• Structural Engineering and Mechanics
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• v.72 no.2
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• pp.181-190
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• 2019

Topology optimization of structures seeking the best distribution of mass in a design space to improve the structural performance and reduce the weight of a structure is one of the most comprehensive issues in the field of structural optimization. In addition to structures stiffness as the most common objective function, frequency optimization is of great importance in variety of applications too. In this paper, an efficient multi-objective Bi-directional Evolutionary Structural Optimization (BESO) method is developed for topology optimization of frequency and stiffness in continuum structures simultaneously. A software package including a Matlab code and Abaqus FE solver has been created for the numerical implementation of multi-objective BESO utilizing the weighted function method. At the same time, by considering the weaknesses of the optimized structure in single-objective optimizations for stiffness or frequency problems, slight modifications have been done on the numerical algorithm of developed multi-objective BESO in order to overcome challenges due to artificial localized modes, checker boarding and geometrical symmetry constraint during the progressive iterations of optimization. Numerical results show that the proposed Multiobjective BESO method is efficient and optimal solutions can be obtained for continuum structures based on an existent finite element model of the structures.

• Structural Engineering and Mechanics
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• v.70 no.2
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• pp.221-231
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• 2019

This paper performs for the first time a simultaneous optimization for members sections along with semi-rigid beam-to-column connections for space steel frames with fixed, semi-rigid, and hinged bases using a biogeography-based optimization algorithm (BBO) and a genetic algorithm (GA). Furthermore, a member's sections optimization for a fully fixed space frame is carried out. A real and accurate simulation of semi-rigid connection behavior is considered in this study, where the semi-rigid base connections are simulated using Kanvinde and Grilli (2012) nonlinear model, which considers deformations in different base connection components under the applied loads, while beam-to-column connections are modeled using the familiar Frye and Morris (1975) nonlinear polynomial model. Moreover, the $P-{\Delta}$ effect and geometric nonlinearity are considered. AISC-LRFD (2016) specification constraints of the stress and displacement are considered as well as section size fitting constraints. The optimization is applied to two benchmark space frame examples to inspect the effect of semi-rigidity on frame weight and drift using BBO and GA algorithms.

• Structural Engineering and Mechanics
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• v.81 no.3
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• pp.267-280
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• 2022

Multiscale structure has attracted significant interest due to its high stiffness/strength to weight ratios and multifunctional performance. However, most of the existing concurrent topology optimization works are carried out under deterministic load conditions. Hence, this paper proposes a robust concurrent topology optimization method based on the bidirectional evolutionary structural optimization (BESO) method for the design of structures composed of periodic microstructures subjected to uncertain dynamic loads. The robust objective function is defined as the weighted sum of the mean and standard deviation of the module of dynamic structural compliance with constraints are imposed to both macro- and microscale structure volume fractions. The polynomial chaos expansion (PCE) method is used to quantify and propagate load uncertainty to evaluate the objective function. The effective properties of microstructure is evaluated by the numerical homogenization method. To release the computation burden, the decoupled sensitivity analysis method is proposed for microscale design variables. The proposed method is a non-intrusive method, and it can be conveniently extended to many topology optimization problems with other distributions. Several numerical examples are used to validate the effectiveness of the proposed robust concurrent topology optimization method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.271-278
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• 2002

Structural optimization using improved higer-order convex approximation is proposed in this paper. The proposed method is a generalization of the convex approximation method. The order of the approximation function for each constraint is automatically adjusted in the optimization process. And also the order of each design variable is differently adjusted. This self-adjusted capability makes the approximate constraint values conservative enough to maintain the optimum design point of the approximate problem in feasible region. The efficiency of proposed algorithm, compared with conventional algorithm is successfully demonstrated in the Three-bar Truss example.

