methods can be overcome by the Infinite Element Method (IEM) (3) . The basic principle of IEM involves discretizing the problem domain in to a large numbers of elements using a suitable partitioning technique and nodal sequence such that each element layer is similar to the other layers. Ying (4) , Han and Ying (5) , and Ying and Pan (6) developed the mathematical foundations of the IEM formulation for the Laplace equation, exterior Stokes problem, corner problem, and planar elasticity problem in fracture mechanics. Ying (7) proved the existence of a transformation matrix relating the nodal displacement vectors of the inner and outer layers, respectively, and showed that the stiffness matrices associated with each layer could therefore be combined to form an overall stiffness matrix defined in terms of the boundary nodes and tractions only. In addition, it was shown that the combined stiffness matrix converges to a certain constant quantity as the number of element layers approaches infinity. Guo (8) proved that the concept of similar elements could be extended to arbitrary isoparametric elements and also presented a transformation procedure for constructing the overall stiffness matrix of the body of interest by combining the local stiffness matrices of each layer. Liu and Chiou (9)-(12) recently developed both 2D (2×2) and 3D (2×2×2) IEM formulations to solve a variety of elasticity and singularity problems. In addition, the authors proposed a convergence criterion for the IEM formulation which extended the imaginary "infinity layer" concept to practical applications and ensured the convergence of the overall IE stiffness matrix.Previous researchers have generally focu...

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“…However, a large number of fine finite elements are required, and mesh modeling is generally a tedious and complicated task, particularly when the aim is to clarify the relationship between the volume fraction of the particles and the rate of moisture diffusion. In a series of related studies, Liu, Chen and Chiou [6][7][8][9][10][11] discussed the recent developments in 2-D and 3-D infinite element methods (IEM). The conventional IEM approach has been implemented in computer codes to deal with various types of classical elasticity and singularity problems.…”

Section: Introductionmentioning

confidence: 99%

“…The conventional IEM approach has been implemented in computer codes to deal with various types of classical elasticity and singularity problems. In [6][7][8][9][10][11], the authors also extended the IEM method to deal with electrostatic problems in which the constituent material properties are heterogeneous. The related background and knowledge of the earlier work are summarized in [12][13].…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of moisture diffusion in composite resins containing multiple particles using hybrid moisture element method

Liu

Zhuang

Lin

2010

2010 5th International Microsystems Packaging Assembly and Circuits Technology Conference

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This paper employs a novel numerical technique, designated as the hybrid moisture element method (HMEM), to model and analyze moisture diffusion in composite resins containing multiple particles. The HMEM scheme is based on a hybrid moisture element (HME), whose properties are determined by equivalent moisture capacitance and conductance matrixes calculated using the conventional finite element formulation. A coupled HME-FE scheme is developed and implemented using the commercial FEM software ABAQUS. The HME-FE scheme is then employed to analyze the moisture diffusion characteristics of a heterogeneous composite resin layer containing multiple particles. The analysis commences by comparing the performance of the proposed scheme with that of the conventional FEM method in modeling the moisture diffusion process. Having validated its performance, the scheme is then employed to investigate the relationship between the volume fraction of the particles in the composite resin and the rate of moisture diffusion. It is found that moisture diffusion is retarded significantly as the volume fraction of particles increases. The HMEM approach proposed in this study provides a straightforward and efficient means of modeling moisture diffusion in a heterogeneous composite resin containing multiple randomly distributed particles since only one HME moisture characteristic matrixes needs to be calculated for all HMEs sharing the same characteristics. Furthermore, different volume fractions can be modeled without modifying the original model simply by controlling the size of the inclusion region within the HME domain.

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A coupled IEM/FEM approach for solving elastic problems with multiple cracks

Cited by 16 publications

References 30 publications

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

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

Development of High-Order Infinite Element Method for Stress Analysis of Elastic Bodies with Singularities

Numerical analysis of moisture diffusion in composite resins containing multiple particles using hybrid moisture element method

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