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In this paper, for topology optimization of double layer grids, an efficient optimization method is presented by combination of Imperialist Competitive Algorithm (ICA) and Gravitational Search Algorithm (GSA) which is called ICA-GSA method. The present hybrid method is based on ICA but the moving of countries toward their relevant imperialist is done using the law of gravity of GSA. In topology optimization process, the weight of the structure is minimized subjected to displacements of joints, internal stress and slenderness ratio of members constraints. Through numerical example, topology optimization of a typical large-scale double layer grid is obtained by ICA, GSA and ICA-GSA methods. The numerical results indicate that the proposed algorithm, ICA-GSA, executes better than ICA, GSA and the other methods presented in the literatures for topology optimization of largescale skeletal structures.

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In this paper the piecewise level set method is combined with phase field method to solve the shape and topology optimization problem. First, the optimization problem is formed based on piecewise constant level set method then is updated using the energy term of phase field equations. The resulting diffusion equation which updates the level set function and optimization problem is solved through finite element method. The proposed method enhances the convergence rate and solution efficiency. Various two-dimensional examples are solved to verify the performance of proposed method.

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This study has been inspired by the paper "An efficient 3D topology optimization code written in MATLAB” written by Liu and Tovar (2014) demonstrating that SIMP-based three-dimensional (3D) topology optimization of continuum structures can be implemented in 169 lines of MATLAB code. Based on the above paper, we show here that, by simple and easy-to-understand modifications we get a few lines longer code, which is able to solve robust topology optimization problems with uncertain load directions. In the presented worst load direction oriented approach, the varying load directions are handled by quadratic constrains, which describe spherical regions about the nominal loads. The result of the optimization is a robust compliance-minimal volume constrained design, which is invariant to the investigated directional uncertainty. The key element of the robustification is a worstload-direction searching process, which is formulated as a small quadratic programming problem with quadratic constraints. The presented approach is a 3D extension of the robust approach originally developed by Csébfalvi (2014) for 2D continuum structures. In order to demonstrate the viability and efficiency of the extension, we present the model and algorithm with detailed benchmark results for robust topology optimization of 3D continuum structures. It will be demonstrated that the computational cost of the robustification is comparable with its deterministic equivalent because its central element is a standard 3D deterministic multi-load structure optimization problem and the worst-loaddirection searching process is formulated as a significantly smaller quadratically constrained quadratic programming problem, which can be solved efficiently by several different ways.

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The Isogeometric Analysis (IA) is utilized for structural topology optimization  considering minimization of weight and local stress constraints. For this purpose, material density of the structure  is  assumed  as  a  continuous  function  throughout  the  design  domain  and approximated using the Non-Uniform Rational B-Spline (NURBS) basis functions. Control points of the density surface are considered as design variables of the optimization problem that can change the topology during the optimization process. For initial design, weight and stresses of the structure are obtained based on full material density over the design domain. The  Method  of  Moving  Asymptotes  (MMA)  is  employed  for  optimization  algorithm. Derivatives of the objective function and constraints with respect to the design variables are determined  through  a  direct  sensitivity  analysis.  In  order  to  avoid  singularity  a  relaxation technique  is  used  for  calculating  stress  constraints.  A  few  examples  are  presented  to demonstrate the performance of the method. It is shown that using the IA method and an appropriate stress relaxation technique can lead to reasonable optimum layouts.