Shape Optimization Of Truss Structures Research Articles

Combined Size and Shape Optimization of Truss Structures Using the Heap-Based Optimizer (HBO) Algorithm

Combined Size and Shape Optimization of Truss Structures Using the Heap-Based Optimizer (HBO) Algorithm

Effects of Limiting the Number of Different Cross-Sections Used in Statically Loaded Truss Sizing and Shape Optimization.

This research aims to show the effects of adding cardinality constraints to limit the number of different cross-sections used in simultaneous sizing and shape optimization of truss structures. The optimal solutions for sizing and shape optimized trusses result in a generally high, and impractical, number of different cross-sections being used. This paper presents the influence of constraining the number of different cross-sections used on the optimal results to bring the scientific results closer to the applicable results. The savings achieved using the cardinality constraint are expected to manifest in more than just the minimization of weight but in all the other aspects of truss construction, such as labor, assembly time, total weld length, surface area to be treated, transport, logistics, and so on. It is expected that the optimal weight of the structures would be greater than when not using this constraint; however, it would still be below conventionally sized structures and have the added benefits derived from the simplicity and elegance of the solution. The results of standard test examples for each different cardinality constraint value are shown and compared to the same examples using only a single cross-section on all bars and the overall optimal solution, which does not have the cardinality constraint. An additional comparison is made with results of just the sizing optimization from previously published research where authors first used the same cardinality constraint.

Combined Gaussian Local Search and Enhanced Comprehensive Learning PSO Algorithm for Size and Shape Optimization of Truss Structures

This paper proposes the use of enhanced comprehensive learning particle swarm optimization (ECLPSO), combined with a Gaussian local search (GLS) technique, for the simultaneous optimal size and shape design of truss structures under applied forces and design constraints. The ECLPSO approach presents two novel enhancing techniques, namely perturbation-based exploitation and adaptive learning probability, in addition to its distinctive diversity of particles. This prevents the premature convergence of local optimal solutions. In essence, the perturbation enables the robust exploitation in the updating velocity of particles, whilst the learning probabilities are dynamically adjusted by ranking information on the personal best particles. Based on the results given by ECLPSO, the GLS technique takes data from the global best particle and personal best particles in the last iteration to generate samples from a Gaussian distribution to improve convergence precision. A combination of these techniques results in the fast convergence and likelihood to obtain the optimal solution. Applications of the combined GLS-ECLPSO method are illustrated through several successfully solved truss examples in two- and three-dimensional spaces. The robustness and accuracy of the proposed scheme are illustrated through comparisons with available benchmarks processed by other meta-heuristic algorithms. All examples show simultaneous optimal size and shape distributions of truss structures complying with limit state design specifications.

Sizing and shape optimization of truss employing a hybrid constraint-handling technique and manta ray foraging optimization

This paper presents an efficient constraint-handling technique (CHT) for metaheuristic algorithms in the size and shape optimization of truss structures. During the search process, the proposed CHT utilizes an improved Deb rule to filter redundant structural analyses and maps the candidate designs onto the feasible boundary for structural optimization to improve its search ability and stability based on the mapping strategy. The performance of the newly developed Manta Ray Foraging Optimization (MRFO) algorithm using the proposed CHT in structural optimization was also examined. Five truss optimization problems are used to examine the efficiency of the hybrid CHT compared with the improved Deb rule, the EDP method, and the mapping strategy. Four widely used metaheuristic algorithms, including HS, PSO, TLBO, and CS, have also been used to evaluate the performance of the MRFO in structural optimization. Numerical results demonstrate that the hybrid CHT can markedly improve both the search capacity and computational efficiency of metaheuristic algorithms. The MRFO does not show obvious weakness compared with existing algorithms in structural optimization. A comparison analysis also shows that the performances of the hybrid CHT vary across optimization algorithms.

A novel hybrid differential evolution and symbiotic organisms search algorithm for size and shape optimization of truss structures under multiple frequency constraints

Although a large number of metaheuristic algorithms and their variants have been proposed for many engineering optimization problems, no paradigms hybridized by differential evolution (DE) and symbiotic organisms search (SOS) to concurrently improve the optimal solution quality and the convergence speed have been published thus far, especially for size and shape optimization of truss structures with multiple frequency constraints. Therefore, this article aims to propose a novel optimization algorithm as a cross-breed of the DE and the SOS, named HDS, for such problems. This algorithm can simultaneously and effectively enhance both global and local searching abilities by utilizing newly developed operators hybridized from the DE and SOS. An automatically adapted parameter is suggested for a better trade-off between those two capabilities. Furthermore, an elitist scheme is used in the selection phase to extract the best solutions for the next generation. As a consequence, the proposed methodology results in high-quality optimal solutions with a lower computational effort in comparison with two original methods, even many other optimization paradigms available in the literature. 26 benchmark mathematical functions are examined first. 5 numerical examples of shape and size optimization of truss structures are then investigated to validate the feasibility of the current paradigm.

