DESIGN OPTIMISATION METHOLOGY

The present research has used experimental and numerical techniques to analyse the static, fatigue and aged performance of a typical hybrid connection. However, it was described in Chapter 3 that the design of the HSC, the full-scale hybrid connection, was performed outside of the present research. This section aims to outline the method that was used to investigate whether there is a better design of the hybrid connection based on two main goals, increased structural performance and reduced weight.

There are a number of techniques that can be used to obtain optimum solutions to a given problem and the selection of the method is dependent on the problem to be solved. Such techniques include Secant and Newton-Raphson methods often used to obtain minima and maxima of single dimension problems, hill-climbing methods for multi-dimensional problems and evolutionary algorithms that are used for non-linear, discrete and often discontinuous problems. In the present research the design space of the hybrid connection could fall into the latter category and is the method implemented. Regardless of the

evolutionary method used there are a number of discrete steps involved in the search for an optimal solution. • Input generation • Encoding • “breeding” • Selection 5.3.1 INPUT GENERATION

The first step in any numerical optimisation method is to describe the object mathematically. In the present research a joint design is being analysed, the principal dimensions of the joint are used as the main information to describe and define the joint in mathematical space. The joint design being analysed in this study is the HSC configuration as it is representative of a real structural connection.

A number of parameters are assumed to be constant throughout the analysis, these are:

• Overall joint length – 700 mm

• Material properties of GRP, steel and Balsa core

• Length of steel beyond the GRP/steel overlap used for attachment of superstructure to the deck of the ship – 110 mm (minimum permitted value due to heat transfer during welding)

The joint can now be described by seven variables: 1. Adhesive thickness

2. Steel thickness 3. Core thickness 4. GRP skin thickness 5. Steel/GRP bond length 6. Taper zone length

7. Adhesive Young’s modulus

Knowledge of these geometric parameters allowed the definition of the HSC specimen and formed the basis of a finite element model, the geometry defining the location of the key points of the joint. A FORTRAN programme was developed to create a finite element model of the joint. A number of important considerations were addressed at this stage. Firstly, it is known that FEA mesh density is important for the accurate modelling of resultant stresses and global response. This was incorporated into the programme by ensuring that the mesh density was constant. Secondly, the location and magnitude of the applied load and boundary conditions were kept constant. These two points ensured that the results were directly comparable. Finally, the mesh aspect ratio was kept within the limits (1:20) of the software to ensure accurate results. The solution to the finite element analysis can be used to obtain information on the joint configuration being analysed and form the basis of the selection methods. The inputs of the basic geometric values mentioned above are provided from within the genetic algorithm.

5.3.2 GENETIC ALGORITHM IMPLEMENTATION

The genetic algorithm methodology is shown in Figure 5.4. The first step involved the physical model definition described in Section 5.3.1. The design space was then constrained by limiting the range in which the geometric variables can be altered. This can be conducted using two methods. Firstly, the range of the variables can be chosen based on realistic and practically achievable geometries, i.e bondlines greater than 20 mm or GRP skin thicknesses less than 1 mm are not practical. This will result in a relatively large design space. Secondly, a technique such as the parametric study from the previous section, can limit the design space to explore only the range of variables that will give favourable results. In the present research the latter of the two methods was implemented and will be discussed in Chapter 8.

Once the design space was established a random number of individuals was created to produce the initial population by randomly selecting a value for each design variable. This process is repeated to achieve the required initial population. The random input variables were then processed to generate finite element models from which solutions were obtained. Information obtained from the FEA and elsewhere was used to form a fitness criteria for each individual in the population, which will be discussed in detail in Section 5.3.3. Based

on the results of the fitness analysis the best individuals are selected to create the new generation. “Breeding” of the chosen individuals requires that each individual’s variables be encoded so that they form a genetic code, analogous to nature’s genome. Binary numbers are often used to achieve this.

The first stage in the “breeding” process is crossover. This is a process whereby two genetic codes (individual joints) are combined to create a new code (new individual). The philosophy is that the new individual may be better than the two individuals used to create it if the new individual takes the best characteristics of each. There are a number of ways in which crossover can be completed. In the present research a single point crossover is conducted. Consider the following binary strings, which represent two individuals, which have been selected for crossover. The symbol ‘|’ is used to indicate the randomly chosen crossover point.

Individual 1: 11001|010 Individual 2: 00100|111

After interchanging the individuals codes at the crossover point two new individuals are created.

New individual 1: 11001111 New individual 2: 00100010

If the genetic algorithm was allowed to run using only crossover as the “breeding” parameter it could be possible for the population to stagnate at a local optimum. Mutation is used to introduce new individuals into the population to prevent this occurring. Again there are a number of ways in which this can be conducted. In the present research a relatively simple ‘flip bit’ method is used. This method is only valid if the individuals are encoded into binary numbers. At a randomly chosen location in the binary code a single bit of information is flipped from being a 1 to a 0 or vice versa, thus creating a new individual. Mutation occurs during the genetic process according to a user-definable mutation probability. Low values will prevent the search turning into a primitive random search. Once the new population has been created through crossover and mutation the binary representation of the individual is decoded into a physical joint. If the genetic algorithm has completed the user-defined number of generations or certain convergence criteria are met

then the process can be stopped. However, if the algorithm is to continue then the evaluation and selection stages are completed once more and a new generation created. 5.3.3 SELECTION CRITERIA

The selection criteria or measure of fitness ensures that joints with favourable attributes are carried forward into the next generation of the genetic algorithm. The method of obtaining a suitable fitness criterion can be complex. This is particularly true if there is more than one objective to the problem, commonly referred to as multi-objective functions. In the present research a single main objective function was used. However, as the optimisation of the main objective occurred a reduction in the fitness of the secondary functions was prevented. This simplified the problem by eliminating the true multi-objective nature of the problem but monitors the secondary objectives as an important feature of the joint design.

Chapter 6