Free Vibration Optimization of Two and Three Dimensional Trusses

IPTEK The Journal for Technology and Science, 2011

During last three decade, many mathematical programming methods have been develop for solving optimization problems. However, no single method has been found to be entirely efficient and robust for the wide range of engineering optimization problems. Most design application in civil engineering involve selecting values for a set of design variables that best describe the behavior and performance of the particular problem while satisfying the requirements and specifications imposed by codes of practice. The introduction of Genetic Algorithm (GA) into the field of structural optimization has opened new avenues for research because they have been successful applied while traditional methods have failed. GAs is efficient and broadly applicable global search procedure based on stochastic approach which relies on "survival of the fittest" strategy. GAs are search algorithms that are based on the concepts of natural selection and natural genetics. On this research Multi-objective sizing and configuration optimization of the two-dimensional truss has been conducted using a genetic algorithm. Some preliminary runs of the GA were conducted to determine the best combinations of GA parameters such as population size and probability of mutation so as to get better scaling for rest of the runs. Comparing the results from sizing and sizing-configuration optimization, can obtained a significant reduction in the weight and deflection. Sizing-configuration optimization produces lighter weight and small displacement than sizing optimization. The results were obtained by using a GA with relative ease (computationally) and these results are very competitive compared to those obtained from other methods of truss optimization.

Passer journal of basic and applied sciences, 2024

In this paper, an optimization study is presented, focusing on steel trusses. The main goal of this study is to reduce the weight of truss structures using a Genetic Algorithm (GA), which is a widely acknowledged evolutionary-based method known for its efficiency in solving intricate optimization problems. The design problem formulation takes into account various constraints, such as displacement, tensile stress, and minimum size requirements. These constraints are implemented in MATLAB, utilizing the ANSI/AISC 360-16 Specification as a guideline for designing tension and compression members. To determine the optimal design, the approach involves considering discrete design variables. This is achieved by selecting sections from a database containing all available steel sections specified in the AISC Steel Construction Manual, ensuring practical and feasible design solutions. The efficiency of the algorithm is validated through its application to several plane truss types. Through a comparison of the outcomes obtained from the proposed algorithm with the results generated by CSI-ETABS software, it is demonstrated that this approach consistently yields better weight optimization. Overall, the study showcases the effectiveness of the GA-based algorithm in optimizing the weight of steel trusses. The results and implications of the findings are thoroughly discussed in the paper; this study has the potential to make a substantial contribution to the field of structural optimization and design.

Engineering structures need to satisfy certain criteria such that it may function properly. This paper presents the results of a study on trusses which need to satisfy optimal conditions, i.e. lowest cost possible with maximal performance. The trusses considered were statically indeterminate steel structures with multi-system of loading. The cost is here represented by the material volume of the structure and the maximal performance is reflected by the high working stresses within allowable stress limits. The material strength was modeled as a random variable with a Log Normal distribution. Beside stresses, the structures are also required to meet a failure probability of P f =10 -3 , which may occur locally within the elements as well as globally on the structure as a whole. The complexity of optimization problems depends in general on the number of the considered variables. The larger the number of variables considered, the more complicated becomes the solution process. Therefore, cases of single variable elements as well as multi variables ones were considered in this study. Optimization problems are usually solved applying iterative procedures, frequently resorting to mathematical programming. In these procedures the process usually converges to unreliable solutions; it even may completely bogged down with no solution at all. To circumvent this problem, iteration was carried out applying Genetic Algorithms where the process proceeds in a stochastic manner. Genetic Algorithms usually deliver reliable solutions.

IEEE, 2018

Trusses are most commonly used structure in industrial buildings, warehouses, bridges, transmission tower etc. There are different types of trusses available for construction. The analysis and design of an economical and stable truss system for utilization in industrial buildings., storage rooms., bridges., warehouses., transmission towers etc. is necessary. The present study is done on static analysis and optimization of truss system to get optimal and economical configuration of truss. Total cost of the structure depends upon mass of the structure and mass is directly relative to the material consumed by the skeleton of the structure. This paper presents the use of programming language MATLAB for static analysis of truss structure using “Finite Element Method” and the ‘Topology Optimization’ will be done based on the energy stored in the member. Static analysis of a 13 bar benchmark truss is done using MATLAB programming code and various results have been obtained. After interpret...

