Isogeometric Analysis: Toward Integration of CAD and FEA

By J. Cottrell, Thomas J. R. Hughes, Yuri Bazilevs. 2009

2,781 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7d58c90dd6b5e8a52d3c36a5109f55a2e706e986

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In Computational Mechanics

Citations in the corpus

A hierarchical approach to adaptive local refinement in isogeometric analysis (2011, methodology): “Advection-diffusion This benchmark example is also taken from [1, 2].”
NURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter (2012, neutral): “More details on their use in FEM are given in [43, 44].”
Isogeometric design of elastic arches for maximum fundamental frequency (2011, background): “…however that the exact solution is singular at the supports, which can not be represented with a class of finite dimensional approximation functions defined in the Sobolev H2 space (Evans et al. 2009; Cottrell et al. 2009). undeformed geometry mode 1 7.3 Isogeometric design of a semi-circular arch”
Isogeometric analysis of nearly incompressible large strain plasticity (2014, background): “[6], where a detailed account may be found.”
Transfer learning enhanced physics informed neural network for phase-field modeling of fracture (2019, methodology): “within the whole domain is not efﬁcient for integrating non-smooth functions, which are common in modeling fracture. Therefore, motivated from ﬁnite element analysis [10,11] and isogeometric analysis [12,13], we divide the computational domain into a number of elements and then, the Gauss points are”
Isogeometric collocation: Neumann boundary conditions and contact (2015, neutral): “Introduction Isogeometric analysis (IGA) was recently introduced by Hughes and coworkers [1,2].”
Modeling of a hydraulic arresting gear using fluid-structure interaction and isogeometric analysis (2017, methodology): “We describe a novel technique for IGA analysis-suitable geometry construction of the arresting gear design.”
Sharp error estimates for spline approximation: Explicit constants, n-widths, and eigenfunction convergence (2018, methodology): “es. In particular, isogeometric Galerkin methods aim to approximate solutions of variational formulations of dierential problems by using spline spaces of possibly high degree and maximal smoothness [5]. In this context, a priori error estimates in Sobolev (semi-)norms and corresponding projectors t”
Comparison of different higher order finite element schemes for the simulation of Lamb waves (2012, methodology): “A NURBS curve can be interpreted as projection of a B-spline curve from Rnþ1 on a defined surface in R [56].”
Isogeometric collocation methods for the Reissner–Mindlin plate problem (2015, neutral): “[1,2] with the main goal of bridging the gap between Computer Aided Design (CAD) and Finite Element Analysis (FEA) and of simplifying the expensive mesh generation process required by standard FEA.”
Isogeometric discretizations of the Stokes problem: stability analysis by the macroelement technique (2013, background): “(2005) and Cottrell et al. (2009). at Isituto di M tem atica A picata e Teologie Iform aiche el C N R on Sptem er (2)5, 2012 hp://im ajna.”
The non-symmetric Nitsche method for the parameter-free imposition of weak boundary and coupling conditions in immersed finite elements (2016, methodology): “Imposing nonzero boundary conditions u(x, 0) = sin(πx) and u = 0 on all other boundaries, we obtain the analytical solution [26] uex(x, y) = [cosh(πy)− coth(π) sinh(πy)] sin(πx) (50) We discretize the domain Ω with a Cartesian mesh that defines B-spline basis functions [24].”
A BEM-isogeometric method for the ship wave-resistance problem (2013, methodology): “…the associated physical quantities are expressed via different basis functions, the IGA approach (see, e.g., Hughes et al. (2005), Hughes (2008), Cottrell et al. (2007, 2009)) is based on using the very same basis for representing both the body geometry and the physical quantities, under the…”