Meshless Large Plastic Deformation Analysis Considering with a Friction Coefficient by Triple-Reciprocity Boundary Element Method

Meshless Large Plastic Deformation Analysis Considering with a Friction Coefficient by Triple-Reciprocity Boundary Element Method

Yoshihiro Ochiai

Department of Mechanical Engineering, Kindai University, Japan

Page: 
989-999
|
DOI: 
https://doi.org/10.2495/CMEM-V6-N6-989-999
Received: 
N/A
| |
Accepted: 
N/A
| | Citation

OPEN ACCESS

Abstract: 

In general, internal cells are required to solve large deformation problems using a conventional boundary element method (BEM). However, in this case, the merit of BEM, which is the ease of data preparation, is lost. Triple-reciprocity BEM enables us to solve elastoplasticity problems with a small plastic deformation. In this study, it is shown that two-dimensional large plastic deformation problems with a friction coefficient can be solved without the use of internal cells, by the triple-reciprocity BEM. Initial stress and strain formulations are adopted and the initial stress or strain distribution is interpolated using boundary integral equations. In this method, only boundary elements are remeshed. A new computer program is developed and used to solve several problems.

Keywords: 

BEM; large plastic deformation; initial stress method; numerical analysis; strain harden- ing; thin plate spline

  References

[1] Telles, J.C.F., The boundary element method applied to inelastic problems, Springer-Verlag, Berlin, 1983.

[2] Brebbia, C.A., Telles, J.C.F. & Wrobel, L.C., Boundary element techniques-theory and applications in engineering, Springer-Verlag, Berlin, pp. 252–266, 1984.

[3] Ochiai, Y. & Kobayashi, T., Initial stress formulation for elastoplastic analysis by improved multiple-reciprocity boundary element method. Engineering Analysis with Boundary Elements, 23, pp. 167–173, 1999.https://doi.org/10.1016/s0955-7997(98)00066-6

[4] Ochiai, Y. & Kobayashi, T., Initial strain formulation without internal cells for elasto-plastic analysis by triple-reciprocity BEM. International Journal for Numerical Method in Engineering, 50, pp. 1877–1892, 2001.https://doi.org/10.1002/nme.100

[5] Ochiai, Y., Three-dimensional elastoplastic analysis by triple-reciprocity boundary element method. Communications in Numerical Methods in Engineering, 23, pp. 721–732, 2007. https://doi.org/10.1002/cnm.922

[6] Ochiai, Y. & Sekiya, T., Generation of free-form surface in CAD for dies. Advances in Engineering Software, 22, pp. 113–118, 1995.https://doi.org/10.1016/0965-9978(94)00030-m

[7] Ochiai, Y. & Yasutomi, Z., Improved method generating a free-form surface using integral equations. Computer-Aided Geometric Design, 17(3), pp. 233–245, 2000. https://doi.org/10.1016/s0167-8396(99)00047-3

[8] Ochiai, Y., Nishitani, H. & Sekiya, T., Stress analysis with arbitrary body force by boundary element method. Engineering Analysis with Boundary Elements, 17, pp. 295–302, 1996.https://doi.org/10.1016/s0955-7997(96)00031-8

[9] Ochiai, Y., Multidimensional numerical integration for meshless BEM. Engineering Analysis with Boundary Elements, 27(3), pp. 241–249, 2003.https://doi.org/10.1016/s0955-7997(02)00112-1

[10] Ochiai, Y. & Sladek, V., Numerical treatment of domain integrals without internal cells in three-dimensional BIEM formulations. CMES (Computer Modeling in Engineering & Sciences), 6(6), pp. 525–536, 2004.

[11] Ochiai, Y., Meshless unsteady thermo-elastoplastic analysis by triple-reciprocity bound-ary element method. CMES (Computer Modeling in Engineering & Sciences), 79(2), pp. 83–101, 2011.https://doi.org/10.3970/cmes.2011.079.083

[12] Ochiai, Y., Three-dimensional thermo-elastoplastic analysis by triple reciprocity boundary element method. Engineering Analysis with Boundary Elements, 35(3), pp. 478–488, 2011. https://doi.org/10.1016/j.enganabound.2010.08.018

[13] Ochiai, Y., Large plastic deformation analysis without use of internal cells by triple-reciprocity BEM, Proceedings of 6th International Conference on Boundary Element Techniques, p. 293, 2005.