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This paper aims to introduce topology optimization as a robust tool for damage detection in plane stress structures. Two objective functions based on natural frequencies and shape modes of the structure are defined to minimize discrepancy between dynamic specifications of the real damaged structure and the updating model. Damage area is assumed as a porous material where amount of porosity signifies the damage intensity. To achieve this, Solid Isotropic Material with Penalization (SIMP) model is employed. Sensitivity analysis is achieved and a mathematical based method is used for solving the optimization problems. In order to demonstrate efficiency and robustness of the method to identify various type of damages in terms of both location and intensity, several numerical examples are presented and the results are discussed.

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In this paper, topology optimization (TO) is applied to determine the form, size and location of holes for the special form of perforated steel plate shear wall (PSPSW). The proposed model is based on the recently presented particular form of PSPSW that is called the ring-shaped steel plate shear wall. The strain energy is selected as the objective function in the optimization. Simple Isotropic Material with Penalization (SIMP) method and the solution algorithms, including sensitivity and condition-based methods are utilized in the TO. Four initial plate forms are presented in the TO with regards to the length of the connection between the plate and column. Based on the solution methods and initial forms of the plate, eight scenarios are proposed and seven different perforated plates obtained using TO. The nonlinear responses of the optimized perforated plates are compared together, and with the ring-shaped model as a benchmark. The nonlinear analysis is conducted under cyclic and monotonic loadings. Key issues include cyclic and monotonic behavior, pinching behavior, stiffness, load-carrying capacity, energy dissipation, fracture tendency and out-of-plane deformation are investigated and discussed. The results demonstrate the optimized models have better behavior than the ring-shaped model without changing the volume of the plate.

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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.

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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.

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This research focuses on the effects of stiffeners and architectural opening on the steel shear wall topology optimization. To this aim, four relevant issues have been considered. The first issue is the optimality Pattern of the shear wall without stiffeners. The second is the Optimality Pattern of the shear wall with stiffeners in two directions. The third is the investigation on the topology optimization of the shear walls with fixed opening and the fourth is the multi-material topology optimization of the above issues. In the optimize process, the level set method based on the shape sensitivity and the finite element analysis for two-dimensional linear elastic problems has been used. The level set function implicitly indicated the boundaries of the design domain. Several numerical examples are used to demonstrate the optimal paths in the steel shear walls. The results show that optimal values have been changed by replacing stiffeners and creating openings in the wall, but the optimal topologies almost have a shape like a concentric bracing. Also, in the conventional shear walls (one material) the horizontal stiffeners have a significant effect on their performance.

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The present study proposes a hybrid of the piecewise constant level set (PCLS) method and isogeometric analysis (IGA) approach for structural topology optimization. In the proposed hybrid method, the discontinuities of PCLS functions is used in order to present the geometrical boundary of structure. Additive Operator Splitting (AOS) scheme is also considered for solving the Lagrange equations in the optimization problem subjected to some constraints. For reducing the computational cost of the PCLS method, the Merriman–Bence–Osher (MBO) type of projection scheme is applied. In the optimization process, the geometry of structures is described using the Non–Uniform Rational B–Splines (NURBS)–based IGA instead of the conventional finite element method (FEM). The numerical examples illustrate the efficiency of the PCLS method with IGA in the efficiency, convergence and accuracy compared with the other level set methods (LSMs) in the framework of 2–D structural topology optimization. The results of the topology optimization reveal that the proposed method can obtain the same topology in lower number of convergence iteration.

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An efficient method is proposed by using time domain responses and topology optimization to identify the location and severity of damages in two-dimensional structures under plane stress assumption. Damage is assumed in the form of material density reduction in the finite element model of the structure. The time domain responses utilized here, are the nodal accelerations measured at certain points of the structure. The responses are obtained by the Newmark method and contaminated with uniformly random noise in order to simulate real conditions. Damage indicators are extracted from the time domain responses by using Singular Value Decomposition (SVD). The problem of damage detection is presented as a topology optimization problem and the Solid Isotropic Material with Penalization (SIMP) method is used for appropriate damage modeling. The objective function is formed based on the difference of singular values of the Hankel matrix for responses of real structure and the analytical model. In order to evaluate the correctness of the proposed method, some numerical examples are examined. The results indicate efficiency of the proposed method in structural damage detection and its parameters such as resampling length in SVD, penalty factor in the SIMP method and number and location of sensors are effective parameters for improving the results.

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In this article, topology optimization of two-dimensional (2D) building frames subjected to seismic loading is performed using the polygonal finite element method. Artificial ground motion accelerograms compatible with the design response spectrum of ASCE 7-16 are generated for the response history dynamic analysis needed in the optimization. The mean compliance of structure is minimized as a typical objective function under the material volume fraction constraint. Also, the adjoint method is employed for the sensitivity analysis evaluated in terms of spatial and time discretization. The ground structures are 2D continua taking the main structural components (columns and beams) as passive regions (solid) to render planar frames with additional components. Hence, building frames with different aspect ratios are considered to assess the usefulness of the additional structural components when applying the earthquake ground motions. Furthermore, final results are obtained for different ground motions to investigate the effects of ground motion variability on the optimized topologies.
 

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Structural topology optimization provides an insight into efficient designing as it seeks optimal distribution of material to minimize the total cost and weight of the structures. This paper presents an optimum design of steel moment frames and connections of structures subjected to serviceability and strength constraints in accordance with AISC-Load and Resistance Factor Design (LRFD). In connection topology optimizations, different beam and column sections and connections and also to optimize two steel moment frames a genetic algorithm was used and their performance was compared. Initially, two common steel moment frames were studied, only for the purpose of minimizing the weight of the structure and the members of structure are considered as design variables. Since the cost of a steel moment frame is not solely related to the weight of the structure, in order to obtain a realistic plan, in the second part of this study, for the other two frames the cost of the connections is also added to the variables. The results indicate that the steel frame optimization by applying real genetic algorithm could be optimal for structural designing. The findings highlighted the prominent performance and lower costs of the steel moment frames when different connections are used.
 

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During the process of continuum topology optimization some pattern discontinuities may arise. It is an important challenge to overcome such irregularities in order to achieve or interpret the true optimal layout. The present work offers an efficient algorithm based on graph theoretical approach regarding density priorities. The developed method can recognize and handle solid continuous regions in a pre-optimized media. An illustrative example shows how the proposed priority guided trees can successfully distinguish the most crucial parts of the continuum during topology optimization.