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In this paper the step by step descent algorithm is extended to continuous optimization problems and applied to the optimal sizing of truss structures. The step by step descent method, recently developed, was applied to the discrete optimization of rigid structures. To solve continuous problems, a multi-stage optimization algorithm is proposed, which involves implementing the step by step descent method in multiple stages. In each stage, the continuous areas of the variables are progressively divided into a finite number of points. The algorithm is based on the search for the steepest gradient descent direction that minimizes the cost function and employs a wise heuristic approach to bypassing local optima. To evaluate the algorithm's performance, a study was carried out on ten mathematical and four truss optimization problems. For unconstrained mathematical problems, the algorithm demonstrates quick converges to optimum solution from any starting point. For truss structures, the starting design point is selected based on structural knowledge to enhance convergence speed. The obtained results surpass those achieved by other state-of-the-art optimization algorithms, affirming the efficiency, robustness and the promptness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a semi-analytic solution for multiple cracks beneath a half-space surface under elastohydrodynamic lubrication (EHL) contact. The solution not only takes into account the fluid-structure interactions in the EHL contact but also the interactions among all the cracks. In developing the governing equation, each crack of mixed modes I and II is modeled as a continuous distribution of climb and glide dislocations with unknown densities. With such a treatment, the original problem for materials with multiple cracks is converted into two subproblems: a homogeneous EHL contact problem with the fluid pressure distribution and the lubricant film thickness to be determined, and a half-space problem with unknown dislocation densities, which are iteratively obtained by a modified conjugate gradient method. A numerical algorithm is developed to integrate the two problems. The computational process is performed until the convergence of the displacements, which are the sum of the displacements due to the fluid pressure and the subsurface cracks. Sample cases are presented to analyze the pressure and lubricant film thickness profiles of EHL contact and the subsurface stresses for cracked materials. [ABSTRACT FROM AUTHOR]