Discrete Fiber Angle Representation : What Is Laminates?

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(1) Discrete Fiber Angle Representation: The laminate is directly modelled with discrete fiber orientation angles at each point in the structure yielding different stacking sequences. The laminate is usually discretized based on the underlying discretization of the structure such as the finite element [17] or cellular automata discretization [18]. Several authors have used direct fiber orientation angle modelling to design variable stiffness laminates. Hyer and Charrete were among the first to investigate variable stiffness laminates by aligning the fibers with the principal directions of the stress field where strength was enhanced without accounting for buckling [19]. A follow up study was conducted by Hyer and Lee to improve buckling…show more content…
The major benefit of using a GA is that it does not require gradient information which is generally computationally expensive. Several authors worked on developing genetic algorithms and improving the genetic operators as well as fine tuning parameters [29,30,31]. However, they can be computationally expensive for more complex design problems and suffer from local optima and convergence issues especially when coupled with finite element analysis [32,33]. (2) Fiber Path Parameterization: This is achieved by using a curvilinear function to describe the fiber path. Gürdal and Olmedo were the first to introduce a fiber path parameterization where the fiber orientation angle varies linearly [34]. The linear angle variation was later generalized by Tatting and Gürdal to vary linearly along an arbitrarily defined axis where it was used to design variable stiffness laminates for strength [7,35,36], thermomechanical response [37], and coupled strength-buckling optimization problems [38,39]. Nagendra et al. used global fiber paths constructed by linear combination of non-uniform rational B-splines (NURBS). They studied optimal frequency and buckling load design where the design variables where multipliers of the different basis fiber paths [40]. Alhajahmad et al. used a non-linear fiber path expressed in terms of more complex functions such as Lobatto polynomials to increase the number of design variables and achieve better

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