Skip to main content
SpringerLink
Log in

Mesh free method based on local cartesian frame

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

A new mesh free method proposed by the authors was presented, in which the derivatives at each node were constructed using whole derivative formulas through the nodes selected around the node using local Cartesian frame in an autonomous manner, so that without any element it could be considered as a completely mesh free method. The method was tested with a numerical example, and reliable solution was obtained with high accuracy and efficiency.

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

References

  1. Onate E, Idelsolm S, Zienkiewicz O C, Fisher T. A finite point method for analysis of fluid flow problem[C]. In: Proceedings of the 9th Int Conference on Finite Element Methods in Fluids. Venize, Italy, 15–21 October, 1995.

  2. Onate E, Idelsolm S, Zienkiewicz O C, Taylor R L. A finite point method in computational mechanics. Applications to convective transport and fluid flow[J]. Int J Num Meth Eng, 1996, 39:3839–3866.

    Google Scholar 

  3. Beissel S, Belytschko B. Nodal integration of the element-free Galerkin method[J]. Comput Methods Appl Mech Engrg, 1996, 139:49–74.

    Article  MathSciNet  Google Scholar 

  4. Furukawa T, Yang C, Yagawa G, Wu C C. Quadrilateral approaches for accurate free mesh method[J]. Int J Num Meth Eng, 2000, 47:1445–1462.

    Article  Google Scholar 

  5. Premoze S, Tasdizen T, Bigler J, Lefohn A, Whitaker R T. Particle-based simulation of fluids[J]. Eurographics, 2003, 22(3): 401–410.

    Google Scholar 

  6. Monaghan J J. Smoothed particle hydrodynamics:Some recent improvement and application[J]. Annu Rev Astron Physics, 1992, 30:543–574.

    Google Scholar 

  7. Liu W K, Jun S, Li S, Adee J, Belytschko T. Reproducing kernel particle method for structure dynamics[J]. Int J Num Meth Eng, 1995, 38:1655–1679.

    MathSciNet  Google Scholar 

  8. Zienkiewicz O C, Taylor R L. The Finite Element Method[M]. Vol.1, 5th ed, Elsevier, 2000.

Download references

Author information

Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, P.R. China

    Liu Gao-lian  (刘高联) & Li Xiao-wei  (李孝伟) (Associate Professor, Doctor)

Authors
  1. Liu Gao-lian  (刘高联)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Li Xiao-wei  (李孝伟)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Li Xiao-wei  (李孝伟).

Additional information

Project supported by the National Natural Science Foundation of China (No.10372055) and the Shanghai Leading Academic Discipline Project (No.Y0103)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, Gl., Li, Xw. Mesh free method based on local cartesian frame. Appl Math Mech 27, 1–6 (2006). https://doi.org/10.1007/s10483-006-0101-1

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-006-0101-1

Key words

Search

Navigation