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

Zhang, Xuefeng; Subbarayan, Ganesh

doi:10.1016/j.advengsoft.2005.08.001

Cited by 20 publications

(9 citation statements)

References 29 publications

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“…The network model used in the present study was verified in our prior work against exhaustive full-field simulations using a sophisticated meshless computational tool [22]. The full-field models themselves were verified in our prior work against experimentally measured effective conductivity values on systems consisting of alumina as well as aluminum in epoxy matrix [19].…”

Section: Introductionmentioning

confidence: 80%

The Effect of Polydispersivity on the Thermal Conductivity of Particulate Thermal Interface Materials

Kanuparthi

Subbarayan

Siegmund

et al. 2009

IEEE Trans. Comp. Packag. Technol.

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A critical need in developing thermal interface materials (TIMs) is an understanding of the effect of particle/matrix conductivities, volume loading of the particles, the size distribution, and the random arrangement of the particles in the matrix on the homogenized thermal conductivity. Commonly, TIM systems contain random spatial distributions of particles of a polydisperse (usually bimodal) nature. A detailed analysis of the microstructural characteristics that influence the effective thermal conductivity of TIMs is the goal of this paper. Random microstructural arrangements consisting of lognormal size-distributions of alumina particles in silicone matrix were generated using a drop-fall-shake algorithm. The generated microstructures were statistically characterized using the matrix-exclusion probability function. The filler particle volume loading was varied over a range of 40-55 %. For a given filler volume loading, the effect of polydispersivity in the microstructures was captured by varying the standard deviation(s) of the filler particle size distribution function. For each particle arrangement, the effective thermal conductivity of the microstructures was evaluated through numerical simulations using a network model previously developed by the authors. Counter to expectation, increased polydispersivity was observed to increase the effective conductivity up to a volume loading of 50%. However, at a volume loading of 55%, beyond a limiting standard deviation of 0.9, the effective thermal conductivity decreased with increased standard deviation suggesting that the observed effects are a trade-off between resistance to transport through the particles versus transport through the inter-particle matrix gap in a percolation chain.

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Section: Introductionmentioning

confidence: 80%

The Effect of Polydispersivity on the Thermal Conductivity of Particulate Thermal Interface Materials

Kanuparthi

Subbarayan

Siegmund

et al. 2009

IEEE Trans. Comp. Packag. Technol.

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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: 93%

“…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%

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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“…As a result, a bunch of FEM-based codes used object-oriented concept as their implementation strategy, such as: a C++ based finite element code developed by Patzak et al (2001), a meshless Object-oriented programming (OOP) code using non-uniform rational b-spline, Zhang et al (2006), Freefem++, Hecht (2012, a fem code to solve two-and three-dimensional problems, a general framework for weak-form meshfree methods by Hsieh et al (2014), and an educational FE software for truss structures presented by .…”

Section: Introductionmentioning

confidence: 99%

Imposition of Dirichlet Boundary Conditions in Element Free Galerkin Method through an Object-Oriented Implementation

Hosseini

Malekan

Pitangueira

et al. 2017

Lat. Am. j. solids struct.

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One of the main drawbacks of Element Free Galerkin (EFG) method is its dependence on moving least square shape functions which don't satisfy the Kronecker Delta property, so in this method it's not possible to apply Dirichlet boundary conditions directly. The aim of the present paper is to discuss different aspects of three widely used methods of applying Dirichlet boundary conditions in EFG method, called Lagrange multipliers, penalty method, and coupling with finite element method. Numerical simulations are presented to compare the results of these methods form the perspective of accuracy, convergence and computational expense. These methods have been implemented in an object oriented programing environment, called IN-SANE, and the results are presented and compared with the analytical solutions.

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

Cited by 20 publications

References 29 publications

The Effect of Polydispersivity on the Thermal Conductivity of Particulate Thermal Interface Materials

The Effect of Polydispersivity on the Thermal Conductivity of Particulate Thermal Interface Materials

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

Imposition of Dirichlet Boundary Conditions in Element Free Galerkin Method through an Object-Oriented Implementation

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