3D IEM formulation with an IEM/FEM coupling scheme for solving elastostatic problems

Liu, D. S.; Chiou, D. Y.; Lin, Cheng‐Tung

doi:10.1016/s0965-9978(03)00036-x

Cited by 14 publications

(5 citation statements)

References 11 publications

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“…To solve two-dimensional (2D) and three-dimensional (3D) crack problems, Go et al [16,17] have used the similarity of quadrilateral elements to generate so-called super elements by using iterative methods. Liu et al [18,19] have combined the IEM with the FEM to solve static linear problems and have continuously extended equations from 2D to 3D. Liu et al [20] further derived a high-order IEM equation for analyzing various 2D elastic static problems; they compared their results with those of the traditional loworder IEM and with analytical solutions provided in the literature.…”

Section: Introductionmentioning

confidence: 99%

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

Liu

Chen

2020

Mathematical Problems in Engineering

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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.

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Section: Introductionmentioning

confidence: 99%

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

Liu

Chen

2020

Mathematical Problems in Engineering

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“…Liu has been working on the study of the IEM since the 2000s. Liu et al [Liu and Chiou (2003a); Liu and Chiou (2003b)] proposed a hybrid IE-FE model to analyze elastic problems with multiple cracks. Liu et al [Liu, Zhuang and Chung (2009)] extended the IE-FE formalism to model and analyze moisture diffusion in a heterogeneous epoxy resin containing multiple randomly distributed particles.…”

Section: Introductionmentioning

confidence: 99%

Eigenvalue Analysis of Thin Plate with Complicated Shapes By a Novel Infinite Element Method

Liu¹,

Chen²

2019

Computer Modeling in Engineering &Amp; Sciences

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A novel infinite element method (IEM) is presented for solving plate vibration problems in this paper. In the proposed IEM, the substructure domain is partitioned into multiple layers of geometrically similar finite elements which use only the data of the boundary nodes. A convergence criterion based on the trace of the mass matrix is used to determine the number of layers in the IE model partitioning process. Furthermore, in implementing the Craig-Bampton (CB) reduction method, the inversion of the global stiffness matrix is calculated using only the stiffness matrix of the first element layer. The validity and performance of the proposed method are investigated by means of four illustrative problems. The first example considers the case of a simple clamped rectangular plate. It is observed that the IEM results are consistent with the theoretical results for first six natural frequencies. The second example considers the frequency response of a clamped rectangular plate with a crack. The main feature of IEM is that a very fine and good quality virtual mesh can be created around the crack tip. The third and fourth examples consider the natural frequency of a multiple point supported plate and a perforated plate, respectively. The results are obtained just need to adjust the reference point or boundary nodes. The parametric analyses for various geometric profiles are easy to be conducted using these numerical techniques. In general, the results presented in this study have shown that the proposed method provides a direct, convenient and accurate tool for eigenvalue analysis of thin plate structure with complicated shapes.

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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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3D IEM formulation with an IEM/FEM coupling scheme for solving elastostatic problems

Cited by 14 publications

References 11 publications

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

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

Eigenvalue Analysis of Thin Plate with Complicated Shapes By a Novel Infinite Element Method

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

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