NURBS-based solutions to inverse boundary problems in droplet shape prediction

Renken, Finn; Subbarayan, Ganesh

doi:10.1016/s0045-7825(00)00168-7

Cited by 28 publications

(12 citation statements)

References 8 publications

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“…This fact has been exploited by the author and his co-workers in their recent research [1,2,[21][22][23][24][25]. The promise of NURBS is that the geometrical changes are naturally reflected in a re-discretization of the behavioural fields without 'remeshing' since the two representations are iso-parametric.…”

Section: Nurbs-based Local Approximation Spacesmentioning

confidence: 99%

“…The analysis techniques on the other hand are not aware of the process used to construct the geometry. While the use of the same basis to represent geometry and behavioural fields (as described in References [1,2]) enables tighter integration, even greater integration is possible if the analysis procedure is cognizant of geometry construction. Ideally, any effect of local domain change would remain localized both during mesh generation as well as during the analysis process.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Renken [1], Grindeanu et al [19], Renken and Subbarayan [2], Bobaru and Mukherjee [20], Natekar [21], Natekar et al [22], Zhang [23], Zhang et al [24], Zhang and Subbarayan [25] have proposed meshless analysis as a means to alleviate the problem of remeshing during shape optimal design. Grindeanu et al used the reproducing particle method [26], Renken, Renken and Subbarayan, Natekar, Natekar et al, Zhang, Zhang et al, and Zhang and Subbarayan used non-uniform rational B-spline (NURBS, [27]) functions to represent the geometry as well as to discretize the behavioural fields.…”

Section: Introductionmentioning

confidence: 99%

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CAD inspired hierarchical partition of unity constructions for NURBS‐based, meshless design, analysis and optimization

Rayasam

Srinivasan

Subbarayan

2007

Numerical Meth Engineering

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SUMMARYIn this paper we develop a unified representational paradigm for design and analysis that is inspired by the set theoretic Boolean operations of the constructive solid geometry (CSG) procedure of computer-aided design (CAD). We develop the notion of a primitive design state (corresponding to a CSG primitive region), which is characterized by a description of the geometrical shape of the primitive and by a description of the material distribution within the primitive. We analogously define a primitive behaviour state that is associated with a primitive design state and that is determined through a global analysis problem. We define a global multi-level design problem to determine the primitive design states. We define Boolean operations on the fields belonging to primitive design and behaviour spaces and show that the compositions of these fields amount to a hierarchical partition of unity construction. We propose to use non-uniform rational Bsplines (NURBS) to discretize the geometry, material, and behavioural fields (local approximations) defined on the primitive regions. We show that this leads to recursive partition of unity constructions on the knot spaces (sub-local approximations) due to the partition of unity property of NURBS basis functions. Since the primitive shapes are parametrically defined using NURBS, the numerical quadrature is carried out on the parametric sub-regions of the NURBS entities. This eliminates the need for either a background mesh or a pseudo-mesh for quadrature. The developed methodology is implemented in a symbolic, meshless computational framework written using the java language (jNURBS) and was demonstrated on two classes of problems. The first class is the simultaneous optimal design of shape and multi-material distributions. The procedure is argued as being a generalization of classical topology optimization to designing objects made of functionally graded materials with pre-defined geometrical constraints, such as holes or fixed boundary shape. The second class of problems demonstrated in the paper is optimal design to mitigate the effects of cracks. Here, we identify the optimal locations of holes introduced to reduce the stress intensity factor of an edge crack.

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Section: Nurbs-based Local Approximation Spacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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CAD inspired hierarchical partition of unity constructions for NURBS‐based, meshless design, analysis and optimization

Rayasam

Srinivasan

Subbarayan

2007

Numerical Meth Engineering

Self Cite

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“…Embedding a curve to a surface is more challenging; the algorithm for converting the twodimensional (in parameterized space) curve into an equivalent three-dimensional curve in explicit coordinates is involved and is discribed in Ref. [23]. An application of the embedded constraint is illustrated in the example problem involving the droplet shape (Section 6.1).…”

Section: Definition Of Constraintsmentioning

confidence: 99%

jNURBS: An object-oriented, symbolic framework for integrated, meshless analysis and optimal design

Zhang

Subbarayan

2006

Advances in Engineering Software

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“…Isogeometric methods have become very popular in the last decade, see [1,7,8,9,10,11] to name a few. These methods consider a CAD description of the entire computational domain and the solution is approximated using the same basis used for the CAD representation of the geometry.…”

Section: Introductionmentioning

confidence: 99%

3D NURBS‐enhanced finite element method (NEFEM)

Sevilla

Fernández‐Méndez

Huerta

2011

Numerical Meth Engineering

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This paper presents the extension of the recently proposed NURBS-Enhanced Finite Element Method (NEFEM) to 3D domains. NEFEM is able to exactly represent the geometry of the computational domain by means of its CAD boundary representation with Non-Uniform Rational B-Splines (NURBS) surfaces. Specific strategies for interpolation and numerical integration are presented for those elements affected by the NURBS boundary representation. For elements not intersecting the boundary, a standard finite element rationale is used, preserving the efficiency of classical FEM. In 3D NEFEM special attention must be paid to geometric issues that are easily treated in the 2D implementation. Several numerical examples show the performance and benefits of NEFEM compared to standard isoparametric or cartesian finite elements. NEFEM is a powerful strategy to efficiently treat curved boundaries and it avoids excessive mesh refinement to capture small geometric features.

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NURBS-based solutions to inverse boundary problems in droplet shape prediction

Cited by 28 publications

References 8 publications

CAD inspired hierarchical partition of unity constructions for NURBS‐based, meshless design, analysis and optimization

CAD inspired hierarchical partition of unity constructions for NURBS‐based, meshless design, analysis and optimization

jNURBS: An object-oriented, symbolic framework for integrated, meshless analysis and optimal design

3D NURBS‐enhanced finite element method (NEFEM)

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