An improved method for optimal shakedown design of circular plates

The paper analyzes the problem of distributing an optimal limit bending moment of elastic-plastic circular and annular plates subjected to variable repeated loading at shakedown. The geometry of the plate is known and variable repeated loading is defined by time-independent upper and lower bounds (unloading phenomenon of a cross section is ignored). Equilibrium finite elements are applied for a discrete model. The safety of the plate is described with reference to nonlinear von Mises yield criterion while serviceability - by displacement limitations. The analysis problem of internal forces and deformations is formulated as a complete system of equations for an elastic-plastic plate in the shakedown state. The implementation of compatibility conditions for residual displacements and MATLAB nonlinear optimization tools allowed creating an improved mathematical model for optimizing the plate and its effective numerical realization. Research methods and numerical results are based on the assumption of small deformations.Original Abstract: Straipsnyje nagrinejamas prisitaikanciu tampriai plastiniu apvaliu ir ziediniu lenkiamu plokseiu ribinio momento optimalaus pasiskirstymo uzdavinys. Plokstes geometrija zinoma, kintama-kartotine apkrova apibudinama tik virsutinemis ir apatinemis nuo laiko nepriklausanciomis kitimo ribomis (galimas skerspjuviu nusikrovimas ignoruojamas). Diskretizacijai pasitelkti pusiausviri baigtiniai elementai, plokstes saugos ribini buvi apsprendzia netiesine Mizeso takumo salyga, tinkamumo - ilinkiu ribojimo reikalavimai. Konstrukcijos irqzu ir deformaciju skaiciavimo (analizes) uzdavinys formuluojamas kaip pilnutine tampriai-plastines plokstes prisitaikomumo buvio lygciu sistema. Liekamuju deformaciju damos lygciu ir MATLAB komplekso netiesiniu uzdaviniu sprendimo galimybiu panaudojimas igalino sukurti pagerinta prisitaikanciu ploksciu optimizavimo uzdavinio matematini modeli, o kartu ir patobulinti sprendimo algoritma. Tyrimai atlikti ir skaitiniu eksperimentu rezultatai gauti, laikantis mazu poslinkiu prielaidos.