In this article, evolutionary algorithms (EAs) are employed for multi-objective Pareto optimum design of group method data handling (GMDH)-type neural networks that have been used for fatigue life modelling and prediction of unidirectional (UD) carbon-fibre-reinforced plastics (CFRP) composites using input—output experimental data. The input parameters used for such modelling are stress ratio, cyclic strain energy, fibre orientation angle, maximum stress, and failure stress level in one cycle. In this way, EAs with a new encoding scheme are first presented for evolutionary design of the generalized GMDH-type neural networks, in which the connectivity configurations in such networks are not limited to adjacent layers. Second, multi-objective EAs with a new diversity preserving mechanism are used for Pareto optimization of such GMDH-type neural networks. The important conflicting objectives of GMDH-type neural networks that are considered in this work are training error (TE), prediction error (PE), and number of neurons ( N). Different pairs of these objective functions are selected for two-objective optimization processes. Therefore, optimal Pareto fronts of such models are obtained in each case, which exhibit the trade-offs between the corresponding pair of conflicting objectives and, thus, provide different non-dominated optimal choices of GMDH-type neural network model for fatigue life of UD CFRP composites. Moreover, all the three objectives are considered in a three-objective optimization process, which consequently leads to some more non-dominated choices of GMDH-type models representing the trade-offs among the TE, PE, and N (complexity of network), simultaneously. The comparison graphs of these Pareto fronts also show that the three-objective results include those of the two-objective results and, thus, provide more optimal choices for the multi-objective design of GMDH-type neural networks.
Molecular dynamics (MD) simulation is used to investigate the vibrational behavior of γ-graphyne and its family. Five different nanosheet types including graphyne, graphdiyne, 3-graphyne, 4-graphyne, and 5-graphyne are considered for investigation. The fundamental natural frequencies of armchair and zigzag nanosheets with different geometrical sizes under different boundary conditions are computed. It is shown that increasing the size of γ-graphyne results in decreasing the natural frequency. Comparing the vibrational behavior of armchair and zigzag nanosheets, it is shown that for large nanosheets, the effect of atomic structure on the fundamental natural frequency can be neglected. Besides, it is represented that increasing the number of acetylene links connecting neighboring hexagons in the structure of nanosheets leads to decreasing the frequency.
In this research, two energy-based techniques, called Lagrange multiplier and conversion matrix, are applied to involve crack parameters into the non-linear finite element relations of Euler-Bernoulli beams made of functionally graded materials. The two techniques, which divide a cracked element into three parts, are implemented to enrich the secant and tangent stiffness matrices. The Lagrange multiplier technique is originally proposed according to the establishment of a modified total potential energy equation by adding continuity conditions equations of the crack point. The limitation of the conversion matrix in involving the relevant non-linear equations is the main motivation in representing the Lagrange multiplier. The presented Lagrange multiplier is a problem-solving technique in the cracked structures, where both geometrical nonlinearity and material inhomogeneity areas are considered in the analysis like the post-buckling problem of cracked functionally graded material columns. Accordingly, some case-studies regarding the post-buckling analysis of cracked functionally graded material columns under mechanical and thermal loads are used to evaluate the results.
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