Shape optimal design of a torsion bar and clamped beams using boundary element method

Abstract

A shape optimal design problems is studied in conjunction with the boundary element method(BEM). The sensitivity coefficients necessary for the optimization are obtained from the material derivative formulars of integrals, which are expressed in line integral forms for two dimensional problems. For the analysis of the system, the boundary element method is utilized, which is found suitable for evaluation of the line integrals. A torsion bar problem to maximize its rigidity is used to check the convergency to the known exact solution. The minimum deflection design of clamped beams under various loading conditions is taken as the second example. The optimal shapes obtained agree well with the results in the literature which are found by other methods. Some of the characteristics of BEM indicate more advantages for the calculation of the sensitivities than other methods, in the sense that in BEM the primary variables are obtained along the boundary and only the nodal points along the boundary need to be specified, which facilitates easy adjustment as the boundary is optimized. However, a detailed study of efficiency and accruacy of this method as compared with others remains to be made, including other constraints not considered here.