Keywords: structural optimisation, finite element modelling, orthotropic plate, weight minimization, finite element simulation.

Structural elements in the form of orthotropic plates are often employed in many engineering structures, for example in superstructure of bridge and ship structures. This paper investigates the optimisation problem of minimizing weight of an orthotropic plate that consists of a thin plate stiffened by stiffeners arranged symmetrically in two orthogonal directions, such that the maximum Mises stress in the whole structure does not exceed a specified value. The design variables are the thickness of the plate and stiffeners, the positions of stiffeners and depths of stiffeners. It was shown that the relationship between the objective function and constraint variable with design variables is very complex resulting in a great number of local minima, often in the neighbourhood of the global minimum. This fact highlights the danger of getting bogged down in a local minimum during the course of an optimisation algorithm.

The optimisation problem of minimizing weight of these orthotropic plates subject to a design stress is basically a sizing optimisation problem. Three methods were used: Subproblem Approximation (SAM), First Order (FOM) and Finite Element Simulation of Durelli's method (FESD). The first two are available in FEM software ANSYS 5.7; the third method, FESD, developed by the author, as a shape optimisation method is adapted into this sizing optimisation problem. SAM and FOM are simple to use, however due to the existence of many local minima, these methods take a long time to converge, and usually converge to a local minimum, in spite of efforts to use various techniques like random design or a global sweep run so as not to overlook the global minimum. FESD used the concept of iterative simulated removing material where the structure is under-stressed and simultaneous adding material where over-stressed, can be adapted to this problem. In the course of an optimisation loop, the FESD algorithm solves the current FEM model, monitor where the over-stressed and under-stressed regions of the structures are, identify the associated design variables and then change the design variables in appropriate direction. It was found that the bottom-up solid modelling method combined with parametric design language of ANSYS 5.7 were suitable for the FESD algorithm. It was found that SAM and FOM are less effective than FESD, in terms of number of iterations to convergence as well as the optimum value of the objective function.

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