OBJECT-ORIENTED PROGRAMMING IN MESHFREE ANALYSIS OF ELASTOSTATIC PROBLEMS

Year 2015, , 1 - 18, 01.06.2015

B. Kanber M.M. Yavuz

https://doi.org/10.24107/ijeas.251244

Abstract

In this work, the main philosophy behind the object-oriented programming (OOP) of meshfree methods is discussed for solution of elastostatic problems. Objects and classes are constructed with respect to the structure of meshfree methods. Local radial point interpolation method (LRPIM) and meshless local Petrov-Galerkin (MLPG) method are used in local weak form in the program. Basic object oriented programming operators; encapsulation, inheritance and polymorphism are used for increasing modularity. Seven main classes and their subclasses are constructed for decreasing complexity. Additional storage modules and solver functions are implemented. As a result of this, new techniques on interpolations and integrations can be easily adapted to construction of shape functions in meshfree program structure. Objects are defined and implemented for solution of 2D elastostatic problems in MATLAB. Two elestostatic problems are solved in MATLAB OOP and their results are compared with results of a procedural program that is written in FORTRAN. Class designs and their hierarchy are discussed in details

Keywords

Object-oriented programming (OOP), meshfree methods, MATLAB, 2D elastostatic problems

References

• [1] Mackie, R.I., Object oriented programming of the finite element method. International Journal for Numerical Methods in Engineering, 35, 425-436, 1992.
• [2] Zimmermann, T., Dubois-Pelerin, Y. and Bomme, P., Object oriented finite element programming: I. governing principles. Computer Methods in Applied Mechanics and Engineering, 98, 291-303, 1992.
• [3] Dubois-Pelerin, Y., Zimmermann, T. and Bomme, P., Object oriented finite element programming: II. a prototype program in Smalltalk. Computer Methods in Applied Mechanics and Engineering, 98, 361-397, 1992.
• [4] Ohtsubo, H. and Kawamura, Y., Development of the object-oriented finite element modeling system – modify. Engineering with Computers, 9, 187-197, 1993.
• [5] Zimmermann, T., Bomme, P., Eyheramendy, D., Vernier, L. and Commend, S., Aspects of an object-oriented finite element environment. Computers and Structures, 68, 1-16, 1998.
• [6] Pantale, O., An object-oriented programming of an explicit dynamics code: application to impact simulation. Advances in Engineering Software, 33, 297–306, 2002.
• [7] Peters, B. and Dziugys, A., Numerical simulation of the motion of granular material using objectoriented techniques. Comput. Methods Appl. Mech. Engrg., 191, 1983–2007, 2002.
• [8] Ma, Y. and Feng, W., Object-oriented finite element analysis and programming in VC++. Applied Mathematics and Mechanics, 23(12), 1437-1443, 2002.
• [9] Yu, L. and Kumar, A.V., An object-oriented modular framework for implementing the finite element method. Computers and Structures, 79, 919-928, 2001.
• [10] Patzak, B. and Bittnar, Z., Design of object oriented finite element code. Advances in Engineering Software, 32, 759-767, 2001.
• [11] Menetrey, P. and Zimmermann, T., Object-oriented non-linear finite element analysis: application to j2 plasticity. Computers & Structures, 49(5), 767-777, 1994.
• [12] Dubois-Pelerin, Y. and Pegon, P., Object-oriented programming in nonlinear finite element analysis. Computers and Structures, 67, 225-241, 1998.
• [13] Zabaras, N. and Srikanth, A., An object-oriented programming approach to the Lagrangian fem analysis of large inelastic deformations and metal forming processes. Int. J. Numer. Meth. Engng., 45, 399–445, 1999.
• [14] Lages, E.N., Paulino, G.H., Menezes, I.F.M. and Silva, R.R., Nonlinear finite element analysis using an object-oriented philosophy – application to beam elements and to the cosserat continuum. Engineering with Computers, 15, 73–89, 1999.
• [15] Commend, S and Zimmermann, T., Object-oriented nonlinear finite element programming: a primer. Advances in Engineering Software, 32, 611-628, 2001.
• [16] Tabatabai, S.M.R., Object-oriented finite element-based design and progressive steel weight minimization. Finite Elements in Analysis and Design, 39, 55–76, 2002.
• [17] Wegner, T. and Peczak, A., Implementation of a strain energy-based nonlinear finite element in the object-oriented environment. Computer Physics Communications, 181, 520–531, 2010.
• [18] Peskin, A.P. and Hardin, G.R., An object-oriented approach to general purpose fluid dynamics software. Computers chem. Engng, 20(8), 1043-1058, 1996.
• [19] Munthe, O. and Langtangen, H.P., Finite elements and object-oriented implementation techniques in computational fluid dynamics. Comput. Methods Appl. Mech. Engrg., 190, 865-888, 2000.
• [20] Sampath, R. and Nicholas, Z., An object oriented implementation of a front tracking finite element method for directional solidification processes. Int. J. Numer. Meth. Engng., 44, 1227-1265, 1999.
• [21] Qiao, H., Object-oriented programming for the boundary element method in two-dimensional heat transfer analysis. Advances in Engineering Software, 37, 248–259, 2006.
