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1 Engineering Transactions

1 2005

1 Bodaszewski W.

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Algorithms of the method of statically admissible discontinuous stress fields (SADSF). P. 3 Software implementations and example problems formulated for fields around nodes

100%

Bodaszewski W.

tom Vol. 53, iss. 1

15-30

Boundary problems, characteristic for the already-known fields around convex and concave corners, are used in this part of the paper as the examples to present juxtaposition of conditions, and to obtain a solution for general conditions of the system - important for the fields that appear around nodes. The presented variants of these systems and the sets of unknowns, after minor completion, give the basis for deriving series of elementary problems, which are necessary to create the algorithm for solving arbitrary boundary problems, such as those encountered in the fields around nodes. The algorithm created on such a basis does not require formulating any particular relationships, and its implementation makes it possible to find any solution to the field around the node. The solution, presented in an illustrative graphical form, can then be easily edited. In effect, it becomes possible to test, almost instantaneously, admissibility of the structures, and verify the existence of solutions on the physical plane. The paper also presents short description of properties of the fields around nodes that facilitates interpretation of the results. It is particularly useful in the cases when one obtains surprising results, for example when structural degenerations (collapses) appear. It is worth mentioning that, with boundary conditions formulated for fields around both the bove-mentioned types of corners, one obtains not only fields identical with the prototype, but also a whole variety of other fields that until now have been treated as different ones. Actually, these are the fields being solutions to the same boundary problem.