Algorithms of the method of statically admissible discontinuous stress fields (SADSF) - Part II

• Autorzy: Bodaszewski W.
• Języki publikacji: EN

Abstrakty

EN

In the paper, the author introduces the sets of conditions that create the algorithms of the functions on which one defines the boundary problems met in the search for discontinuous limit fields existing around isolated nodes. Among those, there are functions describing states of stress in the component homogeneous regions, the parameters of lines that separate these regions, and, first of all, the formulae for determining the domains based on the general conditions of existence. These formulae play a key role in numerical implementations of the method. The fields satisfying the Huber-Mises yield condition are of primary choice however, the derived relationships have a general meaning. To emphasise this fact one presents not only the areas of existence valid for the Huber-Mises condition, but also the areas obtained for several other yield conditions applicable to plastically homogeneous materials. The knowledge of the areas opens the possibility of developing the method of search for the fields that obey these conditions, and for algorithmizing this method. This could be applied even for the fields that are characterised by arbitrary, admissible states of stress. One also presents, basing on a mathematically complete set of conditions, typical formulations of problems concerning the fields around the nodes. One discusses the balance between the set of conditions and the unknowns, as well as the transformations into global systems connected with complex fields. One consequently applies parametrisation of the yield conditions, which not only reduces the number of unknowns and leads to simple, recursive forms of the formulae, but, first of all, makes it possible to find the formulae for generation of domains, without which numerical solution of the fields and algorithmization of the method would not be possible at all.

Słowa kluczowe

EN

stress fields; SADSF method; numerical methods

PL

pole naprężeń; metoda SADSF; metody numeryczne

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Engineering Transactions
• Rocznik: 2004
• Tom: Vol. 52, iss.4
• Strony: 231--252
• Opis fizyczny: Bibliogr.4 poz., rys., wykr.

Twórcy

autor

Bodaszewski W.

• Kielce University of Technology [Politechnika Swiętokrzyska], Tysiąclecia Państwa Polskiego 7, 24-314 Kielce

Bibliografia

• 1. W. SZCZEPIŃSKI, Plastikowe projektowanie części maszyn | po polsku, PWN, Warszawa 1968.
• 2. W. BODASZEWSKI, Struktury linii nieciągłości naprężeń w strefach plastyczności spełniające warunek Hube Mises [po polsku], transakcje techniczne, część l, 36, l, 29-54, 1988; Część 2 i 3, 37, 3, 415-442, 1989.
• 3. W. ZOWCZAK, W przypadku pewnej klasy standardowych pól naprężeń do projektowania tworzyw sztucznych, Engng. Trans., 44, 3-4, 1996.
• 4. W. BODASZEWSKI, P. TERESZKOWSKI, Ewolucja egzystencji domenowej dla układu sprzężonego z nieciągłym stresem w granicy piany Pola Tresca, 32. Konferencja Solid Mechaniki, SolMec'98.