Design of Composite Layers With Curvilinear Fiber Paths Using Cellular Automata

Abstract

The anisotropic advantageous properties of fiber reinforced composites may not be fully exploited unless the fibers are properly placed in their optimal spatial orientations. This paper investigates application of Cellular Automata (CA) for curvilinear fiber design of composite laminae for in-plane responses. CA use local rules to update both field and design variables in an iterative scheme till convergence. In the present study, displacement update rules are derived using a finite element model governing the equilibrium of the cell neighborhood and fiber angles are locally optimized based on a minimum strain energy criterion. A manufacturing improvement is applied on top of the local optimum orientation wherever this angle is not consistent with the cell neighborhood orientation trend. Numerical studies showed convergency of the local update rules and considerable improvements in the stiffness properties for a cantilever bending test and a square plate with a cutout.

A review on design for manufacture of variable stiffness composite laminates

“…This literature was completed with other existing publications and web-based articles gathered through other sources in a less structured manner. Papers related to variable stiffness laminates that were found relevant 1,2,5–11,13–30,32–52,55–69 (a total of 63 papers) have been analysed to assess whether they perform or develop a set of tasks (Figure 9(a)).…”

Design of variable–stiffness laminates using lamination parameters

“…Setoodeh et al [6] showed that the optimality criteria reduce to the minimization of the complementary strain energy at any point in the domain. Numerical studies show that substantial stiffness improvements can be gained only by reorientation of the orthotropic material in an optimal manner [5][6][7]. However, such a formulation requires repeated transformation of the material properties using the classical trigonometric transformations.…”

Topological design using multivariate laminate stackings for tailored fiber placement

“…Since results are based on a fixed stress or strain field, structures that are more complex require numerical investigations due to a varying field. Based on this research, Setoodeh et al [13][14][15] used these principles to develop a framework, which uses cellular automata to update local material orientations iteratively including multiple load cases. Given the fact, that only fiber orientations and layer thicknesses are used as design variables, global optima could not be achieved when considering general laminates.…”