Smooth convex partition of unity on uniform triangulations with Hermite interpolation using radial ERBS

The PU (partition-of-unity) based FE-RPIM QUAD4 (4-node quadrilateral) element was proposed for statics problems. In this element, hybrid shape functions are constructed through multiplying QUAD4 shape function with radial point interpolation method (RPIM). In the present work, the FE-RPIM QUAD4 element is further applied for structural dynamics. Numerical examples regarding to free and forced vibration analyses are presented. The numerical results show that: (1) If CMM (consistent mass matrix) is employed, the FE-RPIM QUAD4 element has better performance than QUAD4 element under both regular and distorted meshes; (2) The DLMM (diagonally lumped mass matrix) can supersede the CMM in the context of the FE-RPIM QUAD4 element even for the scheme of implicit time integration.

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VARIATIONAL MULTISCALE ANALYSIS OF SOLIDS WITH STRAIN GRADIENT PLASTIC EFFECTS USING MESHFREE APPROXIMATION

International Journal of Computational Methods ◽

10.1142/s0219876205000624 ◽

2005 ◽

Vol 02 (04) ◽

pp. 601-626 ◽

Cited By ~ 2

Author(s):

JEOUNG-HEUM YEON ◽

SUNG-KIE YOUN

Keyword(s):

Strain Gradient ◽

Partition Of Unity ◽

Meshfree Method ◽

Internal Variable ◽

Plasticity Theory ◽

Fine Scale ◽

Meshfree Approximation ◽

Gradient Effect ◽

Classical Plasticity ◽

Variational Form

A meshfree multiscale method is presented for efficient analysis of solids with strain gradient plastic effects. In the analysis of strain gradient plastic solids, localization due to increased hardening of strain gradient effect appears. Chen-Wang theory is adopted, as a strain gradient plasticity theory. It represents strain gradient effects as an internal variable and retains the essential structure of classical plasticity theory. In this work, the scale decomposition is carried out based on variational form of the problem. Coarse scale is designed to represent global behavior and fine scale to represent local behavior and gradient effect by using the intrinsic length scale. From the detection of high strain gradient region, fine scale region is adopted. Each scale variable is approximated using meshfree method. Meshfree approximation is well suited for adaptivity. As a method of increasing resolution, partition of unity based extrinsic enrichment is used. Each scale problem is solved iteratively. The proposed method is applied to bending of a thin beam and bimaterial shear layer and micro-indentation problems. Size effects can be effectively captured in the results of the analysis.

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Application of Extended Finite Element Method (XFEM) to Stress Intensity Factor Calculations

Volume 6A: Materials and Fabrication ◽

10.1115/pvp2015-45032 ◽

2015 ◽

Cited By ~ 1

Author(s):

Do-Jun Shim ◽

Mohammed Uddin ◽

Sureshkumar Kalyanam ◽

Frederick Brust ◽

Bruce Young

Keyword(s):

Finite Element Method ◽

Stress Intensity Factor ◽

Finite Element ◽

Stress Intensity ◽

Intensity Factor ◽

Degrees Of Freedom ◽

Extended Finite Element Method ◽

Partition Of Unity ◽

Extended Finite Element ◽

Element Method

The extended finite element method (XFEM) is an extension of the conventional finite element method based on the concept of partition of unity. In this method, the presence of a crack is ensured by the special enriched functions in conjunction with additional degrees of freedom. This approach also removes the requirement for explicitly defining the crack front or specifying the virtual crack extension direction when evaluating the contour integral. In this paper, stress intensity factors (SIF) for various crack types in plates and pipes were calculated using the XFEM embedded in ABAQUS. These results were compared against handbook solutions, results from conventional finite element method, and results obtained from finite element alternating method (FEAM). Based on these results, applicability of the ABAQUS XFEM to stress intensity factor calculations was investigated. Discussions are provided on the advantages and limitations of the XFEM.

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