We present a practical method of numerical analysis for optimization problems of domains in which natural vibration problems of linear elastic bodies are defined. In this paper, we apply the traction method that was proposed as a solution to the domain optimization problems to elliptic boundary value problems. The problems treated are those which determine the domain that minimizes 5 mass under constraints in specified vibration elgenvalues. Using the Lagrange multiplier method, we obtain the shape gradient functions for these domain optimization problems from the optimality criteria. A numerical analysis technique for the multiconstraint problems is also presented. We show the successful resolution of the problems of beamlike plates clamped at both ends.
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