Size Optimization Of Structures Research Articles

Simultaneous sizing, shape, and layout optimization and automatic member grouping of dome structures

This paper presents both discrete and continuous sizing, shape, and layout structural optimization problems concerning the weight minimization of dome structures and considering displacements, stresses, natural frequencies of vibration, and global stability as constraints. The layout optimization searches for the best structural configuration through the maintenance of the bars’ grouping by introducing a new design variable. This variable refers to the number of standard modules used to generate the structural configuration of optimized domes. It can be attractive to use a reduced number of distinct cross-sectional areas, minimizing the costs of fabrication, transportation, storing, checking, and welding, providing labor saving measures. To obtain an automatic member grouping of the bars of the trusses analyzed in this paper, a specific encoding using cardinality constraints is considered. As result, trade-off curves are provided, showing the optimized weights in comparison with the number of distinct cross-sectional areas used in the solutions. Differential Evolution is the search algorithm adopted in this paper. The structural optimization problems showed better solutions when compared with those presented in the literature.

Reliability-based Design Optimization for Structures Using Particle Swarm Optimization

Studies on structure design optimization have been conducted extensively over the past decades because it can increase structural efficiency and maximize the engineers’ profit. One of the significant current discussions is the reliability aspect of structure design in addition to optimal design. This problem becomes more important especially in sizing and shaping optimization of truss structures. To address the problem, this paper applies Reliability-based Design Optimization (RBDO) by combining Latin Hypercube Sampling (LHS) and metaheuristic algorithms which are Particle Swarm Optimization (PSO) and Barebone PSO (BBPSO). The presence of uncertainty is modeled using LHS and the reliability constraint is added to measure the probability of structural failure. This study aims to investigate the performance of these metaheuristic algorithms in optimizing the structure design while still satisfying the reliability constraints. Two case studies, a welded beam design problem and 15-bar planar truss problem, are used in this study. The performance of these two algorithms will be compared. The obtained results indicate that BBPSO has a better performance than PSO.

Research on Transmission Performance of A Seven-gear Three-degree-of-freedom Planetary Gear Automatic Transmission Based on Graph Theory and Matrix Equation

The transmission performance analysis of planetary gear automatic transmission is helpful for the following structural size optimization, hydraulic design and electric control design. The current graphic method has the disadvantages of low calculation accuracy and lack of intuition in numerical analysis method. This paper proposes a method to analyze the transmission performance based on graph theory and matrix equation. Firstly, a graph theory analysis model is established for the self-designed seven-gear three-degree-of-freedom planetary gear automatic transmission, and the structural characteristics of the transmission are analyzed. Then, on the basis of analyzing the shift actuator worksheet, the motion analysis model and torque analysis model of typical gears are designed by taking the first gear and the reverse gear as examples, and the speed and torque values of all gears of the transmission are calculated by using the corresponding matrix equation. Finally, the power flow diagram of the typical gear is established by taking the first gear and the fourth gear as examples, and the direction and numerical value of power flow are identified on the diagram. The results show that the method can realize the combination of qualitative and quantitative analysis for the transmission performance analysis of the planetary gear automatic transmission with multiple gears and multiple degrees of freedom, which is more intuitive, accurate and efficient.

Sizing and prestress optimization of Class-2 tensegrity structures for space boom applications

Design of real engineering structures can benefit from an optimization step in which various parameters can be determined to satisfy a given set of requirements and constraints. Optimization of spatial assemblies such as truss or frame structures involves sizing optimization to minimize the mass of the structure. Optimization of tensegrity structures is more challenging as prestress levels should be optimized as well. In this paper, sizing and prestress optimization of Class-2 tensegrity booms are addressed using a particle swarm optimization approach. Nonlinear finite-element models of tensegrity structures and solution methods provide a starting point. Furthermore, a continuum beam modeling technique for tensegrity structures with repeating units is also useful. The particle swarm optimization algorithm is described and two numerical examples are presented. The first example studies the design and single-objective optimization of a deployable Class-2 tensegrity boom with reinforcing cables to maximize the bending stiffness-to-mass ratio. The results indicate that the optimum structure is capable of competing well with the state-of-the-art deployable booms in terms of stiffness-to-mass ratio. The second example investigates a multi-objective optimization problem of a Class-2 tensegrity boom. The objective functions are selected as minimization of the mass and tip displacement, respectively. The objective functions are at least partially conflicting; therefore, Pareto-optimal solutions are obtained to guide future design decisions. The results show the potential of tensegrity structures for implementation as space structures and the robustness of the particle swarm optimization algorithm, even for multi-objective optimization problems.

