Sensitivity Analysis of Quality of B-spline Parameterization on Isogeometric Analysis

Authors

  • Sangamesh Gondegaon M V J College of Engineering Bangalore, India https://orcid.org/0000-0001-8426-086X
  • Hari Kumar Voruganti National Institute of Technology, Warangal, India

DOI:

https://doi.org/10.13052/ejcm1779-7179.29462

Keywords:

Isogeometric analysis, B-spline, parameterization, first fundamental matrix

Abstract

Isogeometric analysis (IGA) is a mesh free technique which make use of B-spline basis functions for geometry and field variable representation. Parameterization of B-spline for IGA is the counterpart of meshing as in finite element method (FEM). The objective of parameterization is to find the optimum set of control points for B-spline modelling. The position of control points of a B-spline model has huge effect on IGA results. In this work, the effect of B-spline parameterization on IGA result is presented. One dimensional case of bar with self-weight is solved and compared with exact analytical solution. First fundamental matrix is used as evaluation metric to check the quality of parameterization for 2-D domains. A heat conduction problem of a square domain is presented to study the parameterization effect for 2-D case.

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Author Biographies

Sangamesh Gondegaon, M V J College of Engineering Bangalore, India

Sangamesh Gondegaon is currently working as Associate Professor at Department of Mechanical Engineering in M. V. J College of Engineering, Bangalore. He received his B.E degree from Sri Jayachamarajendra College of Engineering, Mysore. He received his master degree in Machine Design from B.M.S College of Engineering, Bangalore. He obtained his Ph.D from Department of Mechanical Engineering, National Institute of Technology, Warangal. His research interest are Isogeometric Analysis, Finite Element Analysis and Geometric modelling using B-splines.

Hari Kumar Voruganti, National Institute of Technology, Warangal, India

Hari Kumar Voruganti is currently working as Associate Professor at Department of Mechanical Engineering in National Institute of Technology, Warangal. He received his B.Tech degree from KITS, Warangal. He received his master degree in Automation and Robotics from Osmania University, Hyderabad. He obtained his Ph.D from Department of Mechanical Engineering, Indian Institute of Technology, Kanpur. He went on pursue his Post-Doctoral Fellowship University of the Witwatersrand, Johannesburg. He was also a visiting scholar for Technical University, Berlin, Germany. He previously worked as Assistant Professor in Indian Institute of Information Technology, Design & Manufacturing, Jabalpur. His research interest are Computer Aided Design, Isogeometric Analysis, Structural Optimization, Robotics, Applied Optimization and Computational Biology.

References

Hughes, T. J., Cottrell, J. A., & Bazilevs, Y. (2005). Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer methods in applied mechanics and engineering, 194(39–41), 4135–4195.

Cottrell, J. A., Hughes, T. J., & Bazilevs, Y. (2009). Isogeometric analysis: toward integration of CAD and FEA. John Wiley & Sons.

Xu, G., Mourrain, B., Duvigneau, R., & Galligo, A. (2011). Parameterization of computational domain in isogeometric analysis: methods and comparison. Computer Methods in Applied Mechanics and Engineering, 200(23–24), 2021–2031.

Martin, T., Cohen, E., & Kirby, R. M. (2009). Volumetric parameterization and trivariate B-spline fitting using harmonic functions. Computer aided geometric design, 26(6), 648–664.

Aigner, M., Heinrich, C., Jüttler, B., Pilgerstorfer, E., Simeon, B., & Vuong, A. V. (2009, September). Swept volume parameterization for isogeometric analysis. In IMA international conference on mathematics of surfaces (pp. 19–44). Springer, Berlin, Heidelberg.

Gondegaon, S., & Voruganti, H. K. (2018). An efficient parametrization of planar domain for isogeometric analysis using harmonic functions. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40(10), 493.

Xia, S., & Qian, X. (2018). Generating high-quality high-order parameterization for isogeometric analysis on triangulations. Computer Methods in Applied Mechanics and Engineering, 338, 1–26.

Pan, M., Chen, F., & Tong, W. (2018). Low-rank parameterization of planar domains for isogeometric analysis. Computer Aided Geometric Design, 63, 1–16.

Pan, M., & Chen, F. (2019). Low-rank parameterization of volumetric domains for isogeometric analysis. Computer-Aided Design, 114, 82–90.

Adan, D. H., & Cardoso, R. (2020). Quasi-Isotropic Initial Triangulation of NURBS Surfaces. European Journal of Computational Mechanics, 27–82.

Piegl, L., & Tiller, W. (1996). The NURBS book. Springer Science & Business Media.

Saxena, A., & Sahay, B. (2007). Computer aided engineering design. Springer Science & Business Media.

Xu, G., Mourrain, B., Duvigneau, R., & Galligo, A. (2013). Optimal analysis-aware parameterization of computational domain in 3D isogeometric analysis. Computer-Aided Design, 45(4), 812–821.

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Published

2021-05-13

How to Cite

Gondegaon, S., & Voruganti, H. K. (2021). Sensitivity Analysis of Quality of B-spline Parameterization on Isogeometric Analysis. European Journal of Computational Mechanics, 29(4-6), 345–362. https://doi.org/10.13052/ejcm1779-7179.29462

Issue

2020: Vol 29 Iss 4-6

Section

Original Article