Fundamental-solution-based finite element model for plane orthotropic elastic bodies

Wang, Hui

doi:10.1016/j.euromechsol.2010.05.003

Cited by 52 publications

(39 citation statements)

References 22 publications

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“…The effect of the locations of source points on the convergence and accuracy of the stress and displacements have been investigated in our previous work [18], which will be omitted in this paper. Figure 4 shows the variations of the stress concentration factors (SCF) of the plate with the increasing ratio b/a of the ellipse.…”

Section: An Anisotropic Plate With An Elliptic Holementioning

confidence: 99%

“…In our analysis, the number of source points is taken to be the same as the number of element nodes, which is free of spurious energy modes and can keep the stiffness equations in full rank, as indicated in [16]. The source point ( 1,2, , ) sj s j n  y  can be generated by [18] 0 0 ( )…”

Section: Assumed Fieldsmentioning

confidence: 99%

“…For each element, two independent fields, i.e. intraelement field and frame field, are assumed [18]. In this approach, the intraelement displacement fields for a particular element e is approximated in terms of a linear combination of fundamental solutions of the problem as   …”

Section: Assumed Fieldsmentioning

confidence: 99%

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Mesh reduction strategy: special element for modelling anisotropic materials with defects

Cao

Qin

2013

Boundary Elements and Other Mesh Reduction Methods XXXVI

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In this paper we present a hybrid finite element method (HFS-FEM) to model efficiently and accurately anisotropic materials with defects by developing special elements for elliptic hole/crack based on their associated Green's functions. The hybrid method is formulated based on two independent assumptions: intra-element field in terms of the combination of fundamental solutions and inter-element frame fields along the element boundary. A modified functional, which is satisfying the governing equation, boundary and continuity conditions between elements, is proposed to derive the element stiffness. In this work, the foundational solutions of the anisotropic materials following Stroh formalism are employed to approximate the intra-element displacement field of general elements, while the special fundamental solutions satisfying the required boundary conditions for hole or crack are used for the special elements containing defects. Two examples are presented to assess the performance of the proposed method. Numerical results obtained for the stress concentration factor (SCF) and stress intensity factor (SIF) are extremely accurate for the investigated cases.

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Section: An Anisotropic Plate With An Elliptic Holementioning

confidence: 99%

Section: Assumed Fieldsmentioning

confidence: 99%

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Mesh reduction strategy: special element for modelling anisotropic materials with defects

Cao

Qin

2013

Boundary Elements and Other Mesh Reduction Methods XXXVI

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“…As an extension of our previous works [10][11][12], in the current computational model, a nanoscale axisymmetric cylindrical representative volume element (RVE) containing a single centered effective solid nanofiber is considered. The FS of axisymmetric problems are employed to construct the intra-element temperature field and an independent frame field along the element boundary is defined using conventional shape functions.…”

Section: Introductionmentioning

confidence: 99%

A fundamental solution based FE model for thermal analysis of nanocomposites

Wang

Qin

2011

Boundary Elements and Other Mesh Reduction Methods XXXIII

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This paper presents a fundamental solution (FS) based finite element (FE) formulation for analyzing the axisymmetric thermal behavior of composites enhanced with carbon nanofibers (CNFs) or carbon nanotubes (CNTs), which are modeled by a cylindrical representative volume element (RVE). The proposed approach utilizes the axisymmetric FS to construct an intra-element approximate field within the element and describes the element boundary field using conventional shape functions. A new hybrid variational functional is developed to establish a linkage between the independent intra-element field and the element boundary fields and generate the final force-displacement equations. Several numerical examples are considered to assess the efficiency and accuracy of the proposed model. The results show that the radius of the nanofiller and the thickness of the interface have little effect on thermal conductivity of the composites, whereas the length of the nanofiller and the material parameters of the interface play an important role in the effective thermal conductivity of the composites.

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“…In this study, another numerical method different to the conventional FEM and BEM (Bathe, 2006;Qin, 1994;1995;2003;Qin and Mai, 2002), called the fundamental solution-based (or Green's function based) hybrid FEM (HFS-FEM), is formulated for solving such problems in two-dimensional isotropic dams and a multi-node element is developed to model the region close to the free surface for simplifying the mesh redefinition. The HFS-FEM was firstly presented by Wang and Qin for heat transfer analysis (Wang and Qin, 2009) and then was extended to analyze elastic stress field (Wang and Qin, 2010b;Wang and Qin, 2011a;Wang and Qin, 2012b), thermal properties of advanced functional/composite materials (Wang and Qin, 2011b;Wang et al, 2012;Wang et al, 2013) and bioheat transfer in biological tissues (Wang and Qin, 2010a;Wang and Qin, 2012a) with general/special elements to achieve the purpose of high accuracy and mesh reduction. It should be mentioned that convergence of the HFS-FEM was fully discussed in these works.…”

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confidence: 99%

Green's function based finite element formulations for isotropic seepage analysis with free surface

Wang

Gao

2015

Lat. Am. j. solids struct.

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A solution procedure using the Green's function based finite element method (FEM) is presented for two-dimensional nonlinear steadystate seepage analysis with the presence of free surface in isotropic dams. In the present algorithm, an iteration strategy is designed to convert the over-specified free surface problem to a regular partial differential equation problem. Then, at each iteration step, the Green's function for isotropic linear seepage partial differential equation is employed to construct the element interior water head field, while the conventional shape functions are used for the independent element frame water head field. Then these two independent fields are connected by a double-variable hybrid functional to produce the final solving equation system. By means of the physical definition of Green's function, all two-dimensional element domain integrals in the present algorithm can reduce to one-dimensional element boundary integrals, so that versatile multinode element is constructed to simplify mesh reconstruction during iteration. Finally, numerical results from the present Green's function based FEM with isotropic Green's function kernels are compared with other numerical results to verify and demonstrate the performance of the present method.

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Fundamental-solution-based finite element model for plane orthotropic elastic bodies

Cited by 52 publications

References 22 publications

Mesh reduction strategy: special element for modelling anisotropic materials with defects

Mesh reduction strategy: special element for modelling anisotropic materials with defects

A fundamental solution based FE model for thermal analysis of nanocomposites

Green's function based finite element formulations for isotropic seepage analysis with free surface

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