Study of composite material damage problem using coupled peridynamics and finite element method

Liu, Shuo; Fang, Guodong; Fu, Maoqing; Bing, Wang; Liang, Jun

doi:10.1360/sst-2019-0068

Cited by 6 publications

(6 citation statements)

References 5 publications

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“…As can be seen, the FPM and PG-FPMs can get a good approximation of the temperature distribution in the global domain even if the subdomain boundaries do not coincide with the crack strictly. These results are also qualitatively consistent with ABAQUS and numerical solutions shown in the previous studies 42,25 .…”

Section: Some Practical Examplessupporting

confidence: 92%

Meshless Fragile Points Methods Based on Petrov-Galerkin Weak-Forms for Transient Heat Conduction Problems in Complex Anisotropic Nonhomogeneous Media

Guan

Atluri

2021

Preprint

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Three kinds of Fragile Points Methods based on Petrov-Galerkin weak-forms (PG-FPMs) are proposed for analyzing heat conduction problems in nonhomogeneous anisotropic media. This is a follow-up of the previous study on the original FPM based on a symmetric Galerkin weak-form. The trial function is piecewisecontinuous, written as local Taylor expansions at the Fragile Points. A modified Radial Basis Function-based Differential Quadrature (RBF-DQ) method is employed for establishing the local approximation. The Dirac delta function, Heaviside step function, and the local fundamental solution of the governing equation are alternatively used as test functions. Vanishing or pure contour integral formulation in subdomains or on local boundaries can be obtained. Extensive numerical examples in 2D and 3D are provided as validations. The collocation method (PG-FPM-1) is superior in transient analysis with arbitrary point distribution and domain partition.The finite volume method (PG-FPM-2) shows the best efficiency, saving 25% to 50% computational time comparing with the Galerkin FPM. The singular solution method (PG-FPM-3) is highly efficient in steady-state analysis. The anisotropy and nonhomogeneity give rise to no difficulties in all the methods. The proposed PG-FPM approaches represent an improvement to the original Galerkin FPM, as well as to other meshless methods in earlier literature.

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Section: Some Practical Examplessupporting

confidence: 92%

Meshless Fragile Points Methods Based on Petrov-Galerkin Weak-Forms for Transient Heat Conduction Problems in Complex Anisotropic Nonhomogeneous Media

Guan

Atluri

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…As can be seen, the FPM and PG‐FPMs can get a good approximation of the temperature distribution in the global domain even if the subdomain boundaries do not coincide with the crack strictly. These results are also qualitatively consistent with ABAQUS and numerical solutions shown in the previous studies 27,44 …”

Section: D Examplessupporting

confidence: 91%

“…These results are also qualitatively consistent with ABAQUS and numerical solutions shown in the previous studies. 27,44 The corresponding computational parameters and times of the different methods in solving Ex. (1.7) are listed in Table 9.…”

Section: Some Practical Examplesmentioning

confidence: 99%

Meshless fragile points methods based on Petrov‐Galerkin weak‐forms for transient heat conduction problems in complex anisotropic nonhomogeneous media

Guan

Atluri

2021

Numerical Meth Engineering

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Three kinds of fragile points methods based on Petrov-Galerkin weak-forms (PG-FPMs) are proposed for analyzing heat conduction problems in nonhomogeneous anisotropic media. This is a follow-up of the previous study on the original FPM based on a symmetric Galerkin weak-form. The trial function is piecewise-continuous, written as local Taylor expansions at the fragile points. A modified radial basis function-based differential quadrature (RBF-DQ) method is employed for establishing the local approximation. The Dirac delta function, Heaviside step function, and the local fundamental solution of the governing equation are alternatively used as test functions. Vanishing or pure contour integral formulation in subdomains or on local boundaries can be obtained. Extensive numerical examples in 2D and 3D are provided as validations. The collocation method (PG-FPM-1) is superior in transient analysis with arbitrary point distribution and domain partition. The finite volume method (PG-FPM-2)shows the best efficiency, saving 25% to 50% computational time comparing with the Galerkin FPM. The singular solution method (PG-FPM-3) is highly efficient in steady-state analysis. The anisotropy and nonhomogeneity give rise to no difficulties in all the methods. The proposed PG-FPM approaches represent an improvement to the original Galerkin FPM, as well as to other meshless methods in earlier literature.

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“…Let us consider the case when the plate contains 18 inclusions in the form of circles with a radius of 0.03 and coordinates of the centres as follows: (1) (0.2, 0.9); (2) (0.5, 0.9); (3) (0.8, 0.9); (4) (0.2, 0.75); (5) (0.5, 0.75); (6) (0.8, 0.75); (7) As can be seen from the results shown in Figure 16, we can say that, for the given boundary conditions, identification is better than in the case of problem 8. With an increase in the value of q, inclusions are identified better.…”

Section: Problem 8: Identification Of 18 Inclusions With Different He...mentioning

confidence: 99%

Identifying inclusions in a non-uniform thermally conductive plate under external flows and internal heat sources using topological optimization

Krysko

Awrejcewicz

Bodyagina³

et al. 2021

Mathematics and Mechanics of Solids

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We propose applying topological optimization methods based on measuring temperature and heat fluxes to estimate the thermal conductivity of inhomogeneous thermally conductive plates and determine the shape and location of foreign inclusions. Examples of plates subjected to external heat fluxes and heat sources are considered. The solutions are obtained with the help of the finite element method combined with the method of moving asymptotes. The results show that identification accuracy depends on the defined boundary conditions, the source intensity value, heat fluxes, temperature distribution and the shape of the inclusions. For the problem of 18 circular inclusions under different heat fluxes, identification accuracy increases with increasing source intensity values.

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Study of composite material damage problem using coupled peridynamics and finite element method

Cited by 6 publications

References 5 publications

Meshless Fragile Points Methods Based on Petrov-Galerkin Weak-Forms for Transient Heat Conduction Problems in Complex Anisotropic Nonhomogeneous Media

Meshless Fragile Points Methods Based on Petrov-Galerkin Weak-Forms for Transient Heat Conduction Problems in Complex Anisotropic Nonhomogeneous Media

Meshless fragile points methods based on Petrov‐Galerkin weak‐forms for transient heat conduction problems in complex anisotropic nonhomogeneous media

Identifying inclusions in a non-uniform thermally conductive plate under external flows and internal heat sources using topological optimization

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