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This paper proposes an effective algorithm based on the level set method (LSM) to solve shape and topology optimization problems. Since the conventional LSM has several limitations, a binary level set method (BLSM) is used instead. In the BLSM, the level set function can only take 1 and -1 values at convergence. Thus, it is related to phase-field methods. We don’t need to solve the Hamilton-Jacobi equation, so it is free of the CFL condition and the reinitialization scheme. This favorable properties lead to a great time advantage in this method. In this paper, the BLSM is implemented with the additive operator splitting (AOS) scheme and several numerical issues of the implementation are discussed. The proposed scheme is much more efficient than the conventional level set method. Several 2D examples are presented which demonstrate the effectiveness and robustness of the proposed method.

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Tuned mass dampers (TMDs) systems are one of the vibration controlled devices used to reduce the response of buildings subject to lateral loadings such as wind and earthquake loadings. Although TMDs system has received much attention from researchers due to their simplicity, the optimization of properties and placement of TMDs is a challenging task. Most research studies consider optimization of TMDs properties. However, the placement of TMDs in a building is also important. This paper considers optimum placement as well as properties of TMDs. Genetic algorithms (GAs) is used to optimize the location and properties of TMDs. Because the location of TMDs at a particular floor of a building is a discrete number, it is represented by binary coded genetic algorithm (BCGA), whereas the properties of TMDS are best suited to be represented by using real coded genetic algorithm (RCGA). The combination of these optimization tools represents a hybrid coded genetic algorithm (HCGA) that optimizes discrete and real values of design variables in one arrangement. It is shown that the optimization tool presented in this paper is stable and has the ability to explore an unknown domain of interest of the design variables, especially in the case of real coding parts. The simulation of the optimized TMDs subject to earthquake ground accelerations shows that the present approaches are comparable and/or outperform the available methods.

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This paper presents the topology optimization of plane structures using a binary level set (BLS) approach and isogeometric analysis (IGA). In the standard level set method, the domain boundary is descripted as an isocountour of a scalar function of a higher dimensionality. The evolution of this boundary is governed by Hamilton–Jacobi equation. In the BLS method, the interfaces of subdomains are implicitly represented by the discontinuities of BLS functions taking two values 1 or −1. The subdomains interfaces are represented by discontinuities of these functions. Using a two–phase approximation and the BLS approach the original structural optimization problem is reformulated as an equivalent constrained optimization problem in terms of this level set function. For solving drawbacks of the conventional finite element method (FEM), IGA based on a Non–Uniform Rational B–Splines (NURBS) is adopted to describe the field variables as the geometry of the domain. For this purpose, the B–Spline functions are utilized as the shape functions of FEM for analysis of structure and the control points are considered the same role with nodes in FEM. Three benchmark examples are presented to investigate the performance the topology optimization based on the proposed method. Numerical results demonstrate that the BLS method with IGA can be utilized in this field.