J. Parvizian et Rt. Fenner, SHAPE OPTIMIZATION BY THE BOUNDARY-ELEMENT METHOD - A COMPARISON BETWEEN MATHEMATICAL-PROGRAMMING AND NORMAL MOVEMENT APPROACHES, Engineering analysis with boundary elements, 19(2), 1997, pp. 137-145
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.