Hossein Ghiasi

A non-dominated sorting hybrid algorithm for multi-objective optimization of engineering problems

Among numerous multi-objective optimization algorithms, the Elitist non-dominated sorting genetic algorithm (NSGA-II) is one of the most popular methods due to its simplicity, effectiveness and minimum involvement of the user. This article develops a multi-objective variation of the Nelder-Mead simplex method and combines it with NSGA-II in order to improve the quality and spread of the solutions. The proposed hybrid algorithm, called non-dominated sorting hybrid algorithm (NSHA), is compared with NSGA-II on several constrained and unconstrained test problems. The higher convergence rate and the wider spread of solutions obtained with NSHA make this algorithm a good candidate for engineering problems that require time-consuming simulation and analysis. To demonstrate this fact, NSHA is applied to the design of a carbon fibre bicycle stem simultaneously optimized for strength, weight and processing time.

Constrained Globalized Nelder—Mead Method for Simultaneous Structural and Manufacturing Optimization of a Composite Bracket

The optimized design of composite structures is a difficult task. It requires optimizing simultaneously both structural and manufacturing objectives. The objectives do not have closed form solutions and have multiple local optima that calls for a global search. This paper improves the global search method called GBNM [1], which is based on several restarts of the Nelder—Mead method. Two issues are addressed here. First, the restart procedure is improved by using a one-dimensional probability function and a weighted selection procedure. Second, nonlinear constraints are included by projecting the infeasible points onto the nonlinear constraints. The improved procedure is applied to four mathematical test functions. Numerical results show the proposed approach is more efficient in terms of computational time and probability of finding the global minimum. The improved GBNM is then applied to the simultaneous structural and manufacturing design of a Z-shaped composite bracket. The results are compared to those obtained with the genetic algorithm.

Effect of Fibre Volume Fraction on Mixed-Mode Fracture of a Fabric Carbon/Epoxy Composite

Variation in fibre volume fraction is a common characteristic of composites made by an injection moulding process. The effect of this variation on fracture toughness is not yet fully investigated. This paper examines the fracture in fabric carbon/epoxy composite laminates under a wide range of combined mode-I and mode-II delamination. A total of 60 double cantilever beam and edge-notched flexure specimens are manufactured by resin transfer moulding with two different fibre volume fractions. It was observed that increasing the fibre volume fraction decreased the initiation fracture toughness in all mixed-mode ratios. This behaviour is believed to relate to the fact that the initiation fracture energy is dominantly absorbed by the resin-rich regions at the delamination tip. In contrast, an increase in fibre volume fraction was found to increase the propagation fracture toughness at high mode-I contribution where the fibre bridging is believed to be the major energy dissipating mechanism. Fractographic analysis also demonstrated that an increase in contribution of mode-II delamination is accompanied by a decrease in fibre bridging and an increase in shear hackles.

Layer Separation for Optimization of Composite Laminates

The excellent mechanical properties of laminated composites cannot be exploited without a careful design of stacking sequence of the layers. An important variable in the search of the optimum stacking sequence is the number of layers. The larger is this number, the harder as well as longer is the search for an optimal solution. To tackle efficiently such a variable-dimensional problem, we introduce here a multi-level optimization technique. The proposed method, called Layer Separation (LS), increases or decreases the number of layers by gradually separating a layer into two, or by merging two layers into one. LS uses different levels of laminate representation ranging from a coarse level parameterization, which corresponds to a small number of thick layers, to a fine level parameterization, which corresponds to a large number of thin layers. A benefit of such differentiation is an increase of the probability of finding the global optimum. In this paper, LS is applied to the design of composite laminates under single and multiple loadings. The results show that LS convergence rate is not inferior to that of other optimization techniques available in the literature. It is faster than an evolutionary algorithm, more efficient than a layerwise method, simple to perform, and it has the advantage of possibility of termination at any point during the optimization process.Copyright

Interaction energy and polymer density profile in nanocomposites: a coarse grain simulation based on interaction stress

A coarse grain approach was selected to simulate nanocomposites made of single-walled carbon nanotubes (SWNTs) and poly(methyl methacrylate) (PMMA). Unlike common coarse grain simulations, which employ Lennard-Jones models as the force field between the beads, the current approach used experiment-based data, and hence is considered a semi-empirical approach. Interaction stress data obtained from atomic force microscopy experiments under water were multiplied by ten to represent the interaction stresses in vacuum and then fed into the simulation. A new planar approach was introduced to simplify the three-dimensional unit cell into a two-dimensional plane. Furthermore, preliminary one-dimensional simulations were carried out to acquire a trade-off between simulation time and accuracy of the results. It was shown that the final results were independent of the initial conditions and converging parameters (the parameters that define the convergence rate). Two sets of planar simulations were performed to model pure PMMA systems and PMMA–SWNT nanocomposites. Polymer chain configuration and density profiles for these systems were obtained and compared. The surface effect on the polymer configuration and density profile was captured and demonstrated to be identical for the two systems. The polymer simulations showed a core section with a constant density, where the surface effect from the free surface did not influence the behaviour of the polymer chains. The effect of nanotube on polymer morphology was observed by layered structures of polymer chains around the nanotube, with preferable bands of peaks and valleys in the radial density profile. Finally, a new method was presented to calculate the interfacial binding energy for nanocomposites. The value of 0.44 kcal mol−1 A−2 obtained for the PMMA–SWNT nanocomposite was shown to be in good agreement with the previously reported results obtained from atomistic simulations.