Morphing Evolutionary Structural Optimization (MESO) is a soft-kill version of Evolutionary Structural Optimization (ESO). This paper proposes a new optimality criteria-based performance index for monitoring the optimization process of the conventional MESO method. Also, a quantitative verification of the MESO for some benchmark problems with equality constraints is presented. For some structures like Michell trusses, a qualitative verification of the ESO method has been already reflected in the literature. However, in this study, a quantitative verification of the MESO method in the shape optimization is shown by comparing the results with analytical solutions. An excellent convergence of the MESO method in stiffness, frequency and weight optimization problems with equality constraints to optimum clearly reveals that this method is a robust optimization technique, which can be easily implemented and applied to a wide range of problems.

Contact problems are one of widely used and important branches in solid mechanics. This paper aims at extending the bi-directional evolutionary structural optimization (BESO) algorithm for optimal contact shape design in structures under the multiple load cases. In this study، the gap elements between the corresponding nodes on both surfaces are used not only to model contact states but also to modify the contact profile by changing the spacing to lengthen or shorten the gap between the corresponding nodes. Using gap elements، the analysis of contact problems by finite element method is simplified and the Enormous volume of non-linear calculations is reduced. Evolutionary structural optimization (ESO) method for obtaining the optimal shape of the contact surface، through a simple process with a gradual increase over the length of inefficient gap elements، the shape of the structure will converge to an optimal design. But in this paper by using the bi-directional evolutionary optimization method، there is the Possibility of increasing and decreasing of length gap elements simultaneously and so the speed of convergence has increased. In this paper، weighted average method and stress criterion are used for evaluation of the performance of gap element in optimization algorithm and finally a uniform distribution of stress along the contact surface is obtained.

This paper presents the bidirectional evolutionary structural optimization (BESO) method for the design of two-phase composite materials with optimal properties of stiffness and thermal conductivity. The composite material is modelled by microstructures in a periodical base cell (PBC). The homogenization method is used to derive the effective bulk modulus and thermal conductivity. BESO procedures are presented to optimize the two individual properties and their various combinations. Three numerical examples are studied. The results agree well with those of the benchmark microstructures and the Hashin-Shtrikman (HS) bounds.

In many structural components, it is usually desirable to have a minimum deflection at specific points. To develop such stiff structures, different optimization methods have been employed by researchers. In this study, the Simulated Annealing (SA) method is used for maximizing the stiffness of two-dimensional structures. The effectiveness of the SA is then evaluated by comparing its results with that of the Evolutionary Structural Optimization (ESO). Three examples are presented including the square plate, the rectangular plate and the MBB beam. These examples are conducted for different loading and mesh refinement. Furthermore, to have a practical shape, the checkerboard pattern is eliminated in the optimization process. The results show that in the square plate with 3 thicknesses the solution obtained with the SA method is 7% better than the Evolutionary Structural Optimization solution. For rectangular plate, SA solution is 4% better than the ESO solution. For the MBB beam the ESO solution is about 3% better than the SA solution. However, the optimum shapes obtained from both methods are quite similar. It can be concluded that the SA is an effective method for optimizing the stiffness of 2D structures when a better accuracy is needed.

Topology optimization methods enable designers to find the best structural layout for required structural performances. Most papers in this area have been concerned with the optimization of structures with linear material. However, there are several structures involving nonlinear material.Evolutionary structural optimization (ESO) is based on the simple concept of systematically removing inefficient material from the structure after each finite element analysis, so that the resulting design is gradually evolved to an optimum. This method has been successfully applied to optimum material distribution problems for continuum structures and has been extended to a wide range of structural optimization problems.
This paper is concerned with optimization of elastic and elasto-plastic bodies, based on the von Misses stress criterion using two method.Several examples are presented to verify the proposed optimization methods. Results are compared for these two criteria and against elastic and elasto-plastic material and also with that of the adaptive method. It is concluded that for elastic and elasto-plastic bodies, the behavior of the both criteria is more or less the same and they can be used alternatively.

