• Stress analysis verification, as by airworthiness regulations
• Maximum displacement verification for shock-isolating mountings elements
• Maximum displacement verification for the overall engine mount

Dynamic characterisation involves modal frequencies which are constrained to not fall too close to the propeller rotation frequency. To obtain the requested objective and state functions, two parametric FEM models of the structure, differently featured about geometry and element composition, have been realised using the Ansys R5.6 program [1,2]. Besides geometric controls, both models include user-defined elements to simulate the shock-isolating mountings and a number of discrete parameters to properly handle topology. According to a preliminary static-modal analysis the simpler beam based model has proved to be adequate enough to capture the structural behaviour without expensive computational activity. In order to avoid weak structures (overlapping bars, kinematic mechanisms) a mathematical description based on a planar graph and related adjacency matrix has been used to model the topology [3]. The building algorithm has been structured in a such mode to generate the whole lattice-work always compatible with structural aims, no matter how the current design set is composed.

Since in a topologically controlled parametric model is not possible to know a priori the amount of the constitutive elements and the label of each one, some cubic-spline based controls have been used to assign geometrical properties to the beam/bar cross-sections. Constraints acting on dynamic frequencies have been defined using a single parametric state function modelled as a filter to get out of the variable number of modal frequencies in the interest range, caused by the topologic modifications. For each modal frequency of the current configuration, a penalty score is calculated by means of a dome-filter function centred on the propeller rotation frequency and cumulated in the state function. This function is finally coupled with a well-suited, non-positive range to evaluate the feasibility.

For the optimisation procedure, a special bit-masking oriented genetic algorithm (BMOGA) has been defined and used [4]. This approach increases the efficiency and flexibility of the reproduction phases and allows the definition of advanced evolutionary operators such as: synthetic crossover operators obtained by superposition of standard methods, multi-level crossovers, locally adjustable mutation operators and a single-step prediction operator [5].

To increase the sensitivity response, discrete topological design variables have been coded with a direct base 2 enumeration instead of the standard scaled codification used for continuous variables. The bit-masking approach has been applied to perform, in the initial phases of the procedure, different specialised evolutionary operators applied on the specific chromosomal sub-strings related to the two types of design variables.

About the topological aspects, the graph theory based approach has proved to be simple to implement and effective.

The optimisation process has shown good results both as overall speed performance and quality design. The best design set has produced a fully feasible light structure with a consistent weight reduction compared to the reference configuration.

1

Swanson Analysis Systems INC., "Ansys user's manual Rev. 5.5", Vol. I, II, III, 1998.

2

Swanson Analysis Systems INC., "Ansys Programmer's guide Rev. 5.5" 1998.

3

J.A. Bondy, U.S.R. Murty, "Graph theory and related topics", Academic Press, London 1979.

4

L. Iuspa, F. Scaramuzzino, "A bit-masking oriented data structure for evolutionary operators implementation in genetic algorithms", Soft Computing Vol. 5 N.1 58-68 2001. doi:10.1007/s005000000066

5

L. Iuspa, F. Scaramuzzino, "Optimal design of deployable pantograph space structures via a hybrid genetic-deterministic technique", 3rd Workshop on Space Environment Applications, 151-163 2000.

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