MFree 2D v2.0

MFree2D is an adaptive stress analysis software package based on meshfree technology...

 

MFree2D is an adaptive stress analysis software package developed by Prof. G.R. Liu and his co-workers, based on meshfree technology.

For a quick demonstration of the software, please click here. (RealPlayer is recommended for viewing.)

MFree2D is designed for 2D stress and strain analysis in solid mechanics and structural mechanics subjected to static and/or dynamic loadings with heat transfer process. The software consists of three major processors : MFreePre, MFreeApp and MFreePost. MFreePre is a preprocessor to formulate the input required by MFreeApp; the latter performs computations and yields the results which are then fed to MFreePost for post processing.

These three processors can work either in an integrated manner or independently. One salient feature of MFree2D is that it is designed to be user-friendly and thus, has fewer requirements for users than many of the existing numerical packages. The first version of MFree2D, is for 2-D elastostatics and was demonstrated during the Fourth Asia Pacific Conference on Computational Mechanics (APCOM 1999).

The main features of MFree2D include :
> Problem domain is discretised using scattered nodes and the discretisation is fully automatic.
> Adaptive refinement techniques are implemented to ensure the results are of a desired accuracy.
> User-friendly graphical-user-interface (GUI).

Latest problem solving methods and technologies have also been incorporated into the software. The effectiveness, reliability and robustness of MFree2D has been tested by numerous sample computations, of which, some are presented below in Figure 1 and 2.

 

The current version of MFree2D V2.0 is free of charge. You may download and install this PC version for your own use. The installation of the software requires a serial number. Please email liugr@uc.edu for the serial number, by providing your basis information: Name, Address, Contacts, Affiliations etc.

We appreciate very much your comments and suggestions. We will be trying to constantly improving the code to incorporate your invaluable comments and suggestions, when our resources allows.

In your installation, please change to a new installation folder, such as, C:/Mfree/, (do not use the default folder, i.e. C:\Program Files\ACES\MFree2D); After successful installation, you should find a folder with examples. For the path of this folder, space is not allowed.

For theoretical background of the software development, please refer to the publications authored by Prof. G. R. Liu and his co-workers. The most relevant papers are listed below :

Any question about this software, please connect to: Prof. G.R. Liu at liugr@uc.edu.

 

Book:

Liu G.R. Mesh Free Methods Moving beyond finite element method, CRC Press LLC, 1st Edition, 2002; 2nd Edition, 2009.

 

Papers:

G. R. Liu and G. Y. Zhang. Upper bound solution to elasticity problems: A unique property of the linearly conforming point interpolation method (LC-PIM). International Journal for Numerical Methods in Engineering, 74: 1128-1161, 2008.

G. R. Liu. A generalized gradient smoothing technique and the smoothed bilinear form for Galerkin formulation of a wide class of computational methods. International Journal of Computational Methods, 5(2): 199-236, 2008.

G. Y. Zhang, G. R. Liu and Y. Li. An efficient adaptive analysis procedure for certified solutions with exact bounds of strain energy for elasticity problems. Finite Elements in Analysis and Design, 44(14): 831-841, 2008.

G. R. Liu, J. Zhang, K. Y. Lam, H. Li, G. Xu, Z. H. Zhong, G. Y. Li and X. Han. A gradient smoothing method (GSM) with directional correction for solid mechanics problems. Computational Mechanics, 41(3): 457-472, 2008.

Y. Li, G. R. Liu, M. T. Luan, K. Y. Dai, Z. H. Zhong, G. Y. Li and X. Han, Contact analysis for solids based on linearly conforming radial point interpolation method, Computational Mechanics, 39: 537-554, 2007.

G. Y. Zhang, G. R. Liu, T. T. Nguyen, C. X. Song, X. Han, Z. H. Zhong and G. Y. Li. The upper bound property for solid mechanics of the linearly conforming radial point interpolation method (LC-RPIM). International Journal of Computational Methods, 4(3): 521-541, 2007.

