Skip to main content
SpringerLink
Log in

Fast visualization of finite element analysis results using multiresolution meshes

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

This paper presents a new method for fast visualization of finite element analysis results using multiresolution meshes. The original mesh of a finite element model is coarsened and simplified to quickly visualize finite element results, and the simplified coarse mesh is overlaid with the original mesh in local regions of high stress gradients. Local regions of high stress gradients are efficiently detected by using pre-computed weights for shape function derivatives of finite elements. A parallelization scheme is applied to further accelerate the visualization speed of finite element analysis results. Numerical results show that the present method can be appliable to fast visualization of finite element analysis results in real-time simulations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

x :

Element x coordinate of the hexahedral element

y :

Element y coordinate of the hexahedral element

z :

Element z coordinate of the hexahedral element

ξ :

Reference ξ coordinate of the master element

η :

Reference η coordinate of the master element

ζ :

Reference ζ coordinate of the master element

σ :

Element von-Mises stress of the hexahedral element

N I :

Shape function of node I of the hexahedral element

x I :

Nodal x coordinate at node I of the hexahedral element

y I :

Nodal y coordinate at node I of the hexahedral element

z I :

Nodal z coordinate at node I of the hexahedral element

ξ I :

Nodal ξ coordinate at node I of the master element

η I :

Nodal η coordinate at node I of the master element

ζ I :

Nodal ζ coordinate at node I of the master element

σ I :

Nodal von-Mises stress at node I of the hexahedral element

\(W_x^I\) :

Weight for the x direction at node I of the hexahedral element

\(W_y^I\) :

Weight for the y direction at node I of the hexahedral element

\(W_z^I\) :

Weight for the z direction at node I of the hexahedral element

∣∇ σ∣e :

Magnitude of the element von-Mises stress gradient at the center of the hexahedral element

∣∇ σ∣FEM :

Magnitude of the element von-Mises stress gradient of FEM at the center of the hexahedral element

∣∇ σ∣Weight :

Magnitude of the element von-Mises stress gradient of weight at the center of the hexahedral element

References

  1. J. Z. Zhu and O. C. Zienkiewicz, Adaptive techniques in the finite element method, Communications in Applied Numerical Methods, 4 (1988) 197–204.

    Article  Google Scholar 

  2. K. M. Mao and C. T. Sun, A refined global-local finite element analysis method, International Journal for Numerical Methods in Engineering, 32 (1991) 29–43.

    Article  Google Scholar 

  3. D. P. Young et al., A locally refined rectangular grid finite element method: application to computational fluid dynamics and computational physics, Journal of Computational Physics, 92 (1991) 1–66.

    Article  MathSciNet  Google Scholar 

  4. N. V. Hattangdy, Coarsening of mesh models for representation of rigid objects in finite element analysis, International Journal for Numerical Methods in Engineering, 44 (1999) 313–326.

    Article  Google Scholar 

  5. J. Liu et al., A new method for coarsening tetrahedral meshes, International Journal for Numerical Methods in Engineering, 112 (2017) 2048–2066.

    Article  MathSciNet  Google Scholar 

  6. Z.-Q. Qu, Model Order Reduction Techniques with Applications in Finite Element Analysis, Springer London (2010).

  7. K. Lu et al., Review for order reduction based on proper orthogonal decomposition and outlooks of applications in mechanical systems, Mechanical Systems and Signal Processing, 123 (2019) 264–297.

    Article  Google Scholar 

  8. K. Martynov and U. Wever, On polynomial hyperreduction for nonlinear structural mechanics, International Journal for Numerical Methods in Engineering, 118 (2019) 701–717.

    Article  MathSciNet  Google Scholar 

  9. S. Chaturantabut and D. C. Sorensen, Nonlinear model reduction via discrete empirical interpolation, SIAM Journal on Scientific Computing, 32 (2010) 2737–2764.

    Article  MathSciNet  Google Scholar 

  10. C. Farhat et al., Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy-based mesh sampling and weighting for computational efficiency, International Journal for Numerical Methods in Engineering, 98 (2014) 625–662.

    Article  MathSciNet  Google Scholar 

  11. H. V. Ly and H. T. Tran, Modeling and control of physical processes using proper orthogonal decomposition, Mathematical and Computer Modelling, 33 (2001) 223–236.

