Optimization of stepped plates in the case of smooth yield surfaces
Kuupäev
2013-10-24
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Abstrakt
Käesolevas väitekirjas vaadeldakse Misese, Hilli ning Tsai-Wu materjalist valmistatud elastsete plastsete astmeliste plaatide optimiseerimisega seotud küsimusi. Antud dissertatsioon põhineb autori seitsmel teaduslikul publikatsioonil, millest kuus on avaldatud viimase kolme aasta jooksul. Käesolev dissertatsioon koosneb neljast peatükist, kirjanduse loetelust ning autori elulookirjeldusest. Esimene peatükk on sisuliselt ülevaade numbriliste meetodite rakendamisest konstruktsioonielementide optimiseerimisel. Selles peatükis antakse ülevaade plaatide ja koorikute optimiseerimisele pühendatud töödest, samuti kirjeldatakse lõplike elementide meetodi ja paralleelarvutuse ajaloolist arengut. Käesoleva uurimise raames on kasutatud lõplike elementide meetodit ning Haari lainikute meetodit harilike ja osatuletistega diferentsiaalvõrrandite lahendamiseks ning on rakendatud kõrgproduktiivse ja paralleelarvutuse põhimõtteid. Teises peatükis vaadeldakse sandwich-tüüpi sümmeetrilise elastse-plastse ümarplaadi painet ühtlaselt jaotatud koormuse mõjul ning otsitakse miinimumkaaluga projekti ette antud maksimumläbipainde korral. Eeldatakse, et plaadi materjal vastab Misese voolavustingimusele. Optimaalse lahendi leidmiseks on kasutatud lõplike elementide meetodit. Kolmandas peatükis uuritakse eelmises peatükis püstitatud probleeme sümmeetriliste elastsete-plastsete astmeliste rõngasplaatide puhul. Optimaalse lahendi leidmiseks on kasutatud lõplike elementide meetodit ning Haari lainikute meetodit, viimast kasutatakse ka harilike diferentsiaalvõrrandite lahendamiseks. Neljandas peatükis on uuritud anisotroopsete rõngasplaatide painet ning on leitud miinimumkaaluga projektid Hilli ja Tsai-Wu voolavustingimuste puhul. Arvutamisel on kasutatud Haari lainikute meetodit. Väitekirjas on välja töötatud paralleelarvutuse metoodika, mis annab võimaluse numbriliselt lahendada elastsete-plastsete plaatide optimiseerimisprobleeme. Saadud lahendeid on võrreldud Ohashi ja Murakami, Turvey ning Upadrasta tulemustega. Töös saadud tulemused on heas kooskõlas teiste autorite töödega. Uurimistöö käigus ilmnes, et optimiseerimisülesannete puhul on mõistlikum kasutada lainikute meetodit, mille paralleeliseerimine hoiab rohkem kokku arvuti ressurssi.
The current work is devoted to the theory of analysis and optimization of stepped circular and annular plates subject to smooth yield surfaces. Chapter 1 provides the brief historical review of the problem and of the finite element method. The Basic ideas of parallel computation, also of the multigrid method are presented herein, as well. In Chapter 2 a method for numerical investigation of axisymmetric plates subjected to the distributed transverse pressure loading was presented. The material of plates studied herein is assumed to be an ideal elastic plastic material obeying the non-linear yield condition of von Mises and the associated flow law. The strain hardening as well as geometrical non-linearity are neglected in the present investigation. Calculations carried out showed that the obtained results are in good correlation with those obtained by ABAQUS when solving the direct problem of determination of the stress strain state of the plate. In Chapter 3 an analytical-numerical study of annular plates operating in the range of elastic plastic deformations was undertaken. The material of plates was assumed to be an ideal elastic plastic material obeying the Mises yield condition. The author succeeded in the analytical derivation of optimality conditions for this highly non-linear problem. The obtained systems of equations were solved by existing computer codes. In Chapter 4 the methods of analysis and optimization of plates with piece wise constant thicknesses developed earlier for homogeneous isotropic materials are extended to plates made of anisotropic materials. The plastic yielding of the material is assumed to take place according to the criterion Tsai-Wu and the associated gradientality law. The traditional bending theory is used, non-linear effects are neglected in the current study.
The current work is devoted to the theory of analysis and optimization of stepped circular and annular plates subject to smooth yield surfaces. Chapter 1 provides the brief historical review of the problem and of the finite element method. The Basic ideas of parallel computation, also of the multigrid method are presented herein, as well. In Chapter 2 a method for numerical investigation of axisymmetric plates subjected to the distributed transverse pressure loading was presented. The material of plates studied herein is assumed to be an ideal elastic plastic material obeying the non-linear yield condition of von Mises and the associated flow law. The strain hardening as well as geometrical non-linearity are neglected in the present investigation. Calculations carried out showed that the obtained results are in good correlation with those obtained by ABAQUS when solving the direct problem of determination of the stress strain state of the plate. In Chapter 3 an analytical-numerical study of annular plates operating in the range of elastic plastic deformations was undertaken. The material of plates was assumed to be an ideal elastic plastic material obeying the Mises yield condition. The author succeeded in the analytical derivation of optimality conditions for this highly non-linear problem. The obtained systems of equations were solved by existing computer codes. In Chapter 4 the methods of analysis and optimization of plates with piece wise constant thicknesses developed earlier for homogeneous isotropic materials are extended to plates made of anisotropic materials. The plastic yielding of the material is assumed to take place according to the criterion Tsai-Wu and the associated gradientality law. The traditional bending theory is used, non-linear effects are neglected in the current study.
Kirjeldus
Märksõnad
plaadid, elastsus- ja plastsusteooria, optimiseerimine, plates, theory of elasticity and ductility, optimization