Discrete Size and Shape Optimization of Truss Structures Based on Job Search Inspired Strategy and Genetic Operations

A meta-heuristic algorithm for discrete size and shape optimization of trusses via a job search inspired strategy together with genetic operators of mutation, selection, and crossover is proposed. The alternation of movements with respect to objective function and load bearing capacity of constructive decisions is provided. Being introduced is an intermediate search goal connected in terms of posed limitations with heightened suitability levels of individuals meeting the current requirements for the initial objective function. As soon as these conditions allow achieving a structure type which meets task limitations, requirements for the function value are redefined. This technique does not demand penalty functions that provide strict control of limitations in any algorithm usage, greater stability of the results received, and finding better solutions. The efficiency of this approach in terms of solution accuracy is demonstrated through five benchmark design examples, in comparison with other methods of discrete truss structure optimization.

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

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...

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.

Enhanced Artificial Coronary Circulation System Algorithm for Truss Optimization with Multiple Natural Frequency Constraints

In this paper, an enhanced artificial coronary circulation system (EACCS) algorithm is applied to structural optimization with continuous design variables and frequency constraints. The standard algorithm, artificial coronary circulation system (ACCS), is inspired biologically as a non-gradient algorithm and mimics the growth of coronary tree of heart circulation system. Designs generated by the EACCS algorithm are compared with other popular evolutionary optimization methods, the objective function being the total weight of the structures.Truss optimization with frequency constraints has attracted substantial attention to improve the dynamic performance of structures. This kind of problems is believed to represent nonlinear and non-convex search spaces with several local optima. These problems are also suitable for examining the capabilities of the new algorithms. Here, ACCS is enhanced (EACCS) and employed for size and shape optimization of truss structures and six truss design problems are utilized for evaluating and validating of the EACCS. This algorithm uses a fitness-based weighted mean in the bifurcation phase and runner phase of the optimization process. The numerical results demonstrate successful performance, efficiency and robustness of the new method and its competitive performance to some other well-known meta-heuristics in structural optimization.

Combined size and shape optimization of truss structures using subset simulation optimization

This paper presents an approach to solve the combined size and shape design optimization problems using recently developed subset simulation optimization for both continuous and discrete design variables. Except for the componentwise Metropolis–Hasting algorithm, a recently developed adaptive conditional sampling algorithm is also employed as an alternative approach for generating new conditional samples (candidate designs) for each simulation level, which enhances the accuracy and stability of the optimization process. Besides, a double-criterion sorting algorithm is used to handle the design constraints and integrate them in the generation of conditional samples during the Markov Chain Monte Carlo simulation, and the inverse transform method is employed to deal with the discrete design variables. Totally, four numerical examples are considered, including a 15-bar 2D truss, an 18-bar 2D truss, a 39-bar 3D truss and a truss-type landing gear of an unmanned aerial vehicle. The optimal designs obtained from subset simulation optimization using either the componentwise Metropolis–Hasting algorithm or the adaptive conditional sampling algorithm succeed in substantially reducing the weights of the truss-type structures under design constraints in terms of the member stress, the Euler buckling and the nodal displacement. The computational results indicate the proposed method can be taken as an alternative tool for structural optimization design on truss structures when involving the combined size and shape design.

Efficient size and shape optimization of truss structures subject to stress and local buckling constraints using sequential linear programming

The advance in digital fabrication technologies and additive manufacturing allows for the fabrication of complex truss structure designs but at the same time posing challenging structural optimization problems to capitalize on this new design freedom. In response to this, an iterative approach in which Sequential Linear Programming (SLP) is used to simultaneously solve a size and shape optimization sub-problem subject to local stress and Euler buckling constraints is proposed in this work. To accomplish this, a first order Taylor expansion for the nodal movement and the buckling constraint is derived to conform to the SLP problem formulation. At each iteration a post-processing step is initiated to map a design vector to the exact buckling constraint boundary in order to facilitate the overall efficiency. The method is verified against an exact non-linear optimization problem formulation on a range of benchmark examples obtained from the literature. The results show that the proposed method produces optimized designs that are either close or identical to the solutions obtained by the non-linear problem formulation while significantly decreasing the computational time. This enables more efficient size and shape optimization of truss structures considering practical engineering constraints.

