Keywords: evolutionary structural optimization, shape optimization, gusset plates, steel structures, finite element discretization, bolted connections, welded connections.

Structural optimization is probably one of the disciplines that has attracted the most attention among researchers in engineering community. A great deal of research has been carried out in the topic over the years. However, optimum design techniques based on deterministic approaches such as mathematical programming and optimality criteria have fallen short of fulfilling the needs of industry. The basic reason behind this is that these algorithms assumed that the availability of design variables was continuous while they were discrete. Although some of these algorithms allowed design variables to be selected from the available set of sections, they were complex and not very efficient in solving the practical, large and multi-constrained design problems. This situation forced the researchers to find an alternative way to be able to accommodate the discrete nature of design variables.

In recent years, structural optimization witnessed the emergence of novel and inspired design techniques. These stochastic search techniques make use of the ideas taken from the nature. With in this context, several algorithms developed which simulate the natural phenomena into a numerical method. Among these genetic algorithms mimic the survival of the fittest to establish a numerical search algorithm. They initiate the search for the fittest among the potential candidates, which are collected randomly in the form of the initial population. The binary or any other types of code are used to express the row number of the available section selected for each design variable. By collecting these binary codes together for all the design variables a potential candidate is obtained for the solution of the optimum design problem. The genetic algorithm produces new populations from the initial one using certain operations. It continues producing populations from one generation to another with the expectation of reaching if not the fittest but a better individual who represents the optimum solution.

Simulating annealing is another approach that is based on the analogy of the physical process of heating and then slowly cooling a substance to obtain a strong crystalline structure. The simulated annealing process lowers the temperature by slow stages until no further changes occur. At each temperature the simulation must proceed long enough for the system to reach a steady state. The sequence of temperatures and the number of iterations to thermalize the system at each temperature comprise an annealing schedule. This procedure allows the system to move consistently towards lower energy states. If the temperature is decreased logarithmically, simulated annealing guarantees an optimal solution.

Immune network modeling is yet another numerical technique that represents a somewhat crude approach to mimic the biological process wherein antigens or harmful foreign substances are first identified and then antibodies capable of attacking these antigens and ultimately eliminating them are produced. This process is simulated using the genetic algorithm approach. A matching function that measures the similarities between antibodies and antigens, substitutes for the fitness function of genetic algorithm.

The harmony search method is based on the natural musical performance process that occurs when a musician searches for a better state of harmony such as during jazz improvisation. Jazz improvisation seeks to find musically pleasing harmony as determined by an aesthetic standard, just as the optimization process seeks to find a global solution as determined by an objective function.

Evolutionary structural optimization makes use of the idea of having uniform stress in structures, which is the case in the skeleton of living beings. It is amazingly astonishing to observe that structural shapes of living beings are all in the optimized form. These shapes are such that they do not have weak places or stress concentrations. The load is fairly distributed and there is a uniform stress distribution under the external loading. The bones of the living beings for example breakdown the material in order not to carry excess load. The idea of obtaining a structural form that has a uniform stress distribution is simulated in a numerical technique by first discretizing the design domain into a mesh of finite elements. The finite element method is then used to determine the stresses in the elements. Those elements with lower stress density are then removed from the domain. This process is continued until a structural form is obtained with almost uniform stress distribution.

In this study evolutionary structural optimization is used to determine the optimum shapes of steel gusset plates. Gusset plates are widely used in steel structures particularly in trusses at the connection of members. The number of different gusset plates with bolted connections and with welded connections subjected to axial loading is considered. It was noticed that the optimum shapes obtained for single layer bolted connections were very similar that are used in practice. However, the optimum shapes for gusset plates where multiple steel members are connected are totally unpredictable. Furthermore the optimum shape obtained for the gusset plate utilized as a splice for a double angle tension member is different from the one used in practice. The one obtained by evolutionary structural optimization has an elliptic shape that has 20% less weight than the original.

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