International Journal of Optimization in Civil Engineering
Volume:5 Issue: 4, Autumn 2015

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.

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.

This study presents shape optimization of a gravity dam imposing stability and principal stress constraints. A gravity dam is a large scale hydraulic structure consisting of huge amount of concrete material. Hence, an optimum design gives a cost-benefit structure due to the fact that small changes in shape of dam cross-section leads to large saving of concrete volume. Three recently developed meta-heuristics are utilized for optimizing the structure. These algorithms are charged system search (CSS), colliding bodies optimization (CBO) and its enhanced edition (ECBO). This article also provides useful formulations for stability analysis of gravity dams which can be extended to further researches.

In this paper, based on maximizing the outrigger-belt truss system’s strain energy, a methodology for determining the optimum location of a flexible outrigger system is presented. Tall building structures with combined systems of framed tube, shear core, belt truss and outrigger system are modeled using continuum approach. In this approach, the framed tube system is modeled as a cantilevered beam with box cross section. The effect of outrigger and shear core systems on framed tube’s response under lateral loading is modeled by a rotational spring placed at the location of belt truss and outrigger system. Optimum location of this spring is obtained when energy absorbed by the spring is maximized. For this purpose, first derivative of the energy equation with respect to spring location as measured from base of the structure, is set to zero. Optimum location for outrigger and belt truss system is calculated for three types of lateral loadings, i.e. uniformly and triangularly distributed loads along structure’s height, and concentrated load at top of the structure. Accuracy of the proposed method is verified through numerical examples. The results show that the proposed method is reasonably accurate. In addition, for different stiffness of shear core and outrigger system, several figures are presented that can be used to determine the optimum location of belt truss and outrigger system.

This paper presents a new model updating approach for structural damage localization and quantification. Based on the Modal Assurance Criterion (MAC), a new damage-sensitive cost function is introduced by employing the main diagonal and anti-diagonal members of the calculated Generalized Flexibility Matrix (GFM) for the monitored structure and its analytical model. Then, the cost function is solved by Democratic Particle Swarm Optimization (DPSO) algorithm to achieve the optimal solution of the problem lead to damage identification. DPSO is a modified version of standard PSO algorithm which is developed for presenting a fast speed evolutionary optimization strategy. The applicability of the method is demonstrated by studying three numerical examples which consists of a ten-story shear frame, a plane steel truss and a plane steel frame. Several challenges such as the efficiency of the DPSO algorithm in comparison with other evolutionary optimization approaches for solving the inverse problem, impacts of random noise in input data on the reliability of the presented method, and effects of the number of available modal data for damage identification, are studied. The obtained results reveal good, robust and stable performance of the presented method for structural damage identification using only the first several modes’ data.

This paper introduces a methodology for considering the uncertainties in stability analysis of gravity dams. For this purpose, a conceptual model based on the fuzzy set theory and Genetic Algorithm (GA) optimization is developed to be coupled to a gravity dam analysis model. The uncertainties are represented by the fuzzy numbers and the GA is used to estimate in what extent the input uncertainties affect the dam safety factors. An example gravity dam is analyzed using the proposed approach. The results show that the crisp safety factors might be highly affected by the input uncertainties. For instance, ±10%uncertainty in the design parameters could result in about −346 to + 146 % uncertainty in the stability safety factors and −59 to + 134 % in the stress safety factor of the example dam.

In rigid plastic analysis one of the most widely applicable methods that is based on the minimum principle, is the combination of elementary mechanisms which uses the upper bound theorem. In this method a mechanism is searched which corresponds to the smallest load factor. Mathematical programming can be used to optimize this search process for simple frames, and meta-heuristic algorithms are the best choice for larger frame structures. In this paper, the Colliding Bodies Optimization (CBO) and its enhanced variant (ECBO) are employed to optimize the process of finding an upper bound for the collapse load factor of the planar frames. The efficiency of these algorithms is compared to that of the Particle Swarm Optimization (PSO) algorithm through four numerical examples form multi-bay multi-story frames and pitched roof frames.

In this paper, optimal design of hybrid low damping base isolation and magnetorheological (MR) damper has been studied. Optimal hybrid base isolation system has been designed to minimize the maximum base drift of low damping base isolation system where for solving the optimization problem, genetic algorithm (GA) has been used. In design procedure the maximum acceleration of the structure has been limited, too. To determine the volatge of semi-active MR damper the H2/LQG and clipped-optimal control algorithm has been applied. For numerical simulations, a three-story frame equipped with the hybrid base isolation and MR damper subjected to the scaled El Centro excitation and optimal hybrid system has been designed. Results of numerical simulations have proven the effectiveness of the optimal hybrid control system in controlling the maximum base drift of isolated structure. Also comparing the performance of hybrid, low and high damping base isolation systems has shown that adding MR damper to low damping base isolation system has improved its performance so that the hybrid system has worked better th an high damping base isolation in reducing the maximum base drift. Testing optimal hybrid control system under different excitations has shown its efficiency.

The present paper tackles the optimization problem of double layer grids considering nonlinear behaviour. In this paper, an efficient optimization algorithm is proposed to achieve the optimization task based on the newly developed grey wolf algorithm (GWA) termed as sequential GWA (SGWA). In the framework of SGWA, a sequence of optimization processes is implemented in which the initial population of each process is selected from the neighboring region of the best design found in the previous optimization process. This procedure is repeated until a termination criterion is met. Two illustrative examples are presented and optimization is performed by GWA and SGWA and two other meta-heuristics. The numerical results indicate that the proposed SGWA utperforms the other algorithms in finding optimal design of nonlinear double layer grids.