A graph-based parameterization concept for global laminate optimization

Abstract

A new graph-based parameterization concept aimed at the global optimization of laminated structures by the means of evolutionary algorithms and finite element analysis is introduced. The motivation to develop this novel parameterization concept is twofold. First, the entire design space is accessible to optimization down to the smallest entity, which is a single finite element, and secondly, this concept guarantees greatest flexibility in terms of laminate layer shape and placement. The finite element mesh of a structure is represented as a mathematical graph. Substructures of this graph form fiber reinforced and possibly overlapping patches and are affiliated to virtual graph vertices representing their properties. Adapted genetic variation operators are directly applied on this graph. The method allows for concurrent optimization of number, size, shape, and position of the patches and an arbitrary number of material related properties for each of them. The novel concept overcomes the limits of traditional geometry-based approaches, as it is able to represent almost arbitrary patch shapes even on curved surfaces. Two numerical examples demonstrate the efficiency of the method.

Global laminate optimization on geometrically partitioned shell structures

“…The method employs graph concepts in the encoding of the geometric region covered by a reinforcement treatment. However, abandoning a purely graph-based genotype like in existing methods (Giger et al 2008;Giger 2007;Kaufmann 2006) leads to more compact representations. The genetic search is assisted by gradient information in operations modifying the patch shape and determining optimal ply angles.…”

“…An extension of the method is proposed in Giger (2007, Chapter 5) where a variable-length genotype in an evolutionary algorithm enables to optimize the number of patches as well. A finite element-wise approach to parameterize the shape of reinforcement patches is investigated in Giger et al (2008). An abstraction of this method to operate on predefined geometrical zones instead of finite elements can be found in Kaufmann (2006) (revisited in Chapter 7 of Giger 2007).…”

“…This approach is borrowed from earlier investigations (Giger et al 2008). The properties of this compliant layer are given for the following examples.…”

“…In a first experiment, the structure shall be reinforced by a single, additional layer of an unidirectional carbon/epoxy prepreg (Table 1, thickness 0.15 mm). The experiment corresponds to problem 5.3.1 presented in Giger (2007) (revisited in Section 7.5 in the same source and also presented in Giger et al 2008).…”

“…Prior investigations require a high number of structural evaluations (Giger et al 2008) or show a considerable spread in the optimization results of different optimization runs (Giger 2007, Chapter 7). This study aims at investigating possibilities to embed gradient information in a genetic encoding in order to improve the solution quality and the rate of convergence of the method.…”