    Article  Google Scholar 

  12. M.-N. Nguyen and H.-G. Kim, An efficient PODI method for real-time simulation of indenter contact problems using RBF interpolation and contact domain decomposition, Computer Methods in Applied Mechanics and Engineering, 388 (2021) 114215.

    Article  MathSciNet  Google Scholar 

  13. J. M. Huang et al., Real-time finite element structural analysis in augmented reality, Advances in Engineering Software, 87 (2015) 43–56.

    Article  Google Scholar 

  14. A. Badías et al., Reduced order modeling for physically-based augmented reality, Computer Methods in Applied Mechanics and Engineering, 341 (2018) 53–70.

    Article  MathSciNet  Google Scholar 

  15. A. Abdulali et al., Realistic haptic rendering of hyper-elastic material via measurement-based FEM model identification and real-time simulation, Computers and Graphics, 89 (2020) 38–49.

    Article  Google Scholar 

  16. Š. Beneš and J. Kruis, Efficient methods to visualize finite element meshes, Advances in Engineering Software, 79 (2015) 81–90.

    Article  Google Scholar 

  17. Š. Beneš and J. Kruis, Approximation of large data from the finite element analysis allowing fast post-processing, Advances in Engineering Software, 97 (2016) 17–28.

    Article  Google Scholar 

  18. R. C. Heap, A. I. Hepworth and C. G. Jensen, Real-time visualization of finite element models using surrogate modeling methods, Journal of Computing and Information Science in Engineering ASME, 15 (2015) 011007.

    Article  Google Scholar 

  19. J. Bender and C. Deul, Adaptive cloth simulation using corotational finite elements, Computers and Graphics, 37(7) (2013) 820–829.

    Article  Google Scholar 

  20. J. Bender, D. Weber and R. Diziol, Fast and stable cloth simulation based on multi-resolution shape matching, Computers and Graphics, 37(8) (2013) 945–954.

    Article  Google Scholar 

  21. P. S. Heckbert and M. Garland, Multiresolution modeling for fast rendering, Proceedings of Graphics Interface, May (1994) 43–50.

  22. P. Lindstrom et al., Real-time, continuous level of detail rendering of height fields, Proceedings of ACM SIGGRAPH, August (1996) 109–118.

  23. M. Duchaineau et al., ROAMing terrain: real-time optimally adapting meshes, Proceedings. Visualization 97 (1997) 81–88.

    Google Scholar 

  24. D. T. Lee and B. J. Schachter, Two algorithms for constructing a delaunay triangulation, International Journal of Computer and Information Science, 9 (1980) 219–242.

    Article  MathSciNet  Google Scholar 

  25. T. Möller and B. Trumbore, Fast, minimum storage ray-triangle intersection, Journal of Graphics Tools, 2(1) (1997) 21–28.

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1A4A2000791).

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Graduate School, Seoul National University of Science and Technology, 232 Gongneung-ro, Nowon-gu, Seoul, 01811, Korea

    Jin-Hoo Kim

  2. Department of Mechanical and Automotive Engineering, Seoul National University of Science and Technology, 232 Gongneung-ro, Nowongu, Seoul, 01811, Korea

    Hyun-Gyu Kim

Authors
  1. Jin-Hoo Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hyun-Gyu Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hyun-Gyu Kim.

Additional information

Jin-Hoo Kim is a master student of the School of Mechanical Engineering, Seoul National University of Science and Technology Graduate School, Seoul, Korea. He received his B.S. in Mechanical & Automotive Engineering from Seoul National University of Science and Technology. His research interests include finite element method, model order reduction and hyper-reduction method.

Hyun-Gyu Kim is a Professor in Department of Mechanical and Automotive Engineering at Seoul National University of Science and Technology. He received his Ph.D. degree from Korea Advanced Institute of Science and Technology in 1998. His research interests are in the area of computational solid mechanics with a particular emphasis on the development of novel numerical methods, fracture mechanics, shape and topology optimization, real-time finite element analysis and multi-scale analysis.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kim, JH., Kim, HG. Fast visualization of finite element analysis results using multiresolution meshes. J Mech Sci Technol 36, 4625–4633 (2022). https://doi.org/10.1007/s12206-022-0824-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-022-0824-0

Keywords

Search

Navigation