DOI 10.1007/s00158-003-0372-x

Solution to boundary shape optimization problem of linear elastic continua with prescribed natural vibration mode shapes A.R. Inzarulfaisham and H. Azegami Abstract This paper presents a practical method of nu-merical analysis for boundary shape optimization prob-lems of linear elastic continua in which natural vibra-tion modes approach prescribed modes on specified sub-boundaries. The shape gradient for the boundary shape optimization problem is evaluated with optimality con-ditions obtained by the adjoint variable method, the La-grange multiplier method, and the formula for the mate-rial derivative. Reshaping is accomplished by the traction method, which has been proposed as a solution to bound-ary shape optimization problems of domains in which boundary value problems of partial differential equations are defined. The validity of the presented method is con-firmed by numerical results of three-dimensional beam-like and plate-like continua