Design optimization using the boundary element method

Abstract

Structural optimization is often confined to sizing simple design variables, such as plate thicknesses and bar cross-sectional areas, while the geometric shapes of components remain largely unchanged. Shape optimization is more complex, changing the shape of the boundary, subject to appropriate constraints. The boundary element method, being a boundary-oriented technique is very appropriate for this purpose. It can overcome a number of the difficulties associated with its main rival, the finite element method. Firstly, because of the continuously changing geometry. the accuracy of the finite element analysis using the initial mesh of elements may become inadequate during the optimization process. Secondly, if during this process, the finite element mesh has to be re-generated, the cost is relatively high. Finally, and most importantly, the sensitivity analysis in the calculation of the derivatives with respect to the design variables may be obtained directly in the boundary element approach rather than by approximate methods such as finite difference schemes. Methods for shape optimal design of two-dimensional elastic structures are formulated, when the objective can be minimum weight design with limiting values of maximum stresses, or the smoothing of stress peaks.