For reliability-based topology optimization (RBTO) of double layer grids, a two-stage optimization method is presented by applying" Solid Isotropic Material with Penalization "and" Ant Colony Optimization" (Simp-ACO method). To achieve this aim, first, the structural stiffness is maximized using Simp. Then, the characteristics of the obtained topology are used to enhance ACO through six modifications. As numerical examples, reliability-based topology designs of typical double layer grids are obtained by ACO and Simp-ACO methods. Their numerical results reveal the effectiveness of the proposed SimpACO method for the RBTO of double layer grids.

The Simp approach is one of the most frequently used methods for topology optimization of structures. In this method, the relative density is expressed as a function of coordinates and varies from 0 to 1 within the design domain. Relative densities of 0 and 1 are associated to the existence and nonexistence of the material, respectively. The finite element approach is usually utilized to analyze the problem while considering a constant relative density within each element. As a result, relative densities of the elements are assumed as the design variables. A common deficiency of such an approach is the introduction of the so-called checkerboard pattern, which is an indication of numerical instability. In this paper, a new algorithm is proposed to overcome this source of instability which is based on the concept of stress and strain smoothing. Benchmarks and practical problems are simulated and discussed in order to verify the proposed approach and to assess its performance.

This paper focuses on reducing stress concentration in a plate with a hole. For this purpose, a novel Reliever Topological Material Elimination (RTME) approach was introduced which uses the topology optimization technique to specify the best areas to remove material in order to refine flow of stress and reduce the Stress Concentration Factor (SCF), consequently. Using the Solid Isotropic Material with Penalization (Simp) method, topology optimization was formulated. Three major elimination areas were determined from material elimination patterns observed in topology optimization. Two possible RTME cases were proposed numerically. To evaluate the efficiency of the method, finite element analyses were conducted for one previous technique and the results werediscussed. In addition, the results of finite element analysis were validated by some experimental tests. According to the final results, RTME approach gives up to 35. 5% stress reduction, 44% SCF mitigation, and decrease about 28% of the initial volume. In comparison with the previous technique, using RTME is more effective in decreasing the SCF and weight of the plate, simultaneously.

The best usage of water resources must be considered as the main axis of agricultural progress. Sprinkler irrigation systems having high application efficiency may be considered to be a safe way in the direction of the best usage of water resources. In order to reach the above mentioned goal, one has to be creation about their performance in the field. The valuation of irrigation of farms is the analysis of any irrigation system which is based on measurements made in the real conditions of the fields and under the normal condition of work. Irrigation systems may or may not be well designed and properly used. The technique for system evaluation described in this study is designed for evaluation actual operation and management and for determining the potential for more economical and efficient operation. This study based on climatic condition, management, soil, and irrigation system were selected in 12 projects in Khorasan Province of Iran. At part of efficiency irrigation used from three parameters such as AE (application efficiency), AELQ (application efficiency of low quarter) and PELQ (potential application efficiency of low quarter).The minimum amount of PELQ at farm of BFV was 45% and maximum amount at THK farm was equal to 67%. Also, in this we’ve evaluated distribution uniformity coefficients like (CU, DU). Minimum distribution uniformity was related to THK farm and it’s maximum was related to MBV farm equal to 75 and 53%. One of the main reasons for low distribution uniformity is existence of wind at area and carelessness at designing. However, all results show that at executed system, maximum irrigation efficiency is 67% which have had en numerous differences with ideal efficiency (75%), so we should be more careful about drawing procedure, efficiency and exploitation management process.

Keeping the eigenfrequencies of a structure away from the external excitation frequencies is one of the main goals in the design of vibrating structures in order to avoid risk of resonance. This paper is devoted to the topological design of freely vibrating continuum structures with the aim of maximizing the fundamental eigenfrequency. Since in the process of topology optimization some areas of domain can potentially be removed, it is quite possible to encounter the problem of localized modes. Hence, the modified Solid Isotropic Material with Penalization (Simp) model is here used to avoid artificial modes in low density areas. As during the optimization process, the first natural frequency increases, it may become close to the second natural frequency. Due to lack of the usual differentiability of the multiple eigenfrequencies, their sensitivity are calculated by the mathematical perturbation analysis. The optimization problem is formulated by a variable bound formulation and it is solved by the Method of Moving Asymptotes (MMA). Two dimensional plane elasticity problems with different sets of boundary conditions and attachment of a concentrated nonstructural mass are considered. Numerical results show the validity and supremacy of this approach.

In this paper, we first obtain two weighted identities for twice partially differentiablemappings. Moreover, utilizing these equalities, we establish the weighted Herrmite-Hadamard typeinequalities and weighted Simpson type inequalities for co-ordinated convex functions in a rectangle from the plane R2, respectivelly. The results given in this paper provide generalizations of someresult established in earlier works.

In this article, MMA which is a mathematical programing method is utilized for solving truss optimization problem. Although this method has been widely used in topology optimization problems of continuous structures, it has received less attention in the case of truss structures. The optimization problem considered here is the problem of minimizing the strain energy of the structure by considering the volume constraint. For the first time, the basics of the Simp method and the application of the penalty exponent of the density function have been used for simultaneous optimization of topology and size of the truss members.To solve the optimization problem, analytical sensitivity analysis has been performed. Various problems have been solved at the end of the paper and the results have been discussed. The results show that if the appropriate penalty exponent is chosen, the correct optimal solution is obtained for the benchmark problems. Also, some more practical problems have been solved and the results have been discussed.

This paper presents an improved approach for handling stress constraints in minimum weight topological design. The Finite Element Method (FEM) and the material model of Solid Isotropic Material with Penalization (Simp) are used to formulate the topology optimization problem. To evaluate the stress values in elements, the von Mises stresses are calculated at the so called super-convergent Gauss quadrature points. To reduce the time and computational cost, a clustering approach is here adopted and the P -norm integrated stress constraints are used. Doing this, a large number of local constraints are replaced with a few global ones and consequently the stress constraint sensitivities are calculated by using the adjoint method. The employed formulation as well as a complete explanation of the sensitivity analysis is provided. Due to the complexity of the topology optimization problem in the presence of stress constraints, the Method of Moving Asymptotes (MMA) is here employed. To demonstrate the performance and capability of the procedure, a couple of plane stress elasticity problems are taken into consideration. The resulted layouts indicate the superiority of the approach in generating acceptable and practical topological designs.

In this paper, topology optimization is utilized for damage detection in three dimensional elasticity problems. In addition, two mode expansion techniques are used to derive unknown modal data from measured data identified by installed sensors. Damages in the model are assumed as reduction of mass and stiffness in the discretized finite elements. The Solid Isotropic Material with Penalization (Simp) method is used for parameterizing topology of the structure. Difference between mode shapes of the model and real structure is minimized via a mathematical based algorithm. Analytical sensitivity analysis is performed to obtain derivatives of objective function with respect to the design variables. In order to illustrate the accuracy of the proposed method, four numerical examples are presented.