Numerical simulation of holes and inclusions using adaptive polygonal finite element method

Ding, Shengyong; Shao, Guojian; Li, Ang; Su, Jingbo; Shi, Hougai

doi:10.1007/s12206-017-0829-2

Cited by 4 publications

(5 citation statements)

References 38 publications

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“…Other recent techniques/methods include analysis of polygonal carbon nanotubes reinforced composite plates by using the first-order shear deformation theory (FSDT) and the element-free IMLS-Ritz method [174], an adaptive polygonal finite element method using the techniques of cut-cell and quadtree refinement [175], new adaptive mesh generation for polygonal element [176], and ultraweak formulations for high-order polygonal finite element methods [177]. New technique for 3-dimensional polyhedral elements can be seen within the framework of the finite volume method [178].…”

Section: Base Forces Element Methods (Bfem)mentioning

confidence: 99%

A Brief Review on Polygonal/Polyhedral Finite Element Methods

Perumal

2018

Mathematical Problems in Engineering

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This paper provides brief review on polygonal/polyhedral finite elements. Various techniques, together with their advantages and disadvantages, are listed. A comparison of various techniques with the recently proposed Virtual Node Polyhedral Element (VPHE) is also provided. This review would help the readers to understand the various techniques used in formation of polygonal/polyhedral finite elements.

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Section: Base Forces Element Methods (Bfem)mentioning

confidence: 99%

A Brief Review on Polygonal/Polyhedral Finite Element Methods

Perumal

2018

Mathematical Problems in Engineering

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“…The nonlocal governing equations in terms of local stress resultants can be obtained by applying the operator  on both sides of the Equations (14)- (18). Making use of the relations in Equation (19), we obtain:…”

Section: Solution Of Nonlinear Equationsmentioning

confidence: 99%

“…These elements can overcome the problems associated with remeshing in standard adaptive finite elements or meshless methods that have issues with imposition of boundary conditions because of lack of Kronecker delta property in the approximation functions. The polygonal elements have many potential applications to a large variety of problems, including constitutive modeling in nonlinear analysis of polycrystalline materials, linear elasticity, analysis of cracked structures, vibration analysis, crack propagation, large deformation problems, topology optimization, hyperelastic analysis, contact‐impact problems, adaptive meshing, plate bending problems, analysis of generalized elastic solids, and multimaterial discretization and optimization . There are other recent works on extension of polygonal FEM for topology optimization, nonlinear analysis of plates, laminates and functionally graded plates, and fracture problems …”

Section: Introductionmentioning

confidence: 99%

An n‐sided polygonal finite element for nonlocal nonlinear analysis of plates and laminates

Aurojyoti

Raghu

Rajagopal

et al. 2019

Numerical Meth Engineering

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Summary In this study, a locking‐free n‐sided C1 polygonal finite element is presented for nonlinear analysis of laminated plates. The plate kinematics is based on Reddy's third‐order shear deformation theory (TSDT). The in‐plane displacements are approximated using barycentric form of Lagrange shape functions. The weak‐form Galerkin formulation based on the kinematics of TSDT requires the C1 approximation of the transverse displacement over the polygonal element. This is achieved by embedding the C0 Lagrange interpolants over a cubic Bernstein‐Bezier patch defined over the n‐sided polygonal element. Such an approach ensures the continuity of the derivative field at the inter‐element edges. In addition, Eringen's stress‐gradient nonlocal constitutive equations are used in the present formulation to account for nonlocality. The effect of geometric nonlinearity is taken by considering the von Kármán geometric nonlinearity. Examples are presented to show the effect of nonlocality, geometric nonlinearity, and the lamination scheme on the bending behavior of laminated composite plates. The results are compared with analytical solutions, conventional FEM results, and with those available in the literature. Shear locking is addressed considering reduced integration and consistent interpolation techniques. The patch test is used to check the convergence of the element developed.

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“…For tackling arbitrary interfaces in the polygonal FEM, Khoei and Biabanaki [6] introduced an approach in which a uniform non-conformal mesh is decomposed into polygonal elements conforming to the internal interfaces and arbitrary geometries using the concept of conformal decomposition FEM and the level set method. Ding et al [7] presented a fast and efficient adaptive polygonal FEM based on the cut-cell method and quadtree refinement for modeling holes and inclusions. Nevertheless, in these approaches, a conformal mesh remains essential to capture the discontinuity in the models.…”

mentioning

confidence: 99%

“…Fig 7. Normal strain in x-direction with and without mat erial points having different mat erial properties included in PDDO for the harmonic average case…”

mentioning

confidence: 99%

An In-depth Investigation of Bimaterial Interface Modeling Using Ordinary State-based Peridynamics

Nguyen

Wang

Tanaka

et al. 2021

J Peridyn Nonlocal Model

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T his study presents an in-depth investigation of interface modeling techniques in ordinary state-based peridynamics (OSB-PD). By performing numerical examples, the accuracy of each technique is investigated by comparison with the finite element solutions for simple bimaterial interface problems. Subsequently, the capabilities of OSB-PD in treating material interfaces with complicated geometries are demonstrated by solving various problems with a single inclusion or multiple inclusions. Finally, a cracked plate containing an inclusion is considered to study effects of t he inclusion on dynamic stress intensity factor (DSIF). The OSB-PD shows its huge potential in modeling a structure with multiple defects due to the effectiveness and ease of implementation.

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Numerical simulation of holes and inclusions using adaptive polygonal finite element method

Cited by 4 publications

References 38 publications

A Brief Review on Polygonal/Polyhedral Finite Element Methods

A Brief Review on Polygonal/Polyhedral Finite Element Methods

An n‐sided polygonal finite element for nonlocal nonlinear analysis of plates and laminates

An In-depth Investigation of Bimaterial Interface Modeling Using Ordinary State-based Peridynamics

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