Structural Reliability Assessment Based on the Improved Constrained Differential Evolution Algorithm

In this work, the reliability analysis is employed to take into account the uncertainties in a structure. Reliability analysis is a tool to compute the probability of failure corresponding to a given failure mode. In this study, one of the most commonly used reliability analysis method namely first order reliability method is used to calculate the probability of failure. Since finding the most probable point (MPP) or design point is a constrained optimization problem, in contrast to all the previous studies based on the penalty function method or the preference of the feasible solutions technique, in this study one of the latest versions of the differential evolution metaheuristic algorithm named improved (μ+λ)-constrained differential evolution (ICDE) based on the multi-objective constraint-handling technique is utilized. The ICDE is very easy to implement because there is no need to the time-consuming task of fine tuning of the penalty parameters. Several test problems are used to verify the accuracy and efficiency of the ICDE. The statistical comparisons revealed that the performance of ICDE is better than or comparable with the other considered methods. Also, it shows acceptable convergence rate in the process of finding the design point. According to the results and easier implementation of ICDE, it can be expected that the proposed method would become a robust alternative to the penalty function based methods for the reliability assessment problems in the future works

Robust Topology Optimization under Load and Geometry Uncertainties by Using New Sparse Grid Collocation Method

In this paper, a robust topology optimization method presents that insensitive to the uncertainty in geometry and applied load. Geometric uncertainty can be introduced in the manufacturing variability. Applied load uncertainty is occurring in magnitude and angle of force. These uncertainties can be modeled as a random field. A memory-less transformation of random fields used to random variation modeling. The Adaptive Sparse Grid Collocation (ASGC) method combined with the uncertainty models provides robust designs by utilizing already developed deterministic solvers. The proposed algorithm provides a computationally cheap alternative to previously introduced stochastic optimization methods based on Monte Carlo sampling by using the adaptive sparse grid method. Numerical examples, such as a 2D simply supported beam and cantilever beam as benchmark problems, are used to show the effectiveness and superiority of the ASGC method

Multi Objective Particle Swarm Optimization (MOPSO) for Size and Shape Optimization of 2D Truss Structures

This paper covers optimization techniques for trusses to find the most efficient cross sections and configuration of joints. The improvement will be achieved by applying changes in one or both of these parameters. Objective functions for optimization are weight and the deflection of the truss’s joints. For optimization of both weight and deflection the MOPSO method is used. This is a powerful method that enables the optimization of huge trusses. The former methods for optimization of the shape or size of the trusses, was done separately and as a single objective while this paper covers a new way via multi objective methods. For proofing the ability of the represented method in this paper, some standard examples are compared. The comparison of the results shows good accuracy and desirable verity of pareto front

Topology Optimization Under Uncertainty by Using the New Collocation Method

In this paper, a robust topology optimization method presents that insensitive to the uncertainty in geometry. Geometric uncertainty can be introduced in the manufacturing variability. This uncertainty can be modeled as a random field. A memory-less transformation of random fields used to random variation modeling. The Adaptive Sparse Grid Collocation (ASGC) method combined with the geometry uncertainty models provides robust designs by utilizing already developed deterministic solvers. The proposed algorithm provides a computationally cheap alternative to previously introduced stochastic optimization methods based on Monte Carlo sampling by using the adaptive sparse grid method. The method is demonstrated in the design of a minimum compliance Messerschmitt-Bölkow-Blohm (MBB) and cantilever beam as benchmark problems

Topology optimization of continuum structures under geometric uncertainty using a new extended finite element method

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.In this article, robust topology optimization under geometric uncertainty is proposed. The design domain is discretized by an extended finite element method. A bi-directional evolutionary structural optimization carries out the optimization process. The performance of the proposed method is compared with the Monte Carlo, solid isotropic material with penalization, perturbation and non-intrusive polynomial chaos expansion methods. The novelty of the present method lies in the following three aspects: (1) this article is among the first to use the extended finite element method in studying the topology optimization under uncertainty; (2) by adopting the extended finite element method for boundary elements in the finite element framework, there is no need for any remeshing techniques; and (3) the numerical results show that the present method has a smoother boundary region and minimum value of the mean and standard deviation of compliance than the other methods, in particular mesh size

Shaping and Sizing-Shaping Optimization of Truss Structures via Triangular Optimizer Algorithm (TOA) Optimization Method

In this article, triangular optimizer algorithm optimization method is presented for minimizing the weight of the truss structures. Triangular optimizer algorithm is a new metaheuristic method which is inspired of triangle. In this method, the initial vector of design variables is considered as the base of the triangle (first row). Then the objective functions are calculated and the best and the worst response are identified. The worst response is removed from the current population and the remaining population after some modifications is defined the second row. This process continues till reaching the apex of triangle, the optimal solution of this triangle. In the second iteration (second triangle), a certain number of the initial design variables are retrieved by the optimal solution of the previous triangle and the remaining of this population are created in the initial interval for escape from local optimums. So base of the second optimal triangle is formed. Then the mentioned algorithm is performed until optimum response of second triangle is achieved. These operations are continued until the convergence condition being satisfied. To prove the capabilities of the proposed algorithm shaping and sizing-shaping optimization of four truss structures are considered. The obtained statistical results of truss structures optimization show that the TOA is able to managed to achieve better optimal solutions compared to different optimization techniques

Optimal Path Planning of Suspended Cable Robot by Polynomial Interpolation of Four Degree and Triangular Optimizer Algorithm

The purpose of this article is finding the optimal path with minimum effort to move the end-effector of the three cable spatial robot in work space. For this work, first, kinematic and dynamic modeling is done of the three cable spatial robot. Then simulation and results extraction are done by both direct and indirect methods. Based on of indirect solution method is the calculus of variations. Optimality necessary condition is given in order to minimize the torque between the two points and is extracted using the pontryagin minimum principle. This optimality condition is formed a boundary value problem of two-point, which can be solved using numerical algorithms. Direct method is created by combining a metaheuristic optimization method, a polynomial interpolation and the robot equations. This article is used the metaheuristic method of triangular optimizer algorithm and the polynomial interpolation of four degree. This new combination created with the polynomial of four degree, instead of using the intermediate values of the path as design variables, specified constants of polynomial puts the design variable in order to path optimization. The indirect method gives the exact response, but extraction of optimality condition its, is the difficult in terms of calculations mathematical. While the direct method gives the approximate response without algebraic calculations. Finally, two examples are done with direct method and indirect method. The results comparisons are show the appropriate efficiency of the suggested direct method