Problems of parametric optimization of rod structure stated in terms of the nonlinear programming problem are considered. Use is made of the method of projection of the gradient of the cost function onto the surface of active constraints while eliminating the residuals in the violated constraints. The equivalent Householder transformations are proposed for the governing equations of the optimization method. They ensure the computational efficiency of the algorithm based on the gradient method. In addition, the equivalent Givens transformations are also proposed for solving the equations of the method. They ensure, in the cases described in this article, the acceleration of the iterative process by reducing the amount of computation. The reliability of the optimal solutions obtained using the proposed modification of the gradient method is confirmed by comparing the results of optimization of rod systems. The efficiency of the proposed improvement of the optimization method is also confirmed by the obtained absolute values of the maximum residuals in the constraints in a small number of iterations.
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Translated from Prikladnaya Mekhanika, Vol. 57, No. 4, pp. 78–95, July–August 2021.
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Peleshko, I.D., Yurchenko, V.V. Parametric Optimization of Metal Rod Structures Using the Modified Gradient Projection Method. Int Appl Mech 57, 440–454 (2021). https://doi.org/10.1007/s10778-021-01096-0
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DOI: https://doi.org/10.1007/s10778-021-01096-0