Grammatical evolution (GE), which is a kind of evolutionary algorithms, is designed to find a function, an executable program or program fragment that will achieve a good fitness value for the given objective function to be minimized. In this study, GE is applied for the coefficient identification problem of the stiffness matrix in the two-dimensional elastic problem. Finite element analysis of the plate with a circular hole is performed for determining the set of the stress and the strain components. Grammatical evolution determines the coefficient matrix of the relationship between the stress and strain components. The coefficient matrix is compared with Hooke's law in order to confirm the validity of the algorithm. After that, three algorithms are shown for improving the convergence speed of the original GE algorithm.
Zaproponowano zmianę sposobu wymuszania płaskiego stanu odkształceń w dyskretnym modelu powłoki Reissnera-Mindlina. Równania więzów wyrażono przez liniową kombinację elementowych stopni swobody globalnym układzie współrzędnych. Pokazano metodę wprowadzania więzów {to układu równań elementowych. Porównano czasy pracy programów opartych na pierwotnym oraz prezentowanym podejściu.
EN
There is modification of a method of enforcing piane strain state in discrete Reissner-Mindlin model presented. Constraints are formulated as linear combinations of elemental degrees of freedom with respect to global coordinate system. A way of introducing these constraints into the system of elemental eąuations is shown. There is a program working-time compared, based on former and proposed approach.
Plane strain compression tests on Al-Li alloy have shown that grains undergo a significant deformation shear. This deformation favours the formation of the Bs(011)<211> texture component. The grain orientations change in accordance with the RC2(epsilon 12) and RC(epsilon 13) models.
PL
Badania procesu odkształcenia stopu Al-Li w płaskim stanie odkształceń wykazały, że ziarna są poddane znacznemu ścinaniu. Ścinanie to ułatwia powstawanie składowej tekstury typu Bs (001)<211>. Orientacje ziaren zmieniają się zgodnie z przewidywaniami modeli opisanych w literaturze pod nazwą RC2(epsilon 12) i RC2(epsilon 13).
4
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Integrity conditions for elastic-plastic, isotropically damaged solids with isotropic and kinematic strain hardening as subjected to cyclic loading, are in question. It is assumed that the damage process is coupled with the process of plastic deformation. The shakedown conditions are assumed to be satisfied. A new sufficient condition for shakedown accounting for a mixed isotropic and kinematic hardening is developed. The problem of evaluating limit yield-condition arguments is reduced to a min-max problem. In the case of plain strain, the problem is equivalent to a hyperbolic equation in partial derivatives of the second order. A method for computing the purely elastic damaged response of the solid to the prescribed loading program is proposed. The limit yield condition with specified arguments makes it possible to obtain upper and lower estimates for the local actual limit values of the damage parameter admitted by the yield condition for the given loading program. The estimates lead to necessary and sufficient conditions of integrity. The proposed method is illustrated by an example.
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