A two-stage optimization method is presented by employing the evolutionary structural optimization (ESO) and ant colony optimization (ACO), which is called ESO-ACO method. To implement ESO-ACO, size optimization is performed using ESO, first. Then, the outcomes of ESO are employed to enhance ACO. In optimization process, the weight of double layer grid is minimized under various constraints which artificial ground motion is used to calculate the structural responses. The presence or absence of elements in bottom and web grids and also cross-sectional areas are selected as design variables. The numerical results reveal the computational advantages and effectiveness of the proposed method.

Reliability and optimization are two key elements for structural design. The reliability-based topology optimization (RBTO) is a powerful and promising methodology for finding the optimum topologies with the uncertainties. In this paper, the particle swarm algorithm (PSO) using performance measure approach (PMA) is proposed in the RBTO procedure. Conventionally, the approximate limit state function along with the most probable point (MPP) search algorithms is used for calculation the reliability index. On the other hand, the choice of penalty function for having a convergent search plays a critical role. In addition one does not need to use approximate limit state function and calculating the derivatives of limit state function with respect to random variables. Furthermore, the convergence problem of the MPP search algorithms for complicated limit state functions does not exist. This paper presents RBTO using bi-directional evolutionary structural optimization (BESO) with an improved filter scheme. The topologies obtained by RBTO are compared with that of obtained by deterministic topology optimization (DTO). Results of the RBTO using PSO show that PSO can be effectively applied to RBTO and its use is quite simple.

Recently, some researchers proposed a new algorithm for the bidirectional evolutionary structural optimization (BESO) in which adding and removing of elements is controlled by a signal parameter of removal ratio of volume (or weight). Nevertheless, their BESO improvement suffers from some restrictions like premature stopping of the iterative process due to the closeness of the adding and removing coefficients. In this study, the BESO method is modified such that eliminates the previous restrictions and increase its efficiency significantly. Several examples are presented for structural optimization of a plate in two states of elastic and elastoplastic with stiffness and stress criteria. From the three examples, one can conclude that the modified BESO algorithm is more robust than the ESO and BESO algorithm previously proposed. It is also concluded the maximum stress and the performance index are improved in comparison with the case when the signal parameter is the same. Overall, the proposed modification prevent the premature termination of the optimization process when the optimization process is based on the hard kill method with both adding and removing the elements.

In this paper, the bi-directional evolutionary structural optimization (BESO) method is used to find optimal layouts of 3D prestressed concrete beams. Considering the element sensitivity number as the design variable, the mathematical formulation of topology optimization is developed based on the ABAQUS finite element software package. The surface-to-surface contact with a small sliding between concrete and prestressing steels is assumed to accurately model the prestressing effects. The concrete constitutive model used is the concrete damaged plasticity (CDP) model in ABAQUS. The integration of the optimization algorithm and finite element analysis (FEA) tools is done by using the ABAQUS scripting interface. A pretensioned prestressed simply supported beam is modeled to show capabilities of the proposed method in finding optimal topologies of prestressed concrete beams. Many issues relating to topology optimization of prestressed concrete beams such as the effects of prestressing stress, geometrical discontinuities and height constraints on optimal designs and strut-and-tie models (STMs) are studied in the example. The results show that the proposed method can efficiently be used for layout optimization of prestressed concrete beams.

In this paper, the reliability based design optimization of columns under buckling load is investigated using evolutionary structural optimization. To determine the reliability index, the Hasofer-Lind method is employed and results are compared with the Monte Carlo method. The standard response surface method with central composite design is used to estimate the limit state function. An optimization algorithm for optimal design of columns against buckling with different cross-sections and boundary conditions is presented while keeping the column weight constant.The Taguchi method is used to provide the most suitable levels of the design variables. Then by introducing reliability constraints into the algorithm, the optimized shape of the column under buckling load based on reliability is obtained. Optimized design obtained from Deterministic Optimization (DO) and Reliability Based Design Optimization (RBDO) are compared. Numerical examples show that maximum buckling load capacity is increased compared to the initial uniform design and also RBDO model is more reliable than DO.