Vibration and stability of plates using finite elements

Simple displacement functions for the flexure of triangular plate elements have proved successful in static solutions. Here the same element is used for calculating frequencies and buckling loads of plates. Excellent accuracy is attainable in frequency calculations, and reasonably good stability predictions may be made using quite coarse element subdivisions. Numerical integration is used in deriving element properties, permitting thickness variation within an element. Some implications of this process are discussed. Finally, a powerful “eigenvalue economizer” technique is presented which permits very fine subdivisions of elements with eigenvalue calculations of limited size. Пpocтыe фy;нкции пepeмeщeний для изгибa элeмeнтob тpeчy;гoльныч плacтинoк b чacнe пpигoдны для cтaтичecкич peщeний. b нacтoящeй paбoтe иcпoльзy;eтcя этoт cпocoб для oпpeдeлeния чacтoт и cил bыпy;чиbaния плacтинoк. Пoлy;чeнa oтличнaя тoчиocть b pacчeтaч чacтoты и мoжнo пpeдy;cмoтpeть пoчти чopoщиe y;cлobия y;cтoйчиbocти, кoгдa иcчoдитcя из cobepшeннoгo кpy;пнoгo paздeлeния элeмeнтa. Иcпoльзy;eтcя чиcлeннoe интeгpиpobaниe для oпpeдeлeния cboйcтb элeмeнтa. Этo интeгpиpobaниe пoзbaляeт y;чecть измeнeниe тoлщины элeмeнтa. Paccмaтpиbaютcя нeкoтopыe дeтaли cпocoбa pacчeтa. B зaключeниe пpeдcтabляeтcя cy;щecтbeнный мeтoд cooтbeтcтbeнныч знaчeний c тoчки зpeния экoнoмии, кoтopый дoпy;cкaeт чopoшoe paздeлeниe элeмeнтob пpи pacчeтaч coбcтbeнныч знaчeний oгpaничeнoгo paзмepa.