Size optimization of MEMS gyroscopes using substructuring

In this paper we present an innovative approach to the automatic design of MEMS gyroscopes, based on structural size optimization. A novel design environment, called feMEMS, is fully developed in Matlab: it allows the parametric generation of the structure geometry, the simulation of its behaviour and the layout optimization by means of gradient based techniques.The gyroscope layout is parametrized by a set of design variables, that describe the geometry and position of the mechanical elements composing the structure, namely the internal masses and flexure springs. The dynamic behaviour of the gyroscope is simulated through a finite element discretization, focusing on the computation of the structure resonant frequencies and of the mechanical response to the external angular rate. Also, the use of substructuring techniques based on static reduction is suggested, in order to reduce the computational cost of the simulations and of the optimization procedure.The working scheme of feMEMS is demonstrated considering the mechanical design of a triaxial beating-heart MEMS gyroscope. Two possible formulations of the optimization problem are presented and compared: the design objectives are respectively the maximization of the sensor response to the external angular rate and the maximization of spurious modes frequencies, while constraints are imposed to properly tune the drive and sense resonant frequencies and to satisfy the requirements on the available design space.

Structural Analysis and Size Optimization of a Fine-Blanking Press Frame Based on Sensitivity Analysis

The fine-blanking press, which has been widely used in the sheet-cutting industry, is high-end equipment. The frame is a core component of the fine-blanking press. In this paper, the sensitivity analysis and size optimization method were used to optimize a fine-blanking press frame. First, a shell element model of the frame was established to analyse the mechanical properties of the initial frame. Then, the mathematical expressions for sensitivity analysis and size optimization of the frame were formulated. Based on the established model, the response sensitivities for plate thicknesses were analysed, and a 12.94 % weight reduction was achieved through size optimization. Moreover, the effect of material distribution on dynamic performance was investigated. The result indicated that for a constrained structure, distributing material close to the constraint location increases the modal frequencies.

Structural Size Optimization of an External Fixation Device

Structural Size Optimization of an External Fixation Device

An enhanced social engineering optimizer for size and shape optimization of truss structures with dynamic constraints

An enhanced social engineering optimizer for size and shape optimization of truss structures with dynamic constraints

A new fuzzy strategy for size and topology optimization of truss structures

Most of the metaheuristic optimization techniques are the general optimization tools with the ability of solving various class of problems. However, in the case of more complex engineering problems, adding extra customizing procedure(s) can improve their performance. In this regard, the current study deals with introducing a new auxiliary fuzzy decision mechanism to enhance these methods’ capability on handling the structural size and topology optimization problems. The proposed mechanism aims to reduce the complexity level of the structural size and topology optimization problems by converting their complex search spaces into simpler fuzzy domains. Introduced fuzzy mechanism, during the optimization process, permanently monitors the population updating process and emphasizes either size or topology search behavior of each agent. Proposed mechanism evaluates agents via two predefined concepts so-called Normalized Objective Function (NOFi) and Normalized Members Density (NMDi). Since the presented fuzzy strategy designed as an independent regulator module, it can be integrated with different optimization algorithms. In the current work, it is combined with the Interactive Search Algorithm (ISA) optimization method and the compound method is named as Fuzzy Tuned Interactive Search Algorithm (FTISA). Eventually, its performance is comparatively assessed on solving a number of structural size and topology optimization problems with dynamic and static constraints. Achieved results demonstrate that the introduced fuzzy strategy not only significantly enhances the computational cost of the process but also improves the accuracy of the solutions and stability of the algorithm.

Topology optimization of nonlinear single-layer domes by an improved electro-search algorithm and its performance analysis using statistical tests

In this paper, an improved electro-search algorithm is proposed to solve topology optimization problem of nonlinear single-layer domes. The electro-search algorithm is one of the newly developed metaheuristics inspirited by the movement of electrons around the nucleus of atoms in a molecule. This algorithm exhibits a good performance in solving optimization problems of benchmark functions. However, this algorithm cannot present appropriate performance in tackling discrete structural optimization problems. In the proposed improved algorithm, to reduce the probability of getting stuck in local minima, one electron is assigned to each nucleus and a new equation is defined to determine its orbital’s radius. Moreover, a new scheme is developed to update the position of nuclei in design space. In addition, in order to increase the convergence speed, a memory containing some historically best solutions is added to the algorithm. Parametric and nonparametric statistical tests are applied to analyze the performance of the algorithms. The numerical results are presented in two parts including size optimization of benchmark steel structures and topology optimization problems of single-layer domes. The results demonstrate that the proposed improved algorithm is superior over other well-known metaheuristic algorithms in terms of optimum solution, convergence rate, and overall performance.

