The heterogeneity and anisotropy of structural composites make the application of the standard mesh-based methods using the meshing of interfacial region between matrix and fibers a difficult task. The objective of this study is to present the EFG formulation for problems of composite micromechanics. It is expected that the tediousness and approximations involved in mesh generation, and hence inaccuracies in the results can be avoided using the new meshless techniques such as the Element Free Galerkin (EFG) method. The theoretical methodologies, computer implementations and practical application are carried out. Periodic boundary conditions of the unit cell under tensile load are set up. The method of Lagrange multipliers is introduced for the treatment of material discontinuity at the fiber-matrix interface in which both the displacement continuity and traction reciprocity are satisfied. The EFG method is formulated for the generalized plane strain problems. Examples are presented to illustrate the effectiveness of the proposed micromechanical model, and it is validated by comparing the results with available numerical solutions.
The greatest advantage of fiber-reinforced composite materials is the freedom to tailor their strength and stiffness properties, while the most significant disadvantage consists in their high costs. Therefore, the design process and especially the optimization phase becomes an important step. The geometry of the fabric of each lamina as well as their stacking sequence need to be carefully defined, starting from some basic geometric variables. The input parameters are the widths and the heights of the tows, the laminate-stacking sequence and the gaps between two successive tows or the height of the neat matrix. This paper is a follow-up to a previous work on using and improving an in-house software called SOMGA (Satin Optimization with a Modified Genetic Algorithm), aimed to optimize the geometrical parameters of satin-reinforced multi-layer composites. The final goal is to find out the way in which various types of woven fabrics can affect the best possible solution to the problem of designing a composite material, able to withstand a given set of in-plane loads. The efficiency of the composite structure is evaluated by its ultimate strains using a fitness function that analyses and compares the mechanical behavior of different fabric-reinforced composites. Therefore, the ultimate strains corresponding to each configuration are considered intermediate data, being analyzed comparatively until obtaining the optimal values. When the software is running, for each analysis step, a set of intermediate values is provided. However, the users do not have to store these values, because the final result of the optimization directly provides the composite configuration with maximum efficiency, whose structural response meets the initially imposed loading conditions. To illustrate how the SOMGA software works, six different satin-woven-fabric-reinforced composites, starting from plain weave (satin 2/1/1), then satin 3/1/1, satin 4/1/1, satin 5/1/1, satin 5/2/1 and finally satin 5/3/1, were evaluated in the SOMGA interface. The results were rated against each other in terms of the composite efficiency and the case characterized by minimal reinforcement undulation (thinnest laminate) were highlighted.
For solving a partial different equation by a numerical method, a possible alternative may be either to use a mesh method or a meshless method. A flexible computational procedure for solving 1D linear elastic beam problems is presented that currently uses two forms of approximation function (moving least squares and kernel approximation functions) and two types of formulations, namely the weak form and collocation technique, respectively, to reproduce Element Free Galerkin (EFG) and Smooth Particle Hydrodynamics (SPH) meshless methods. The numerical implementation for beam problems of these two formulations is discussed and numerical tests are presented to illustrate the difference between the formulations.
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