• [22] Liu, J., Lin, I., Shih, M., Chen, R. and Hsieh, M., Object-oriented programming of adaptive finite element and finite volume methods. Applied Numerical Mathematics, 21, 439-467, 1996.
• [23] Phongthanapanich, S. and Dechaumphai, P., EasyFEM - an object-oriented graphics interface finite element/finite volume software. Advances in Engineering Software, 37, 797–804, 2006.
• [24] Marczak, R.J., Object-oriented numerical integration—a template scheme for FEM and BEM applications. Advances in Engineering Software, 37, 172–183, 2006.
• [25] Lage, C., The application of object-oriented methods to boundary elements. Comput. Methods Appl. Mech. Engrg., 157, 205-213, 1998.
• [26] Wang, W., Ji, X. and Wang, Y., Object-oriented programming in boundary element methods using C++. Advances in Engineering Software, 30, 127-132, 1999.
• [27] Dubois-Pelerin, Y. and Zimmermann, T., Object-oriented finite element programming: III an efficient implementation in C++. Computer Methods in Applied Mechanics and Engineering, 108, 165-183, 1993.
• [28] Cary, J.R., Shasharina, S.G., Cummings, J.C., Reynders, J.V.W. and Hinker, P.J., Comparison of C++ and Fortran 90 for object-oriented scientific programming. Computer Physics Communications, 105, 20-36, 1997.
• [29] Archer, G.C., Fenves, G. and Thewalt, C., A new object-oriented finite element analysis program architecture. Computers and Structures, 70, 63-75, 1999.
• [30] Kromer, V., Dufosse, F. and Gueury, M., On the implementation of object-oriented philosophy for the design of a finite element code dedicated to multibody systems. Finite Elements in Analysis and Design, 41, 493–520, 2005.
• [31] Krysl, P. and Belytschko, T., ESFLIB: a library to compute the element free Galerkin shape functions. Comput. Methods Appl. Mech. Engrg., 190, 2181-2205, 2001.
• [32] Seidl, A. and Schmidt, T., Object oriented approach to consistent implementation of Meshless and classical FEM. Systemics, Cybernetics and Informatics, 4(1), 58-64, 2005.
• [33] Zhang, X. and Subbarayan, G., jNURBS: an object-oriented, symbolic framework for integrated, meshless analysis and optimal design. Advances in Engineering Software, 37, 287–311, 2006.
• [34] Sánchez, J.M.M. and Gonçalves, P.B., Shape function object modeling for meshfree methods. Mecánica Computacional, 29, 4753-4767, 2010.
• [35] Barbieri, E. and Meo, M., A fast object-oriented Matlab implementation of the Reproducing Kernel Particle Method. Comput Mech, 49, 581–602, 2012.
• [36] Lucy, L.B., A numerical approach to the testing of the fission hypothesis. Astron. J., 82, 1013– 1024, 1977.
• [37] Nayroles, B., Touzot, G. and Villon, P., Generalizing the finite element method: diffuse approximation and diffuse elements. Comput. Mech., 10, 307-318, 1992. [38] Belytschko, T., Lu, Y.Y. and Gu, L., Element-Free Galerkin methods. Int. J. Numer. Meth. Engng., 37, 229-256, 1994.
• [39] Atluri, S.N. and Zhu, T., A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Computational Mechanics, 22, 117-127, 1998.
• [40] Liu, G.R. and Gu, Y.T., A point interpolation method for two-dimensional solids. Int. J. Numer. Methods Engrg., 50, 937-951, 2001.
• [41] Liu, G.R. and Gu, Y.T., A local radial point interpolation method (LR-PIM) for free vibration analyses of 2-D solids. J. of Sound and Vibration, 246(1), 29-46, 2001.
• [42] Liu, G.R., Zhang, G.Y. and Dai, K.Y., A linearly conforming point interpolation method (LCPIM) for 2D solid mechanics problems. International Journal of Computational Methods, 2(4), 645– 665, 2005.
• [43] Liu, G.R., Zhang, G.Y., Wang, Y.Y., Zhong, Z.H., Li, G.Y. and Han, X., A nodal integration technique for meshfree radial point interpolation method (NI-RPIM). International Journal of Solids and Structures, 44, 3840–3860, 2007.
• [44] Cui, X.Y., Liu, G.R. and Li, G.Y., A cell-based smoothed radial point interpolation method (CSRPIM) for static and free vibration of solids. Engineering Analysis with Boundary Elements, 34, 144–157, (2010).
• [45] Liu, G.R. and Gu, Y.T., An introduction to Meshfree methods and their programming, Springer, Berlin, 2005.
• [46] Kanber, B. and Bozkurt, O.Y., A diagonal offset algorithm for the polynomial point interpolation method. Commun. Numer. Meth. Engng., 24, 1909-1922, 2008.
• [47] Liu, G.R., Zhang, G.Y., Gu, Y.T. and Wang, Y.Y., A meshfree radial point interpolation method (RPIM) for three-dimensional solids. Comput. Mech., 36, 421-430, 2005.
• [48] Liu, G.R., Mesh free methods: moving beyond the finite element method, CRC press; 2nd edition, New York, 2009.
• [49] Berry, A., Bordat, J., Heggernes, P., Simonet, G. and Villanger, Y., A wide-range algorithm for minimal triangulation from an arbitrary ordering. Journal of Algorithms, 58, 33-66, 2006.
• [50] Eklund, A., Andersson, M. and Knutsson, H., fMRI analysis on the GPU - possibilities and challenges. Computer Methods and Programs in Biomedicine, 105, 145-161, 2012.
• [51] Wang, J. and Hopke, P.K., Equation-oriented system: an efficient programming approach to solve multilinear and polynomial equations by the conjugate gradient algorithm. Chemometrics and Intelligent Laboratory Systems, 55, 13-22, 2001.