Water strider algorithm: A new metaheuristic and applications

The present paper proposes a novel nature-inspired optimization paradigm, which is called the Water Strider Algorithm (WSA). The WSA is a population-based optimizer inspired by the life cycle of water strider bugs. The WSA mimics territorial behavior, intelligent ripple communication, mating style, feeding mechanisms and succession of water striders. The algorithm is mathematically formulated and benchmarked on forty-four numerical problems, four classic examples, two large scale structural size optimization and one structural damage identifying applications. In two phases, the algorithm is investigated to prove its promising performance against possible biases. Different parametric and nonparametric tests, as well as comparison with well-established and state of the art algorithms, indicate the efficient performance of the proposed WSA. The algorithm is applied to classical constrained, unconstrained, continuous and discrete structural design problems confirming its capability of tackling various challenging problems. The paper also presents a real application of the proposed method in structural health monitoring, in which the WSA effectively identified the damage scenarios.

Optimal design of planar steel frame structures utilizing meta-heuristic optimization algorithms

Meta-heuristic algorithms are applied in optimization problems in a variety of fields, including engineering, economics, and computer science. In this paper, seven population-based meta-heuristic algorithms are employed for size optimization of two-dimensional steel frame structures. These algorithms consist of the Artificial Bee Colony algorithm, Big Bang-Big Crunch algorithm, Cyclical Parthenogenesis Algorithm, Cuckoo Search algorithm, Thermal Exchange Optimization algorithm, Teaching-Learning-Based Optimization algorithm, and Water Evaporation Optimization algorithm. Optimization aims to minimize the weight of rigid-jointed steel frame structures while satisfying some constraints on displacement and stress limits. The design is based on the requirements of the AISC Load and Resistance Factor Design (LRFD). The capability and robustness of the algorithms are investigated through three well-known steel frame benchmarks.

Size and layout optimization of truss structures with dynamic constraints using the interactive fuzzy search algorithm

Optimizing truss structures considering natural frequency constraints can fundamentally enhance their dynamic behaviour under transient loadings. In this regard, the current investigation assesses the search capability of the interactive fuzzy search algorithm (IFSA) in solving this class of problem. Since the natural frequencies are very sensitive to configuration changes in the system, throughout the optimization process the algorithm should be able to adaptively shift its search behaviour. To meet this aim, the IFSA utilizes two nine-rule fuzzy modules which permanently monitor the optimization process and try to balance the exploration and exploitation search behaviours of the algorithm. Then, the search capability of the proposed method is tested on five structural benchmark problems. The numeric results reveal that the IFSA, by systematically reducing the number of ineffective iterations, considerably decreases the required computational cost. In addition, considering solution accuracy and process stability, IFSA provides promising results in solving structural optimization problems.

Buckling Restrained Sizing and Shape Optimization of Truss Structures

AbstractAn integrated strategy for sizing and shape optimization of truss structures, taking buckling constraints implicitly into truss design, is demonstrated here. Because the associated objectiv...

Coupling SAP 2000 with ABC algorithm for truss optimization

In this work, a numerical tool is implemented for size optimization of spatial truss structures. To achieve this goal, the metaheuristic artificial bee colony (ABC) algorithm based on the vivid behavior of honey bees is combined with the commercial software package SAP 2000 via its Application Programming Interface (API). Linking the optimization algorithm to SAP 2000 will allow access to the complete finite element library and potential of the commercial software. In order to do so, the numerical tool is developed within the Excel environment by using macros with the Visual Basic Programming Language. A complete picture is then presented to practitioners of the elaborated numerical tool, which can be used in daily design applications. The correct functionality is demonstrated by means of two challenging practical examples. Extension to other optimization applications can be easily adapted

Automated static structural FEA environment in MATLAB using Solid Edge and Femap

Nowadays, CAD and FE software are getting integrated to each other. However, these new integrated pieces of software cannot be customized enough to analyze different optimization methods or model behavior. In this paper, a MATLAB environment is developed that connects to C# and VB programs, which use Solid Edge and Femap API functions, in order to automate the geometry modification and the FE model building and solving functions. A simple static structural size optimization problem is solved with the fmincon solver of MATLAB.

