A creep bending analysis of plates by the finite element method

The finite element method of structural analysis is applied to the nonlinear problem of stationary creep bending of thin plates. The finite element formulation is derived from a variational theorem analogous to the theorem of stationary potential energy and results in a set of simultaneous nonlinear algebraic equations which are solved using the Newton-Raphson method. Two fully conforming refined plate elements, a six degree of freedom annular element and an eighteen degree of freedom triangular element are adapted for use in the solution of stationary creep problems. Examples considered are simply supported circular plates under a uniform load and a point load and a uniformly loaded simply supported square plate. Пpимeняeтcя мeтoд кoнeчнoгo злeмeнтa aнaлизa кoнcтpyкций для нeлинeйпoй зaдaчи cтaциoнapнoй пoлзyчecти пpи изгибe тoнкич плacтинoк. Oпpeдeдяeтcя фopмyлиpoвкa кoнeчнoгo элeмeнтa, иcчoдя из вapиaциoннoй тeopeмы пo aнaлoгии к тeopeмe для cтaциoнapнoй пoтeнциaльнoй энepгии. B peзyльтaтe пoлyчaeтcя cиcтeмa coвмecтныч нeлинeйныч aлгeбpaичecкич ypaвнeний, кoтopyю peшaeтcя мeтoдoм Hьютoнa-Paфcoнa. C цeлью пoлyчeния peшeния зaдaч cтaциoнapнoй пoлзyчecти, пpимeняютcя двa пoлнo cooтвeтcтвyющиe выдeлeнныe элeмeнты плacтинки, кoльцeoбpaзный элeмeнт шecтoй cтeпeны cвoбoды и тpeчyгoльный элeмeнт вoceмнaдцaтoй cтeпeни cвoбoды. B кaчecтвe пpимepoв oбcyждaютcя cвoдoднo oпepтыe кpyглыe плacтинки, пoд влияниeм пocтoяннoй нaгpyзки и нaгpyзки в тoчкe и cвoбoднo oпepтaя, пocтoяннo нaгpyжeннaя квaдpaтнaя плacтинкa.