Leszek Małyszko Stanisław Jemioło Piotr Bilko Marcin Gajewski MES i modelowanie konstytutywne w analizie zniszczenia konstrukcji murowych Tom 2 Implementacja i przykłady Monografia pod redakcją naukową Leszka Małyszko
Spis treści 1 Wprowadzenie 1 1.1 Uwagi ogólne.................................. 1 1.2 Zakres opracowania............................... 3 2 Izotropowy model muru 5 2.1 Zastosowanie skaningu laserowego....................... 5 2.2 Charakterystyki dynamiczne konstrukcji murowych............. 16 2.3 Wytrzymałość cegły na rozciąganie przy zginaniu.............. 27 2.4 Sklepienie krzyżowe............................... 33 2.5 Modelowanie muru za pomocą elementów interfejsowych.......... 38 3 Ortotropowy model muru 49 3.1 Równania teorii małych przemieszczeń.................... 49 3.2 Związek Hooke a dla materiałów anizotropowych............... 51 3.3 Równania teorii plastycznego płynięcia.................... 61 3.4 Ortotropowy makroskopowy model muru................... 68 3.5 Ortotropowe kryteria wytężenia........................ 70 4 Implementacja i testy numeryczne 81 4.1 Całkowanie równań konstytutywnych..................... 81 4.2 Numeryczna implementacja modelu...................... 86 4.3 Metoda elementów skończonych i procedury iteracyjno-przyrostowe.... 95 4.4 Testy elementarne................................ 100 4.5 Test rozłupywania................................ 111 5 Przykładowe symulacje numeryczne 115 5.1 Wytrzymałość muru na ściskanie....................... 115 5.2 Ścinanie muru w jego płaszczyźnie....................... 127 5.3 Zginanie muru prostopadle do płaszczyzny.................. 139 6 Podsumowanie i wnioski 147 Bibliografia 152 A Źródłowe wersje programów 161 A.1 Procedura USRMAT (DIANA)........................ 161 A.2 Procedura UMAT (ABAQUS)......................... 168 B Oznaczenia 173 B.1 Lista operacji rachunku tensorowego..................... 173 B.2 Wykaz ważniejszych oznaczeń......................... 176 iii
iv SPIS TREŚCI
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