Shape optimisation by the boundary element method: a comparison between mathematical programming and normal movement approaches

摘要

the aim of this work is to find the best boundary shape of a structural component under certain loading, to have minimum weight, or uniformly distributed equivalent stresses. Two shape optimisation algorithms are developed. One of them is a mathematical programming method, and considers nodal coordinates on the design boundary directly as the design variables, while the other one is rather an optimality criterion approach, based on normal movement of the design boundary. Solving the optimisation problem of stress concentration for a perforated plate which ahs an analytical solution, shows that the presented mathematical programming method results in almost the same as the analytical solution.