THE PERFORMANCE COMPARISON OF THREE METAHEURISTIC ALGORITHMS ON THE SIZE, LAYOUT AND TOPOLOGY OPTIMIZATION OF TRUSS STRUCTURES

The structural optimization problem mostly deals with the weight minimization of the structural system. This issue can be assessed from the size, layout and topology aspects. No matter which of these aspects are targeted, to solve them an optimization technique is required. In the last decades the metaheuristic techniques, as the non-gradient optimization algorithms, are widely applied on solving these classes of problems. In the structural optimization, the most time consuming part of the process is the objective function evaluation. Based on this fact, in the current work, these techniques are divided into three main groups as single phase, double phase and multi-phase algorithms. Then based on the author knowledge, three representative methods are picked for each group and their search performance comparatively inspected on solving size, shape and topology optimization of truss structures. To meet this aim, Integrated Particle Swarm Optimization (iPSO), Teaching and Learning Based Optimization (TLBO) and Drosophila Food-Search Optimization (DSO) algorithms are selected, respectively. Different properties like accuracy, convergence rate and complexity of the algorithms are investigated. The outcomes are provided via illustrative diagrams and tables. Based on the achieved results, DSO shows the most complexity level among the other algorithm while the iPSO and TLBO can outperform it on both accuracy and convergence rate. Consequently, iPSO presents a higher accuracy level on finding optimal solutions and TLBO with the lowest standard deviation value through the process shows the highest level of stability on finding optimal solutions.

Size and Shape Optimization of Truss Structures with Natural Frequency Constraints Using Modified Simulated Annealing Algorithm

In this article, a recently developed metaheuristic named modified simulated annealing algorithm (MSAA) is proposed for size and shape optimization of truss structures with frequency constraints. These kinds of problems represent nonlinear and non-convex search spaces with several local optima and are well-known as challenging optimization problem. MSAA is a newly improved version of the simulated annealing (SA) algorithm with three modifications: preliminary exploration, search step and a new probability of acceptance. Six benchmark truss optimization problems with frequency constraints are explored for the validity of the present algorithm. Numerical results indicate that MSAA is more reliable, stable and efficient than those found by other state-of-the-art metaheuristics optimization methods.

Exporting water wave optimization concepts to modified simulated annealing algorithm for size optimization of truss structures with natural frequency constraints

This paper proposes an improved version of a recently proposed modified simulated annealing algorithm (MSAA) named as an improved MSAA (I-MSAA) to tackle the size optimization of truss structures with frequency constraint. This kind of problem is problematic because its feasible region is non-convex while the boundaries are highly non-linear. The main motivation is to improve the exploitative behavior of MSAA, taking concept from water wave optimization metaheuristic (WWO). An interesting concept of WWO is its breaking operation. Thirty functions extracted from the CEC2014 test suite and four benchmark truss optimization problems with frequency constraints are explored for the validity of the proposed algorithm. Numerical results indicate that I-MSAA is more reliable, stable and efficient than those found by other existing metaheuristics in the literature.

Different Discrete ACCS Algorithms for Optimal Design of Truss Structures: A Comparative Study

Many optimization techniques based on swarm intelligence have been developed for size optimization of skeletal structures. Cuckoo search algorithm, artificial bee colony algorithm, colliding bodies optimization, artificial coronary circulation system (ACCS) are only some examples of these algorithms. In these methods, the sizing variables are often assumed to be continuous. However, in most practical structural engineering design problems, the design variables are discrete. The aim of this study is to present an optimization algorithm based on the ACCS algorithm for the discrete optimum design of truss structures. Here, the discrete search strategy using the ACCS algorithm is presented by three different scenarios in detail and their effectiveness and robustness are compared to those of the recently developed discrete optimization methods. The ACCS optimization algorithm uses the visual center point of populations in each iteration and simulates the process of growing coronary arteries of heart. Finally, it is shown that the discrete ACCS has the fastest convergence rate among the considered algorithms and can be effectively used to solve optimal design of truss structures with discrete variables.