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.
경계요소법을 이용하여 비틀림 축과 고정보의 최적형상을 구하였다. 형상최적설계에 필요한 민감도는 적분의 질점 미분식으로 부터 구해지고, 이 식은 경계요소법으로 구하기 쉬운 경계적분 형태가 되기 때문에 경계요소법을 이용하여 해석하였다.
먼저 이 방법의 수렴성을 검사해 보기 위해 엄밀해가 알려져 있는 비틀림 축 문제에 적용 시켰다. 고정보의 경우 처짐의 제한조건을 사용하였으며 다른 방법으로 구해진 결과와 잘 일치하였다.
형상최적설계에서는, 경계변화에 따른 경계요소의 재조정이 간편하고, 필요한 경계에서의 해만을 구하게 되는 경계요소법의 장점이 잘 활용된다.
