The existing need to develop methods whereby the shape design efficiency can be improved through the use of high-quality approximation methods is addressed. An efficient approximation method for stress constraints in three-dimensional shape design problems is proposed, based on expanding the nodal forces in Taylor series with respect to shape variations. The significance of this new method is shown through elementary beam theory calculations and via numerical computations using three-dimensional solid finite elements. Numerical examples, including the classical cantilever beam structure and realistic automotive parts like the engine connecting rod, are designed for optimum shape using the proposed method. The numerical results obtained from these methods are compared with other published results to assess the efficiency and the convergence rate of the proposed method. It is concluded that, by taking advantage of this high-quality approximation, the total number of finite-element analyses required for structural shape optimization can be reduced significantly, resulting in the same level of efficiency achieved previously in sizing problems.
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