International Journal of Computational Materials Science and Engineering

Butterfly Optimization Algorithm (BOA) is a novel meta-heuristic algorithm inspired by the food foraging behavior of the butterflies. The performance of BOA critically depends upon the probability parameter which decides whether the butterfly has to move towards the best butterfly of the population or perform a random search. Therefore, in order to increase the potential of the BOA, which focuses on exploration phase in the initial stages and on exploitation in the later stages of the optimization, learning automata have been embedded in BOA in which a learning automaton takes the role of configuring the behavior of a butterfly in order to create a proper balance between the process of global and local search. The introduction of learning automata accelerates the global convergence speed to the true global optimum while preserving the main feature of the basic BOA. In order to validate the effectiveness of the proposed algorithm, it is evaluated on 17 benchmark test functions and 3 classical engineering design problems with different characteristics, having real-world applications. The simulation results demonstrate that the introduction of learning automata in BOA has significantly boosted the performance of BOA in terms of achievement of true global optimum and avoidance of local optima entrapment.

We have investigated the electronic and magnetic properties of the doped Heusler alloys Cu₂Cr${}_{1-x}$V${}_x$Ga ($x=0$, 0.5, and 1) using first-principles density functional theory within the generalized gradient approximation scheme. Lattice constants of all phases were determined, and the absence of energy gap in both the spin channels predicts that the materials are metallic. The calculated formation energies are negative, indicating stability of these compounds. Electronic structure and magnetic behavior are reported for the first time for the Cu₂Cr${}_{0.5}$V${}_{0.5}$Ga alloy. It was found that the alloys are ferromagnetic, and metallic witch is confirmed by GGA$+$U calculation.

In this paper, the interpolating moving least-squares (IMLS) method based on a nonsingular weight function is applied to obtain the approximation function. The penalty method is applied to impose the displacement boundary condition, and Galerkin weak form of elastic large deformation problems based on total Lagrange formulation is used to form the final equations which is solved with the Newton–Raphson iteration method, then the improved element-free Galerkin (IEFG) method based on a nonsingular weight function for elastic large deformation problems is presented. The IMLS method can overcome the disadvantage of singular weight functions in the traditional MLS method, then the IEFG method in this paper has high computational accuracy and efficiency, which are shown by numerical examples of elastic large deformation problems. And the influences of the weight functions, scale parameter of influence domain, step number and penalty factor on the numerical results are discussed.

We propose here a theoretical model for the study of band gap opening in graphene-on- polarizable substrate taking the effect of electron–electron and electron–phonon (EP) interactions at high frequency phonon vibrations. The Hamiltonian consists of hopping of electrons upto third nearest- neighbors and the effect substrate, where A sublattice site is raised by energy $+\mathrm{\Delta }$ and B sublattice site is suppressed by energy $-\mathrm{\Delta }$, hence producing a band gap energy of $2\mathrm{\Delta }$. Further, we have considered Hubbard type electron–electron repulsive interactions at A and B sublattices, which are considered within Hartree–Fock meanfield approximation. The electrons in the graphene plane interact with the phonon’s present in the polarized substrate in the presence of phonon vibrational energy within harmonic approximation. The temperature-dependent electron occupancies are computed numerically and self-consistently for both spins at both the sublattice sites. By using these electron occupancies, we have calculated the electron band dispersion and density of states (DOS), which are studied for the effects of EP interaction, high phonon frequency, Coulomb energy and substrate induced gap.

This paper investigates the differences in structural response of lightweight internal structures using finite element (FE) simulation to provide quantitative comparison of the advantages of each type of structure. Various configurations, corresponding to different amounts of weight savings, were studied under distributed pressure loading and bending moment loading conditions. It was found that for configurations with less weight savings, the kagome possesses better performance than the honeycomb structure. However, as the amount of weight savings increases, the trend was observed to be reversed, with the honeycomb structure providing much better performance than the kagome structure. In general, it was shown that the honeycomb structure possesses better performance than the kagome structure under cantilever loading conditions.

Butterfly optimization algorithm (BOA) is an interesting bio-inspired algorithm that uses a nature inspired simulation model, based on the food foraging behavior of butterflies. A common problem with BOA is that in early stages of simulation process, it may converge to sub-optimal solutions due to the loss of diversity in its population. The sensory modality is the critical parameter which is responsible for searching new solutions in the nearby regions. In this work, an adaptive butterfly optimization algorithm is proposed in which a novel phenomenon of changing the sensory modality of BOA is employed during the optimization process in order to achieve better results in comparison to traditional BOA. The proposed Adaptive butterfly optimization algorithm (ABOA) is tested against seventeen standard bench mark functions. Its performance is then compared against existing standard optimization algorithms, namely artificial bee colony, firefly algorithm and standard butterfly optimization algorithm. The results indicate that the proposed adaptive BOA with improved parameter calculation mechanism produces superior results in terms of convergence and achievement of the global optimal solution efficiently.

Peridynamics (PD) is a new nonlocal theory that unifies the mechanics of discrete particles, continuum, and continuum with discontinuities, and it has inherent advantages in calculating the mixed-mode crack propagating. Functionally graded materials (FGMs) are the advanced composite materials, fracture behavior of which is complicated to be simulated by the traditional continuum mechanics. Hence, a PD model for FGMs is given to investigate the mixed-mode fracture behavior under quasi-static loading. Basic PD equations, damage model, and PD $J$-integral for FGMs are discussed. A FORTRAN program of PD algorithm is coded to calculate the $J$-integral and crack propagation of FGMs. The $J$-integral and the crack paths of the PD model are verified by comparing with the published numerical and experimental results. Effects of the material gradient, the material gradient direction, and the stress load magnitude on the fracture behavior are investigated. It is shown that the PD $J$-integral and the crack path are strongly affected by the material gradient and the gradient direction under the same stress load. When the gradient of FGMs is linear, the material gradient direction decides whether the mixed-mode crack kinks or not and the magnitude of stress determines the kinking angle.