文件列表:

create_mesh.m (9294, 2008-06-25)
get_bc.m (1322, 2008-06-19)
mises.m (1328, 2008-06-20)
P1ShapeFunction.m (164, 2008-06-25)
plast_radial.m (4089, 2008-06-20)
plast_semi.m (4541, 2008-06-25)
plast_sqp.m (5430, 2008-06-20)
quad_nodes.m (1039, 2008-06-20)
radial_step.m (3924, 2008-06-19)
radial_step_loc.m (1226, 2008-06-20)
script.m (2207, 2008-06-25)
semi_step.m (4162, 2008-06-20)
semi_step_loc.m (1054, 2008-06-20)
sqp_step.m (3954, 2008-06-20)
sqp_step_loc.m (1203, 2008-06-20)
apply_bc.m (2174, 2008-06-25)
compute_stress.m (1848, 2008-06-20)

%%% THREE SOLUTION METHODS FOR PERFECT PLASTICITY %%% This programme provides three different methods for the computation of perfectly plastic problems. In addition to the familiar radial return algorithm, two modern approaches to nonlinear problems have been applied to the elastoplastic problem, namely a semi-smooth Newton method and an SQP method. Since both methods are not classical, we refer to the following books and papers to understand the programmes better: 1. Radial Return Algorithm - Simo/Hughes: Computational Inelasticity, Springer-Verlag, 19*** 2. Semi-smooth Newton Method - Christensen: A nonsmooth Newton method for elastoplastic problems, Comput. Methods Appl. Mech. Engrg. (191), 2001, p. 1189-1219 3. SQP Method - Wieners: Nonlinear solution methods for infinitesimal perfect plasticity, Univ. Karlsruhe, 2006, Preprint 06/11 In this collection of programmes, we also provide three different examples for the comparison of the three methods. The user may apply each method to the well-known perforated sheet problem, to Cook's membrane problem, and to a symmetric ring problem. All these examples have been taken with slight modifications from the paper - Carstensen/Klose: Elastoviscoplastic Finite Element Analysis in 100 lines of Matlab, J. Numer. Math. (10), 2002, p. 157-192. The main script has been realised in the file SCRIPT.M. The three solution methods have been implemented in the files PLAST_RADIAL.M, PLAST_SEMI.M, and PLAST_SQP.M. Note that for the radial return method, a linear isotropic hardening parameter has been included to illustrate an extension of the perfectly plastic case. A simple finite element implementation using linear finite elements in space is included in the files RADIAL_STEP.M, SEMI_STEP.M, and SQP_STEP respectively. These functions assemble the global system matrices and the right hand side resulting from a local algorithmic step. The main local work is done in the functions RADIAL_STEP_LOC.M, SEMI_STEP_LOC.M, and SQP_STEP_LOC.M where the trial stress is projected onto the set of admissible stresses. Here, the essential differences between the three methods become most apparent. For the semi-smooth Newton method, an additional model parameter "r" may be adjusted. The default value is set to "2*mu" in the function PLAST_SEMI.M. You may choose any real number here. Check the above mentioned article for the impact of this parameter. Three different output possibilities are provided within the programme. You may plot the von Mises stress at the last time step or a triangle mesh showing the displacements only. In addition, the error decay of Newton's method during the last time step can be plotted. We do not claim that the implementation of the three solution methods is optimal in performance. However, we expect that our implementation may be helpful for research and for teaching purposes.

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