Abstract
In this paper we present a numerical analysis method for shape determination of continua based on a strength criterion to control the stress distribution to a desired one. As an objective functional, we introduce a squared stress error norm on the prescribed domains. Using the Lagrange multipliers, an optimization problem subjected to a volume constraint is formulated. The shape gradient function and the optimality condition are derived using the material derivative method and the adjoint method. With the traction method, the domain variation that minimizes the objective functional is numerically and iteratively determined. The shape determination system is developed using a general-purpose FEM code, which is used to solve the state equation and the adjoint equation. The calculated results show the effectiveness of the proposed method in controlling the stress distribution.
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