Algorithms of the Method of Statically Admissible Discontinuous Stress Fields (SADSF)
The algorithms presented in this paper break up with the individual approach to a particular field. The algorithms are the first ones of general character, as they apply to the fundamental problems of the method. The algorithms aid solving practically any boundary problem that one encounters in the tasks of construction of 2D statically admissible, discontinuous stress fields, first of all the limit fields. In the presented approach, one deals first with the fields arising around isolated nodes of stress discontinuity lines (Parts II and III), then integrates these fields into 2D complex fields (Part IV).
The software, created on the basis of the algorithms, among other things, allows one to quickly find all the existing solutions of the discontinuity line systems and present them in a graphical form. It gives the possibility of analysing, updating and correcting these systems. In this way, it overcomes the greatest difficulty of the SADSF method following from the fact that the systems of discontinuity lines are not known a priori, and appropriate relationships are not known either, so that they could only be found in an arduous way by postulating the line systems, and verifying them.
Application version of the SADSF method is not described in this paper; however, a reference is given to inform the reader where it can be found.
W. SZCZEPIŃSKI, Plastic design of machine parts [in Polish], PWN, Warszawa 1968.
W. BODASZEWSKI, Stress discontinuity line structures in yield zones satisfying the Huber-Misses condition [in Polish], Engineering Transactions, Part l, 36, l, 29–54, 1988; Part 2, 37, 3, 415–442, 1989.
I. MARKIEWICZ, Numerical determination of statically admissible link systems of stress discontinuity lines in limit Huber-Mises's fields [in Polish], Doctoral Thesis, Warsaw University of Technology, 1996.
W. SZCZEPIŃSKI, J. SZLAGOWSKI, Plastic design of complex shape structures, Ellis Horwood & PWN, Warszawa – Chichester 1990.
W. BODASZEWSKI, Problems of optimisation defined on parameter sets of statically admissible discontinuous stress fields, The Archive of Mechanical Engineering, 44, 4, 311–342, 1997.
W. BODASZEWSKI, The software package KNPN for approximation of shaping complex thin-walled structures [in Polish], XII Conference on Computer-Aided Engineering, Warsaw University of Technology, 45–52, 1997.
P. GOMOLIŃSKI, J. SZLAGOWSKI, The software package to the method of statically admissible stress fields, Proc. of Conf. on GAD, Miskolc 1991.
W. BODASZEWSKI, The software package KNPN for approximated shaping of complex plastic structures, VIII-th Symposium on Stability of Structures, Łódź University of Technology, Poland, 25–30, 1997.
W. BODASZEWSKI, Statically admissible nets of stress discontinuity lines [in Polish], IFTR Reports, 43, 1983.
P. DUYISINX, P. BENDSOE, Topology optimization of continuum structures with local stress constrains, Int. J. Meth. Engng., 43, 1453–1478, 1998.
M.P. BENDSOE, Optimization of Structural Topology, Shape, and Material, Springer, Berlin 1995.
Internet website: www.sadsf.net.
Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland