SHAPE OPTIMIZATION BY THE BOUNDARY-ELEMENT METHOD - A COMPARISON BETWEEN MATHEMATICAL-PROGRAMMING AND NORMAL MOVEMENT APPROACHES

The aim of this work is to find the best boundary shape of a structura l component under certain loading, to have minimum weight, or uniforml y distributed equivalent stresses. Two shape optimisation algorithms a re developed. One of them is a mathematical programming method, and co nsiders nodal coordinates on the design boundary directly as the desig n variables, while the other one is rather an optimality criterion app roach, based on normal movement of the design boundary. Solving the op timisation problem of stress concentration for a perforated plate whic h has an analytical solution, shows that the presented mathematical pr ogramming method results in almost the same as the analytical solution . Nevertheless, increasing the number of design variables to find more smooth shapes in mathematical methods can cause severe programming pr oblems. Comparing the result of this method with that of the optimalit y criterion indicates that the latter is much easier to apply without any limit on the number of design variables. To calculate stresses at every iteration, the boundary element method (BEM) is used. Therefore both algorithms benefit from a simple mesh generation based on equal l ength elements, which provides the possibility of solving multiply-con nected domains or geometrically complicated mechanical components. Bot h methods are used to find the optimum shape of a circular plate under radial loading with four design holes. Finally, the problem of the be st topology and shape of circular disks is solved by the optimality cr iterion approach. Also it is proposed that 'a fully stressed design al gorithm which starts from the best topology design, has the best shape for weight optimisation. (C) 1997 Elsevier Science Ltd.