Object-oriented realization of the FE solver for compression test

by

Object-oriented realization of the FE solver for compression test

 Paweł J. Matuszyk

AGH University of Science and Technology.

DOI:

https://doi.org/10.7494/cmms.2004.4.0062

Abstract:

The paper deals with developing and implementing object-oriented model of finite element solver for simulation of compression material tests. First, mathematical model of compression on the basis of incompressible nonlinear viscoplastic low is considered. A weak form is developed using SUPG stabilization method. Several methods providing convergence of Newton-Raphson method for linearization of discretized model are presented. Then, purposefulness of applying of object-oriented technique is shortly discussed. Finally, description of object-oriented model of the FE solver is presented with short description of all classes.

Cite as:

Matuszyk,  P.J. (2004).  Object-oriented realization of the FE solver for compression test. Computer Methods in Materials Science, 4(4), 127 – 143. https://doi.org/10.7494/cmms.2004.4.0062

Article (PDF):

Keywords:

,

References:

Blank, H., Rudgyard, M., Wathen, A.J. (1999). Stabilised finite element methods for steady incompressible flow. Comp. Meth. Appl. Mech. Eng., 174:, 91-105.

Brezzi, F., Fortin, M. (1991). Mixed and Hybrid Finite Element Methods. Springer-Verlag.

Chen, C.C., Kobayashi, S. (1978). Rigid-plastic-finite-element analysis of ring compression. Application of Numerical methods to Forming Processes, ASME, ADM, 28:, 163-174.

Dubois-Pelerin, Y., Zimmermann, T., Bomme, P. (1992). Objectoriented finite element programming: II. A prototype programm in Smalltalk, Comp. Meth. Appl. Mech. Eng., 98.

Dubois-Pelerin, Y.,Zimmermann, T. (1993). Object-oriented finite element programming: HI. An efficient implementation in C++, Comp. Meth. Appl. Mech. Eng., 108.

Elman, H.C., Silvester, D.J., Wathen, A.J. (1996). Iterative Methods for Problems in Computational Fluid Dynamics. Technical Report. CS-TR-3675. Hartley, P. and Pillinger, I. and Sturgess, C. ed., 1992., Numerical Modelling of Material Deformation Processes, Springer-Verlag.

Hughes, T.J.R., Franca, L.P. (1987). A new finite element method for computational fluid dynamics: VII. The Stokes problem with various well-posed boundary conditions: Symmetric formulations that converge for all velocity/pressure spaces, Comp. Meth. Appl. Mech. Eng., 65:, 85-96.

Hughes, T.J.R., Franca, L.P., Balestra, M. (1986). A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuska-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accomodating equal-order intrpolations, Comp. Meth. Appl. Mech. Eng., 59:, 85-99.

Jansen, K., Collis, S., Whiting, C., Shakib, F. (1999). A better consistency for low-order stabilized finite element methods.

Maniaty, A.M., Liu, L., Klaas, O., Shephard, M.S. (2001). Stabilized finite element method for viscoplastic flow: formulation and a simple progressive solution strategy. Comp. Meth. Appl. Mech. Eng., 190:, 4609-4625.

Saad, Y. (2000). Iterative Methods for Sparse Linear Systems. SIAM.

Wagoner, R.H., Chenot, J.L. (2001). Metal Forming Analysis. Cambridge University Press.

Zimmermann, T., Dubois-Pelerin, Y., Bomme, P. (1992). Objectoriented finite element programming: I. Governing principles, Comp. Meth. Appl. Mech. Eng., 98. Artykuł otrzymano 30 grudnia 2004 r.