Adaptive isogeometric analysis in structural frames using a layer-based discretization to model spread of plasticity

Liu, Ning; Jeffers, Ann E.

doi:10.1016/j.compstruc.2017.10.016

Cited by 38 publications

(19 citation statements)

References 27 publications

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“…The first 10 mode shapes of the plate with a heart-shape cutout [Colour figure can be viewed at wileyonlinelibrary.com] reference solutions are available in the literature. [8][9][10] The dimensionless parameter Ω nd defined in Equation (37) is used to measure the natural frequency. The automatically generated meshes are shown in Figure 12, in which we can observe that the proposed approach is able to handle sharp geometric corners fairly easily.…”

Section: Figure 13mentioning

confidence: 99%

“…The patch interface is either C 0 ‐continuous or simply not closed (ie, nonphysical gaps). To regain control of the smoothness across the patch boundaries, additional efforts such as the imposition of geometric constraints or the bending strip method are necessary, which requires extra computational time. On the other hand, a variety of local refinement techniques have been developed to overcome the problematic tensor product structure of NURBS, such as hierarchical B‐splines, truncated hierarchical B‐splines, T‐splines, locally refined splines, and polynomial splines over hierarchical T‐meshes .…”

Section: Introductionmentioning

confidence: 99%

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A geometrically exact isogeometric Kirchhoff plate: Feature‐preserving automatic meshing and C¹ rational triangular Bézier spline discretizations

Liu

Jeffers

2018

Numerical Meth Engineering

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Summary The analysis of the Kirchhoff plate is performed using rational Bézier triangles in isogeometric analysis coupled with a feature‐preserving automatic meshing algorithm. Isogeometric analysis employs the same basis function for geometric design as well as for numerical analysis. The proposed approach also features an automatic meshing algorithm that admits localized geometric features (eg, small geometric details and sharp corners) with high resolution. Moreover, the use of rational triangular Bézier splines for domain triangulation significantly increases the flexibility in discretizing spaces bounded by complicated nonuniform rational B‐spline curves. To raise the global continuity to C1 for the solution of the plate bending problem, Lagrange multipliers are leveraged to impose continuity constraints. The proposed approach also manipulates the control points at domain boundaries in such a way that the geometry is exactly described. A number of numerical examples consisting of static bending and free vibration analysis of thin plates bounded by complicated nonuniform rational B‐spline curves are used to demonstrate the advantage of the proposed approach.

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Section: Figure 13mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A geometrically exact isogeometric Kirchhoff plate: Feature‐preserving automatic meshing and C¹ rational triangular Bézier spline discretizations

Liu

Jeffers

2018

Numerical Meth Engineering

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“…Because of many advantages of the IgA, the method has been successfully applied in various practical problems, like linear elasticity, structural vibrations, phase transition phenomena, fluid flow simulation, plate and shell analysis, heat transfer analysis, shape optimization, etc., see e.g. [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Lid-Driven Cavity Flow by Isogeometric Analysis

et al. 2021

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In this paper, we present numerical results obtained by an in-house incompressible fluid flow solver based on isogeometric analysis (IgA) for the standard benchmark problem for incompressible fluid flow simulation – lid-driven cavity flow. The steady Navier-Stokes equations are solved in their velocity-pressure formulation and we consider only inf-sup stable pairs of B-spline discretization spaces. The main aim of the paper is to compare the results from our IgA-based flow solver with the results obtained by a standard package based on finite element method with respect to degrees of freedom and stability of the solution. Further, the effectiveness of the recently introduced rIgA method for the steady Navier-Stokes equations is studied.The authors dedicate the paper to Professor K. Kozel on the occasion of his 80th birthday.

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“…There also are researches focusing on analyzing microstructures using isogeometric analysis (IGA) in combination with different plate theories [90][91][92][93]. IGA has been successfully applied in several fields like: [94][95][96][97][98][99][100][101][102][103][104][105]. Ref.…”

Section: Introductionmentioning

confidence: 99%

Size-dependent thermo-mechanical free vibration analysis of functionally graded porous microbeams based on modified strain gradient theory

Zanoosi

2020

J Braz. Soc. Mech. Sci. Eng.

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In present study, vibration analysis of functionally graded (FG) porous microbeam under thermal effects is investigated considering modified strain gradient theory (MSGT) of elasticity. As the main novelty of this study, in order to effectively acquire the effects of size of size-dependent porous structures, MSGT is employed (considers three material length scale parameters) rather than modified couple stress theory (MCST) (considers one material length scale parameter). The nonlinear governing equation of microbeam based on MSGT is derived from Hamilton's principle and to determine the natural frequency of the system under simply supports, Navier solution is employed. Numerical results presented for different beam models and theories and are compared with those available in previous studies. The obtained results show that frequencies from MSGT are higher than those from MCST and also classical theory (CT), especially when the microbeam thickness is comparable to the microbeam length scale parameter. Also, increases in the temperature of microbeam working environment, lead to decrease of microbeam natural frequency. Finally, parametric study is performed on natural frequency of FG microbeams to indicate the effects of: temperature changes, length scale parameter, slender ratio, and gradient index and porosity volume fraction.

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Adaptive isogeometric analysis in structural frames using a layer-based discretization to model spread of plasticity

Cited by 38 publications

References 27 publications

A geometrically exact isogeometric Kirchhoff plate: Feature‐preserving automatic meshing and C¹ rational triangular Bézier spline discretizations

A geometrically exact isogeometric Kirchhoff plate: Feature‐preserving automatic meshing and C¹ rational triangular Bézier spline discretizations

Numerical Simulation of Lid-Driven Cavity Flow by Isogeometric Analysis

Size-dependent thermo-mechanical free vibration analysis of functionally graded porous microbeams based on modified strain gradient theory

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Adaptive isogeometric analysis in structural frames using a layer-based discretization to model spread of plasticity

Cited by 38 publications

References 27 publications

A geometrically exact isogeometric Kirchhoff plate: Feature‐preserving automatic meshing and C1 rational triangular Bézier spline discretizations

A geometrically exact isogeometric Kirchhoff plate: Feature‐preserving automatic meshing and C1 rational triangular Bézier spline discretizations

Numerical Simulation of Lid-Driven Cavity Flow by Isogeometric Analysis

Size-dependent thermo-mechanical free vibration analysis of functionally graded porous microbeams based on modified strain gradient theory

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A geometrically exact isogeometric Kirchhoff plate: Feature‐preserving automatic meshing and C¹ rational triangular Bézier spline discretizations

A geometrically exact isogeometric Kirchhoff plate: Feature‐preserving automatic meshing and C¹ rational triangular Bézier spline discretizations