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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]

In this paper a new graph-based evolutionary algorithm, gM-PAES, is proposed in order to solve the complex problem of truss layout multi-objective optimization. In this algorithm a graph-based genotype is employed as a modified version of Memetic Pareto Archive Evolution Strategy (M-PAES), a well-known hybrid multi-objective optimization algorithm, and consequently, new graph-based crossover and mutation operators perform as the solution generation tools in this algorithm. The genetic operators are designed in a way that helps the multi-objective optimizer to cover all parts of the true Pareto front in this specific problem. In the optimization process of the proposed algorithm, the local search part of gM-PAES is controlled adaptively in order to reduce the required computational effort and enhance its performance. In the last part of the paper, four numeric examples are presented to demonstrate the performance of the proposed algorithm. Results show that the proposed algorithm has great ability in producing a set of solutions which cover all parts of the true Pareto front. [ABSTRACT FROM AUTHOR]

In this paper, the constitutive relations of the finite element method are constructed and used for solving two- and three-dimensional problems of the asymmetric theory of elasticity. Different variants of finite elements are considered. The numerical experiments are carried out to evaluate the reliability and computational efficiency of the finite element algorithm based on the comparison between the numerical and analytical solutions, numerical estimation of the convergence and checking of the degree of accuracy, to which the natural boundary conditions are satisfied. The obtained solutions to the two- and three-dimensional problems are interpreted from the viewpoint of their applicability to a design of experiments capable of revealing the facts of couple-stress effects in material under elastic deformation and identification of material constants for the asymmetric theory of elasticity. The capabilities of the finite element algorithm to interpret experimental data and estimate the errors occurring in real experiments have been tested by solving several example problems. [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]

In this work, mathematical models of physically nonlinear plates and beams made from multimodulus materials are constructed. Our considerations are based on the 3D deformation theory of plasticity, the von Mises plasticity criterion and the method of variable parameters of the theory of elasticity developed by Birger. The proposed theory and computational algorithm enable for solving problems of three types of boundary conditions, edge conditions and arbitrary lateral load distribution. The problem is solved by the finite element method (FEM), and its convergence and the reliability of the results are investigated. Based on numerical experiments, the influence of multimodulus characteristics of the material of the beam and the plate on their stress–strain states under the action of transverse loads is illustrated and discussed. [ABSTRACT FROM AUTHOR]