G. Y. Zhang, G. R. Liu, Y. Y. Wang H. T. Huang, Z. H. Zhong, G. Y. Li and X. Han. A linearly conforming point interpolation method (LC-PIM) for three-dimensional elasticity problems. International Journal for Numerical Methods in Engineering, 72: 1524-1543, 2007.

K. Y. Dai, G. R. Liu and T. T. Nguyen. An n-sided polygonal smoothed finite element method (nSFEM) for solid mechanics. Finite Elements in Analysis and Design, 43: 847-860, 2007.

G. R. Liu, Y. Li, K. Y. Dai, M. T. Luan, W. Xue, A Linearly conforming radial point interpolation method for solid mechanics problems, International Journal of Computational Methods, 3(4):401-428, 2006.

G. R. Liu, G. Y. Zhang, K. Y. Dai, Y. Y. Wang, Z. H. Zhong, G. Y. Li and X. Han, A linearly conforming point interpolation method (LC-PIM) for 2D solid mechanics problems, International Journal of Computational Methods, 2(4): 645-665, 2005.

Liu, G.R. and Gu, Y.T., Coupling of Element Free Galerkin And Hybrid Boundary Element Methods Using Modified Variational Formulation, Computational Mechanics. Vol.26, 2000, 166-173.

Liu, G.R. and Gu, Y.T., Meshless Local Perov-Galerkin (MLPG) Method In Combination With Finite Element And Boundary Element Approaches, Computational Mechanics. Vol.26, 2000, pp.536-546.

Liu, G.R. and Gu, Y.T., A Local Point Interpolation Method For Stress Analysis Of Two-Dimensional Solids, Structural Engineering and Mechanics. Vol. 11, No. 2, 2001, pp. 221-236.

Liu, G.R. and Gu, Y.T., A Point Interpolation Method For Two-Dimensional Solids, Int. J. Num. Methods in Engrg. Vol.50, 2001, pp.937-951.

Gu, Y.T., Liu, G.R., A Meshless Local Petrov-Galerkin (MLPG) Method For Free And Forced Vibration Analyses For Solids, Computational Mechanics 27 (2001) 3, 188-198.

Gu Y.T., Liu G.R., A Coupled Element Free Galerkin/Boundary Element Method For Stress Analysis Of Two-Dimension Solid, Computer Methods in Applied Mechanics and Engineering. Vol 190(34), pp 4405-4419. 2001.

Liu, G.R., and Chen, X.L., A Mesh Free Method For Static And Free Vibration Analyses Of Thin Plates Of Complicated Shape. Journal of Sound and Vibration. 241 (5) 2001, pp. 839-855.

Liu, G. R. and Gu, Y. T., A Local Radial Point Interpolation Method (LRPIM) For Free Vibration Analyses Of 2-D Solids, Journal of Sound and Vibration, (2001) 246 (1), 29-46.

Gu, Y.T., and Liu, G.R. A Meshless Local Petrov-Galerkin (MLPG) Formulation For Static And Free Vibration Analyses Of Thin Plates, Computer Modeling in Engineering & Sciences, 2(4), 2001, pp: 463-476.

Liu, G.R. A Point Assembly Method For Stress Analysis For Two-Dimensional Solids, International Journal of Solids and Structures. Vol.39, 2002, pp.261-276.

Gu, Y.T. and Liu, G.R., A Boundary Point Interpolation Method For Stress Analysis Of Solids, Computational Mechanics. 28, 2002, pp. 47-54.

Wang, J.G. and Liu, G.R. On The Optimal Shape Parameters Of Radial Basis Functions Used For 2-D Meshless Methods. Computer Methods in applied Mechanics and Engineering, 191, 2002, pp. 2611-2630.

Wang, J.G., Liu, G.R. and Lin, P., Numerical Analysis Of Biot's Consolidation Process By Radial Point Interpolation Method, International Journal of Solids and Structures 39(6), 2002, pp. 1557 - 1573.

Liu, G.R. and Tu, Z. H., An Adaptive Procedure Based On Background Cells For Meshless Methods, Computer Methods In Applied Mechanics And Engineering, 191, 2002, pp. 1923-1943.