Analiza niezawodności i optymalizacja odpornościowa złożonych konstrukcji i procesów technologicznych

Stocki, R.

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Analiza niezawodności i optymalizacja odpornościowa złożonych konstrukcji i procesów technologicznych

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Stocki R.

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Za główny cel pracy należy uznać opracowanie sformułowań teoretycznych oraz algorytmów numerycznych, które umożliwiają analizę stochastyczną złożonych konstrukcji i procesów technologicznych. Przez analizę stochastyczną rozumieć będziemy tu szereg zagadnień, a w szczególności: o analizę losowego charakteru odpowiedzi układów konstrukcyjnych, wy- znaczenie parametrów rozkładu prawdopodobieństwa odpowiedzi, o analizę niezawodności, tj. oszacowanie prawdopodobieństwa awarii konstrukcji, bądź procesu technologicznego, o optymalizację odpornościową, gdzie oprócz wartości średnich wybranych kryteriów minimalizuje się wariancje tych kryteriów. Podkreślenie, iż opisana analiza stochastyczna dotyczyć ma złożonych konstrukcji i procesów służy w istocie zaakcentowaniu konieczności opracowania wyspecjalizowanych, nieklasycznych metod rozwiązania. Jako przykłady zaawansowanych zagadnień mechaniki, które uznać można za reprezentatywne dla złożoności obliczeniowej współcześnie przeprowadzanych analiz numerycznych, wybrano zagadnienia wytrzymałości zderzeniowej elementów konstrukcji pojazdów oraz proces głębokiego tłoczenia blachy. Jakościowy charakter odpowiedzi tego typu konstrukcji modelowany również będzie za pomocą szeregu specjalnie dobranych przykładów analitycznych, jak również mniejszych, testowych zadań mechaniki konstrukcji. Pomimo nieustannego postępu techniki komputerowej, sam wzrost mocy obliczeniowej nie jest wystarczającym środkiem do zapewnienia "ekspansji" analizy stochastycznej na nowe, niedostępne dotychczas obszary zastosowań. W dalszym ciągu, szczególnie gdy problemy mechaniki reprezentowane są przy pomocy złożonych modeli MES, użycie klasycznych metod symulacji Monte Carlo wiąże się z ogromnym nakładem obliczeniowym. W większości przypadków dodatkowy koszt generowany przez analizę stochastyczną jest niewspółmiernie wysoki, co podważa zasadność przeprowadzania tego typu pogłębionej analizy. Z drugiej strony, np. w analizie niezawodności złożonych konstrukcji i procesów technologicznych, najczęściej nie jest możliwe bezpośrednie zastosowanie bardziej efektywnych metod oszacowania wartości prawdopodobieństwa awarii, takich które wykorzystują koncepcję punktu projektowego. Użycie gradientowych algorytmów lokalizacji punktu projektowego w analizie niezawodności elementów absorbujących energię zderzeń, skazane jest z góry na niepowodzenie. Funkcje graniczne, z którymi ma się tam do czynienia, zazwyczaj nie są różniczkowalne, a obserwowany numeryczny szum skutecznie utrudnia zastosowanie jakichkolwiek metod niesymulacyjnych. Nieróżniczkowalne, a jednocześnie kosztowne obliczeniowo, są także funkcje celu i funkcje ograniczeń zadania optymalizacji odpornościowej. Wszystko to sprawia, że niezbędnym składnikiem efektywnej analizy stochastycznej złożonych konstrukcji są wyspecjalizowane algorytmy, które nie są wrażliwe na silnie nieliniowy charakter odpowiedzi konstrukcji, a jednocześnie są w stanie wykorzystać możliwości przetwarzania równoległego oferowane przez współczesne komputery. W niniejszej pracy szczególny nacisk położony zostanie na następujące elementy budowanych algorytmów: o Efektywne symulacyjne metody analizy losowego rozrzutu odpowiedzi konstrukcji. Zastosowane będą metody typu "descriptive sampling", wykorzystujące koncepcję łacińskiej hiperkostki oraz optymalnej łacińskiej hiperkostki. Metody te łączą dobrą efektywność estymacji momentów statystycznych funkcji losowych z małą wrażliwością na charakter zmienności tych funkcji oraz na typy rozkładów prawdopodobieństwa zmiennych losowych. Użyte zostaną efektywne algorytmy tworzenia optymalnych hiperkostek (ang. optimal Latin hypercube - OLH). o Nowoczesne techniki aproksymacji nieliniowych funkcji wielu zmiennych (metody powierzchni odpowiedzi). Wykorzystywane będą przede wszystkim: metoda ważonej liniowej regresji oraz metoda krigingu. To właśnie metoda krigingu, obok efektywnych technik symulacji losowych, stanowić będzie kluczowy element algorytmu rozwiązania zadania optymalizacji odpornościowej. Jako dominujący plan eksperymentów używany będzie plan punktów generowanych przez optymalne łacińskie hiperkostki. o Wykorzystanie rozwiązań niewrażliwych na szum numeryczny, charakterystyczny dla jawnego schematu całkowania równań ruchu oraz algorytmów kontaktu stosowanych w modelach MES. Jest to niezbędny warunek zapewnienia zbieżności zarówno algorytmów analizy niezawodności jak też optymalizacji odpornościowej. Ponadto, dodatkowym celem autora było bliższe przedstawienie koncepcji optymalizacji odpornościowej. Ten typ optymalizacji jest jeszcze ciągle mało znany, szczególnie w polskiej literaturze, i czasami mylony z optymalizacją nie- zawodnościową. Nawet zaproponowana przez autora nazwa "optymalizacja odpornościowa" nie jest jeszcze powszechnie przyjętym tłumaczeniem angielskiego terminu robust optimization. Mając to na uwadze, w niniejszej pracy podjęto próbę usystematyzowania wiedzy na temat alternatywnych sformułowań zadania niedeterministycznej optymalizacji konstrukcji. Przedstawione będą sformułowania oraz zaproponowane zostaną strategie rozwiązania zadania optymalizacji odpornościowej. Wszystkie rozwijane w pracy metody zaimplementowano w obiektowo zorientowanym programie STAND, który współtworzony jest przez autora w ramach badań prowadzonych w Pracowni Niezawodności i Optymalizacji IPPT PAN. Efektywne tworzenie dużego programu do analizy stochastycznej konstrukcji, przeznaczonego zarówno do analizy niezawodności jak i optymalizacji odpornościowej, a także zadanie jego integracji z zewnętrznymi pakietami obliczeniowy- mi MES, stanowią ciekawe i nietrywialne problemy informatyczne. Zagadnienia te, o niebagatelnym znaczeniu w praktyce, zostaną w pracy szczegółowo omówione. Zaproponowanych będzie szereg rozwiązań programistycznych dotyczących architektury kodu programu STAND.

Słowa kluczowe

mechanika mechanika konstrukcji optymalizacja odpornościowa analiza niezawodności metoda elementów skończonych modelowanie

mechanics modelling

Wydawca

Instytut Podstawowych Problemów Techniki PAN

Czasopismo

Prace Instytutu Podstawowych Problemów Techniki PAN

Rocznik

2010

Tom

nr 2

Strony

3--337

Opis fizyczny

Bibliogr. 279 poz., il.

Twórcy

autor

Stocki R.

Bibliografia

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