Obratnye Zadachi V Teorii Tonkikh Obolochek

Monografiya posvyashchena razvitiyu metoda obratnykh zadach dlya vybora adekvatnykh matematicheskikh modeley nablyudaemykh deformiruemykh obolochek. Ispol'zovana variatsionnaya postanovka zadachi - parametry modeley opredelyayutsya kak dostavlyayushchie minimum funktsionalu-nevyazke. Dlya resheniya obratnoy zadachi predlagaetsya dvukhetapnyy iterativnyy algoritm, baziruyushchiysya na metode N'yutona-Gaussa, vybor nachal'nogo priblizheniya osushchestvlyaetsya putem vydeleniya kompaktnogo podmnozhestva vozmozhnykh resheniy. Privodyatsya resheniya granichnykh obratnykh zadach - zadach rekonstruktsii real'nykh nagruzok, deystvuyushchikh na obolochku, zadach identifikatsii usloviy zakrepleniya granichnogo kontura; geometricheskikh obratnykh zadach - zadach opredeleniya oblasti, zanyatoy obolochkoy, v tom chisle zadach opredeleniya mestopolozheniya povrezhdeniy v vide proboin i treshchin; koeffitsientnykh obratnykh zadach - zadach opredeleniya geometricheskikh parametrov obolochki, a takzhe svoystv materiala obolochki. Predlozhennyy metod resheniya, algoritm i programmnaya realizatsiya mogut byt' ispol'zovany v protsesse monitoringa real'noy nesushchey sposobnosti obolochechnykh konstruktsiy. Dlya nauchnykh i inzhenerno-tekhnicheskikh rabotnikov v oblasti mekhaniki deformiruemogo tverdogo tela.