Signed algebraic level sets on NURBS surfaces and implicit Boolean compositions for isogeometric CAD–CAE integration

Upreti, Kritika; Subbarayan, Ganesh

doi:10.1016/j.cad.2016.09.006

Cited by 15 publications

(12 citation statements)

References 25 publications

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“…By applying SolidWorks, a parametric CAD model of the fluid domain is established with multiple design variables considering the process constraints of AM. Subsequently, the CAD model of the solid domain with the feature of the wall thickness is built by Boolean operation [42] and the spline interpolation method [43]. All design variables in modeling constitute design points.…”

Section: System Architecturementioning

confidence: 99%

Intelligent Design Optimization System for Additively Manufactured Flow Channels Based on Fluid–Structure Interaction

Zou

et al. 2022

Micromachines

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Based on expert system theory and fluid–structure interaction (FSI), this paper suggests an intelligent design optimization system to derive the optimal shape of both the fluid and solid domain of flow channels. A parametric modeling scheme of flow channels is developed by design for additive manufacturing (DfAM). By changing design parameters, a series of flow channel models can be obtained. According to the design characteristics, the system can intelligently allocate suitable computational models to compute the flow field of a specific model. The pressure-based normal stress is abstracted from the results and transmitted to the solid region by the fluid–structure (FS) interface to analyze the strength of the structure. The design space is obtained by investigating the simulation results with the metamodeling method, which is further applied for pursuing design objectives under constraints. Finally, the improved design is derived by gradient-based optimization. This system can improve the accuracy of the FSI simulation and the efficiency of the optimization process. The design optimization of a flow channel in a simplified hydraulic manifold is applied as the case study to validate the feasibility of the proposed system.

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Section: System Architecturementioning

confidence: 99%

Intelligent Design Optimization System for Additively Manufactured Flow Channels Based on Fluid–Structure Interaction

Zou

et al. 2022

Micromachines

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“…This is because the behavioral influence of the immersed boundaries decays monotonically with distance. While traditionally distances are estimated using Newton-Raphson iterations, recently, Upreti et al [23,24] developed algebraic procedures for efficient computation of distance estimates from curves and surfaces. The method developed by Upreti et al relies on converting the parametric NURBS geometry to its implicit form using the Dixon resultant, and constructing level sets on the implicit form of the geometry.…”

Section: Background On Algebraic Level Setsmentioning

confidence: 99%

“…Next, as before, Equations (20), (23) and (24) can be exploited to obtain the physical footpoint x f in three-dimensional space. Earlier statements on efficiency of the algebraic point projection for rational parametric curves also apply to rational parametric surfaces except that the size of the Dixon matrix M D is 2pq × 2pq, where p and q are the degrees of the rational parametric surface in each dimension.…”

Section: Projection In Physical Spacementioning

confidence: 99%

Algebraic Point Projection for Immersed Boundary Analysis on Low Degree NURBS Curves and Surfaces

et al. 2020

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Point projection is an important geometric need when boundaries described by parametric curves and surfaces are immersed in domains. In problems where an immersed parametric boundary evolves with time as in solidification or fracture analysis, the projection from a point in the domain to the boundary is necessary to determine the interaction of the moving boundary with the underlying domain approximation. Furthermore, during analysis, since the driving force behind interface evolution depends on locally computed curvatures and normals, it is ideal if the parametric entity is not approximated as piecewise-linear. To address this challenge, we present in this paper an algebraic procedure to project a point on to Non-uniform rational B-spline (NURBS) curves and surfaces. The developed technique utilizes the resultant theory to construct implicit forms of parametric Bézier patches, level sets of which are termed algebraic level sets (ALS). Boolean compositions of the algebraic level sets are carried out using the theory of R-functions. The algebraic level sets and their gradients at a given point on the domain are then used to project the point onto the immersed boundary. Beginning with a first-order algorithm, sequentially refined procedures culminating in a second-order projection algorithm are described for NURBS curves and surfaces. Examples are presented to illustrate the efficiency and robustness of the developed method. More importantly, the method is shown to be robust and able to generate valid solutions even for curves and surfaces with high local curvature or G 0 continuity—problems where the Newton–Raphson method fails due to discontinuity in the projected points or because the numerical iterations fail to converge to a solution, respectively.

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“…Mullen et al [6] reconstructed robust and accurate algebraic surface functions to sign the unsigned from scattered and unorganized three-dimensional data point sets. Upreti et al [7] used a technique to sign algebraic level sets on NURBS surface and algebraic Boolean level sets on NURBS surfaces. Rouhani et al [8] applied the algebraic function for polynomial representation system.…”

Section: Introductionmentioning

confidence: 99%

An Improved Curvature Circle Algorithm for Orthogonal Projection onto a Planar Algebraic Curve

2019

Mathematics

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Point orthogonal projection onto planar algebraic curve plays an important role in computer graphics, computer aided design, computer aided geometric design and other fields. For the case where the test point p is very far from the planar algebraic curve, we propose an improved curvature circle algorithm to find the footpoint. Concretely, the first step is to repeatedly iterate algorithm (the Newton’s steepest gradient descent method) until the iterated point could fall on the planar algebraic curve. Then seek footpoint by using the algorithm (computing footpoint q ) where the core technology is the curvature circle method. And the next step is to orthogonally project the footpoint q onto the planar algebraic curve by using the algorithm (the hybrid tangent vertical foot algorithm). Repeatedly run the algorithm (computing footpoint q ) and the algorithm (the hybrid tangent vertical foot algorithm) until the distance between the current footpoint and the previous footpoint is near 0. Furthermore, we propose Second Remedial Algorithm based on Comprehensive Algorithm B. In particular, its robustness is greatly improved than that of Comprehensive Algorithm B and it achieves our expected result. Numerical examples demonstrate that Second Remedial Algorithm could converge accurately and efficiently no matter how far the test point is from the plane algebraic curve and where the initial iteration point is.

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Signed algebraic level sets on NURBS surfaces and implicit Boolean compositions for isogeometric CAD–CAE integration

Cited by 15 publications

References 25 publications

Intelligent Design Optimization System for Additively Manufactured Flow Channels Based on Fluid–Structure Interaction

Intelligent Design Optimization System for Additively Manufactured Flow Channels Based on Fluid–Structure Interaction

Algebraic Point Projection for Immersed Boundary Analysis on Low Degree NURBS Curves and Surfaces

An Improved Curvature Circle Algorithm for Orthogonal Projection onto a Planar Algebraic Curve

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