Numerical integration over polygons using an eight-node quadrilateral spline finite element

Li, Chong–Jun; Lamberti, Paola; Dagnino, Catterina

doi:10.1016/j.cam.2009.07.017

Cited by 17 publications

(22 citation statements)

References 3 publications

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“…This feature makes the computational cost of our method lower than that one of another Fig. 1 The 8 nodes and 13 domain points on a quadrilateral element similar composite strategy, using a basic (polynomial) interpolatory type cubature, whose interior nodes are not kept in the procedure of subdivision, as remarked in [5].…”

Section: Introductionmentioning

confidence: 88%

“…In this section, we review some results on the interpolation operator and cubature by L8 element basis presented in [4] and [5].…”

Section: L8 Spline Operator and Cubaturementioning

confidence: 99%

“…The cubature is exact for quadratic polynomials on arbitrary convex quadrangulations, and for cubic polynomials on rectangulations [5].…”

Section: L8 Spline Operator and Cubaturementioning

confidence: 99%

“…We evaluate I 2 by the cubature formula over polygons, having degree of exactness 2 [5] and based on the spline finite element method presented in [4], combined with the subdivision technique also of adaptive kind [3]. Then, we apply the same finite element method to evaluate I 1 .…”

Section: Introductionmentioning

confidence: 99%

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Finite-part integrals over polygons by an 8-node quadrilateral spline finite element

Demichelis

Dagnino

2010

Bit Numer Math

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In this paper we consider the numerical integration on a polygonal domainwhere F becomes infinite of order two. We approximate either the finite-part or the two-dimensional Cauchy principal value of the integral by using a spline finite element method combined with a subdivision technique also of adaptive type. We prove the convergence of the obtained sequence of cubatures. Finally, to illustrate the behaviour of the proposed method, we present some numerical examples.

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Section: Introductionmentioning

confidence: 88%

“…In this section, we review some results on the interpolation operator and cubature by L8 element basis presented in [4] and [5].…”

Section: L8 Spline Operator and Cubaturementioning

confidence: 99%

“…The cubature is exact for quadratic polynomials on arbitrary convex quadrangulations, and for cubic polynomials on rectangulations [5].…”

Section: L8 Spline Operator and Cubaturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite-part integrals over polygons by an 8-node quadrilateral spline finite element

Demichelis

Dagnino

2010

Bit Numer Math

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“…Concerning the numerical evaluation of 2D integrals, we mention the cubatures proposed in [8-10, 22, 30, 32], based on tensor product of univariate splines, on C 1 quadratic and C 2 quartic quasi-interpolating splines, defined on criss-cross triangulations and on Powell-Sabin partitions. Furthermore, numerical integration over polygons using an eight-node quadrilateral spline finite element is presented and studied in [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Numerical integration based on trivariate C 2 quartic spline quasi-interpolants

2013

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In this paper we consider the space generated by the scaled translates of the trivariate C 2 quartic box spline B defined by a set X of seven directions, that forms a regular partition of the space into tetrahedra. Then, we construct new cubature rules for 3D integrals, based on spline quasi-interpolants expressed as linear combinations of scaled translates of B and local linear functionals.We give weights and nodes of the above rules and we analyse their properties. Finally, some numerical tests and comparisons with other known integration formulas are presented.

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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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Numerical integration over polygons using an eight-node quadrilateral spline finite element

Cited by 17 publications

References 3 publications

Finite-part integrals over polygons by an 8-node quadrilateral spline finite element

Finite-part integrals over polygons by an 8-node quadrilateral spline finite element

Numerical integration based on trivariate C 2 quartic spline quasi-interpolants

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

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