• Structural Engineering and Mechanics
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• v.47 no.2
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• pp.209-225
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• 2013

A procedure employing a Teaching-Learning Based Optimization (TLBO) method is developed to design discrete pin jointed structures. TLBO process consists of two parts: the first part represents learning from teacher and the second part illustrates learning by interaction among the learners. The results are compared with those obtained using other various evolutionary optimization methods considering the best solution, average solution, and computational effort. Consequently, the TLBO algorithm works effectively and demonstrates remarkable performance for the optimization of engineering design applications.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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• pp.187-194
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• 2000

Weight reduction for an automobile body is being sought for the fuel efficiency and the energy conservation. One way of the efforts is adopting Ultra Light Steel Auto Body (ULSAB) concept. The ULSAB concept can be used for the light weight of an automobile door with the tailor welded blank (TWB). A design process is defined for the TWB. The inner panel of door is designed by the TWB and optimization. The design starts from an existing component. At first, the hinge and inner reinforcements are removed. In the conceptual design stage, topology optimization is conducted to find the distribution of variable thicknesses. The number of parts and the welding lines are determined from the topology design. In the detailed design process, size optimization is carried out to find thickness while stiffness constraints are satisfied. The final parting lines are determined by shape optimization.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.10a
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• pp.296-303
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• 1996

This paper proposes a method for shape optimization of trusses. The potential savings offered by shape optimization will certainly be more significant than those resulting from fixed-geometry optimization. On the other hand, difficulties associated with topology and geometry optimization are still in existence. Even with a known topology, the geometry optimization problem is still a difficult task. An evolutionary procedure to be adopted and improved in this work, however, offers a means to achieve optimization in topology and geometry together. A plane truss structure is modelled within a specified domain and made to include a great number of nodes and members. Then the structure is analyzed and those members with stresses below a certain level are progressively eliminated from the structural system In this manner the structure evolves into a truss with a better topology and geometry by removing less important parts. Through the worked examples, we can see that the method presented in this Paper shows much promise.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.369-372
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• 2000

ESO(Evolutionary Structural Optimization) method is known that elements involved low stress value are removed from the previous model or that elements are added around elements involved high stress level on it and then the optimized model is obtained with required weight. Rejection ratio/addition ratio and evolutionary ratio are predefined and elements having lower/higher stress than reference stress, which average Mises stress on edge elements times rejection ratio, are deleted/added. In this study, when the plate having a cutout is subjected various in-plane load, a cutout shape is optimized using ESO method. ANSYS is used to analyse a finite element model and optimization procedure is made by APDL (ANSYS Parametric Design Language). ESO method is useful in rather than a complex structure optimization as well as a cutout shape optimization.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.12
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• pp.2101-2109
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• 2003

Structural shape optimization offers engineers with numerous advantages in designing shapes of structures. However, excessive relocation of nodes often cause distortion of elements and eventually result in degrade of accuracy and even halts of processes. To overcome these problems, an effective method, Selective Element Method(SEM), has been developed. This paper describes the basic concept of SEM and processes to implement into real-world problem. 2-D and 3-D shape optimization problems have been chosen to show the performance of the method. Though some limitations have been found, it was concluded that SEM can be useful in general shape optimization and even in some special cases such as decision of optimal weld line location.

• Structural Engineering and Mechanics
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• v.52 no.3
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• pp.445-468
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• 2014

In this paper a new particle swarm ray optimization algorithm is proposed for truss shape and size optimization with natural frequency constraints. These problems are believed to represent nonlinear and non-convex search spaces with several local optima and therefore are suitable for examining the capabilities of new algorithms. The proposed algorithm can be viewed as a hybridization of Particle Swarm Optimization (PSO) and the recently proposed Ray Optimization (RO) algorithms. In fact the exploration capabilities of the PSO are tried to be promoted using some concepts of the RO. Five numerical examples are examined in order to inspect the viability of the proposed algorithm. The results are compared with those of the PSO and some other existing algorithms. It is shown that the proposed algorithm obtains lighter structures in comparison to other methods most of the time. As will be discussed, the algorithm's performance can be attributed to its appropriate exploration/exploitation balance.