Algorithms of the Method of Statically Admissible Discontinuous Stress Fields (SADSF)

SUMMARY OF THE WHOLE PAPER: By now, the SADSF method is practically the only tool of shape design of complex machine elements that provides an effective solution even to the problems of 3D distribution of the material, and at the same time it is still enough user friendly to be useful for engineers. This unique property of the method is due to the existence of its simple, application version. When using it, a design engineer does not need to solve by oneself any statically admissible field – which could be very difficult – but obtains such a solution by assembling various ready-made particular solutions. The latter are in general obtained by means of individual and complex analyses and provided to a designer in a form of libraries. 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.