Optimum shape and topology design using the boundary element method

A procedure is developed for simultaneous shape and topology design optimization of linear elastic twodimensional continuum structures. An intuitive approach is presented to treat such topological problems whereby material is eliminated from within the structure (by introducing holes at regions of low stress) through a sequence of shape optimization processes. A mathematical programming technique coupled with the boundary element (BE) method of response and sensitivity analyses enables the optimal positioning of these holes plus optimization of the overall structural shape. The analytical derivative BE formulation is explained together with the use of appropriate design velocity fields, and example problems are solved to demonstrate the optimization procedure