Enhanced particle swarm optimization for size and shape optimization of truss structures

ABSTRACTThis article presents an enhanced particle swarm optimization (EPSO) algorithm for size and shape optimization of truss structures. The proposed EPSO introduces a particle categorization mechanism into the particle swarm optimization (PSO) to eliminate unnecessary structural analyses during the optimization process and improve the computational efficiency of the PSO-based structural optimization. The numerical investigation, including three benchmark truss optimization problems, examines the efficiency of the EPSO. The results demonstrate that the particle categorization mechanism greatly reduces the computational requirements of the PSO-based approaches while maintaining the original search capability of the algorithms in solving optimization problems with computationally cheap objective function and expensive constraints.

Enhanced Biogeography-based Optimization: A New Method for Size and Shape Optimization of Truss Structures with Natural Frequency Constraints

The current study presents an enhanced biogeography-based optimization (EBBO) algorithm for size and shape optimization of truss structures with natural frequency constraints. The BBO algorithm is one of the recently developed meta-heuristic algorithms inspired by the mathematical models in biogeography science and is based on the migration behavior of species among the habitats in the nature. In this study, the overall performance of the standard BBO algorithm is enhanced by new migration and mutation operators. The efficiency of the proposed algorithm is demonstrated by utilizing four benchmark truss design examples with frequency constraints. Numerical results show that the proposed EBBO algorithm not only significantly improves the performance of the standard BBO algorithm, but also finds competitive results compared with recently developed optimization methods.

Chaotic biogeography algorithm for size and shape optimization of truss structures with frequency constraints

Size and shape optimization of truss structures with natural frequency constraints is inherently nonlinear dynamic optimization problem with several local optima. Therefore theoptimization method should be sagacious enough to avoid being trapped in local optima and in this way to reduce premature convergence. To address this problem, we develop a Chaotic Biogeography-Based Optimization (CBBO) algorithm which combines the chaos theory and the biogeography-based optimization (BBO) to achieve an ecient optimization method. In this method, new chaotic migration and mutation operators are proposed to enhance the exploration ability of BBO. The performance of the method is demonstrated through five benchmark design examples with size and shape variables associated by multiply frequency constraints. The results show the eciency and robustness of proposed method and in most cases, CBBO finds a relatively lighter structural weight than those previously reported results in the literature.

Shape and size optimization of trusses with multiple frequency constraints using harmony search and ray optimizer for enhancing the particle swarm optimization algorithm

In this paper, size and shape optimization of truss structures is performed using an efficient hybrid method. This algorithm uses a particle swarm strategy and ray optimizer, and utilizes additional harmony search for a better exploitation. Here, multiple frequency constraints are considered making the optimization a highly nonlinear problem. Some basic benchmark problems are solved by this hybrid method, and the numerical results demonstrate the efficiency and robustness of this method compared to other mathematical and heuristic algorithms.

하모니 서치 알고리즘과 고유진동수 제약조건에 의한 트러스의 단면과 형상 최적설계

We present the optimum design for the cross-sectional(sizing) and shape optimization of truss structures with natural frequency constraints. The optimum design method used in this paper employs continuous design variables and the Harmony Search Algorithm(HSA). HSA is a meta-heuristic search method for global optimization problems. In this paper, HSA uses the method of random number selection in an update process, along with penalty parameters, to construct the initial harmony memory in order to improve the fitness in the initial and update processes. In examples, 10-bar and 72-bar trusses are optimized for sizing, and 37-bar bridge type truss and 52-bar(like dome) for sizing and shape. Four typical truss optimization examples are employed to demonstrate the availability of HSA for finding the minimum weight optimum truss with multiple natural frequency constraints.

Ray optimization for size and shape optimization of truss structures

In this paper, the recently developed method, so-called ray optimization, is employed for size and shape optimization of truss structures. The goal function of the present optimization method is the minimization of truss weight under the required constraints. In ray optimization, each agent is modeled as a ray of light that moves in the search space in order to find the global or near-global optimum solution. Comparison of the obtained results with those of some previous studies demonstrates the efficiency of this new algorithm.

ON QUADRATIC APPROXIMATION METHOD FOR OPTIMUM DESIGN OF TRUSS STRUCTURES

Structural optimization method using the quadratic approximation functions for the structural responses are studied. There are two kinds of the design variables in the shape optimization of truss structures. For the sectional variables, the linear approximation functions are used for the calculations of the structural responses. For the geometric variables, the quadratic approximation functions are proposed. The functions are approximately generated by using the elements on the main diagonal and ignoring the off-diagonal elements of the Hessian. Several numerical examples show the reliability and the efficiency of the method proposed

Optimum shape design of truss structures based on reliability

A procedure is presented for the shape optimization of truss structures based on the reliability concept. Nodal coordinates are taken as the shape design variables together with the sizing design variables such as the cross-sectional areas of the members. These variables are determined to minimize the structural volume under the constraint on the structural failure probability.