An extended isogeometric thin shell analysis based on Kirchhoff–Love theory

Nguyen‐Thanh, Nhon; Valizadeh, Navid; Nguyen, Minh Ngoc; Nguyen‐Xuan, H.; Zhuang, Xiaoying; Areias, P.; Zi, Goangseup; Bazilevs, Yuri; Lorenzis, Laura De; Rabczuk, Timon

doi:10.1016/j.cma.2014.08.025

Cited by 323 publications

(84 citation statements)

References 75 publications

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“…in which L K and NL K are the linear and nonlinear stiffness matrices, respectively, whilst 0 K is the initial stress stiffness matrix due to the initial compressive load by temperature  ˆd (38) and F is the load vector depending on mechanical and thermal loads…”

Section: Non-linear Temperature Change Across the Thicknessmentioning

confidence: 99%

“…The major strengths of this method are that it is flexible to control the high continuity of basis shape functions, e.g. C p-1 -continuity for p th -order NURBS, which naturally fulfil higher-order continuity requirement of plate/shell models [36][37][38] Furthermore, by removal mesh generation feature, this method produces a seamless integration of computer aid design (CAD) and finite element analysis (FEA) tools. As a result, IGA simplifies the cost-intensive computational model generation procedure which is the major bottleneck in engineering analysis-design [39].…”

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confidence: 99%

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Isogeometric analysis for nonlinear thermomechanical stability of functionally graded plates

Tran

Phung‐Van

Lee

et al. 2016

Composite Structures

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Section: Non-linear Temperature Change Across the Thicknessmentioning

confidence: 99%

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confidence: 99%

Isogeometric analysis for nonlinear thermomechanical stability of functionally graded plates

Tran

Phung‐Van

Lee

et al. 2016

Composite Structures

Self Cite

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“…Over the last decade, IGA has become a well-established method used in a wide range of problems including structural mechanics [3][4][5][6][7][8][9][10][11][12] with recent developments for spatial Bernoulli beams [13,14], turbulent flow and fluid-structure interaction [15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams

Marino

2016

Computer Methods in Applied Mechanics and Engineering

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Highlights• Isogeometric collocation is extended to geometrically exact beams.• Consistent linearization of the strong form of the governing equations is derived.• Incremental rotations are parametrized through Eulerian rotation vectors.• Numerical tests show efficiency and high accuracy. AbstractWe extend the isogeometric collocation method to the geometrically nonlinear beams. An exact kinematic formulation, able to represent three-dimensional displacements and rotations without any restriction in magnitude, is presented without the introduction of the moving frame concept. A displacement-based formulation is adopted. Full linearization of the strong form of the governing equations is derived consistently with the underlying geometric structure of the configuration manifold. Incremental rotations are parametrized through Eulerian rotation vectors and configuration updates are performed by means of the exponential map. Numerical tests demonstrate that the proposed combination of isogeometric collocation method with the chosen rotations parametrization results in an efficient computational scheme able to model complex problems with high accuracy.

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“…In its original, finite element based form, IGA does not completely suppress the need to create a mesh, as the CAD data provides only a 'shell' for the component, but gives no information about the parametrization of the interior of the volume which it encloses. Although the finite element version of IGA was used for fracture analysis [58][59][60][61]. This motivated the inception of a boundary element version of IGA for elasticity problems in [62][63][64].…”

Section: Dealing With Component Complexitymentioning

confidence: 99%

Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth

Peng

Atroshchenko

Kerfriden

et al. 2017

Computer Methods in Applied Mechanics and Engineering

202

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Highlights• We implement an isogeometric BEM routine for fracture by use of dual boundary integral equations.• We propose a singular integration scheme to improve the quadrature accuracy for elements with high aspect ratios.• We investigate the approaches to compute stress intensity factors based on a NURBS representation of the crack surfaces.• We outline a geometric algorithm to propagate the crack based on the fatigue Paris law. AbstractWe present a novel numerical method to simulate crack growth in 3D, directly from the Computer-Aided Design (CAD) geometry of the component, without any mesh generation. The method is an isogeometric boundary element method (IGABEM) based on non-uniform rational B-splines (NURBS). NURBS basis functions are used for the domain and crack representation as well as to approximate the physical quantities involved in the simulations. A stable quadrature scheme for singular integration is proposed to enhance the robustness of the method in dealing with highly distorted elements. Convergence studies in the crack opening displacement is performed for a penny-shaped crack and an elliptical crack. Two approaches to extract stress intensity factors (SIFs): the contour M integral and the virtual crack closure integral are compared using dual integral equations. The results show remarkable accuracy in the computed SIFs, leading to smooth crack paths and reliable fatigue lives, without requiring the generation of any mesh from the CAD model of the component under consideration.

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An extended isogeometric thin shell analysis based on Kirchhoff–Love theory

Cited by 323 publications

References 75 publications

Isogeometric analysis for nonlinear thermomechanical stability of functionally graded plates

Isogeometric analysis for nonlinear thermomechanical stability of functionally graded plates

Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams

Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth

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