IOP Conference Series: Materials Science and Engineering

Conceptual design in structural engineering entails a large amount of trial and errors or extensive expertise to obtain the most economical and functional design solutions for large engineering projects. In this paper a modern optimization technique called Genetic algorithm, adopting its concept from genetic evolution is used to optimize the shape, size and topology of a plane truss structure with the aim of minimizing the total weight of the truss. A genetic algorithm developed in MATLAB was implemented in this paper to optimize the weight of plane truss structures. The objective function of the optimization problem is subjected to constraints such as stress limits, buckling constraints, tension and compression capacity according to British steel design code BS 5950. The plane trusses which were subject to point loads were tested in the genetic algorithm, the resulting optimized truss structures were then subject to real life loading to determine their feasibility to withstand real life loading. The optimized trusses presented by the algorithm were modelled in a structural analysis and design software called SAP 2000, where they were subjected to dead and live loads. After design the weight saving discovered between the original trusses and the optimized version was between 37-47%. The results show that the genetic algorithm implemented in this study is useful in optimizing the weight of a plane truss structure.

Structural and Multidisciplinary Optimization, 2002

A displacement-based optimization strategy is extended to the design of truss structures with geometric and material nonlinear responses. Unlike the traditional optimization approach that uses iterative finite element analyses to determine the structural response as the sizing variables are varied by the optimizer, the proposed method searches for an optimal solution by using the displacement degrees of freedom as design variables. Hence, the method is composed of two levels: an outer level problem where the optimal displacement field is searched using general nonlinear programming algorithms, and an inner problem where a set of optimal cross-sectional dimensions are computed for a given displacement field. For truss structures, the inner problem is a linear programming problem in terms of the sizing variables regardless of the nature of the governing equilibrium equations, which can be linear or nonlinear in displacements. The method has been applied to three test examples, which include material and geometric nonlinearities, for which it appears to be efficient and robust.

In this paper we propose the use of the genetic algorithm (GA) as a tool to solve multiobjective optimization problems in structures. Using the concept of min±max optimum, a new GA-based multiobjective optimization technique is proposed and two truss design problems are solved using it. The results produced by this new approach are compared to those produced by other mathematical programming techniques and GA-based approaches, proving that this technique generates better trade-os and that the genetic algorithm can be used as a reliable numerical optimization tool. 7

International Journal of Scientific & Technology Research, 2020

Structural design optimization is a mathematical approach that concerns in finding the maxima and minima function subject to some constraints. This involves various optimization technique to find the best possible design in terms of weight, reliability and thus the overall cost. Various researchers have worked on different optimization techniques in finding out the efficient and light weight structures that are essential for the actual design of tall structures. This paper summarizes the various techniques of optimization of steel truss or towers that have been used till now. For this purpose, different optimization techniques have been studied which involves the various geometric constraints like changing the base width, bracing pattern, area of cross section. By reviewing the literature of the works done, the common objective emphasizes the need for finding the minimum weight of the structure. From studies we see optimization using metaheuristic algorithm are effective in order to solve truss problems. Metaheuristic algorithms are nature-inspired and most widely used due to its applicability and feasibility to various types of structures with many numbers of design variables. In this paper a 25-bar space benchmark truss has been considered for demonstrating the performance of various optimization algorithm. A comparative study is done based on the performance in lowering the weight of the total truss. Results shows that optimal weight of the truss structure can be obtained effectively using Whale optimization algorithm and it proved to be robust and efficient than other algorithms.

Proceedings of the Ninth International Conference on the Application of Artificial Intelligence to Civil, Structural and Environmental Engineering, 2007

The present paper describes a new genetic algorithm (GA) for geometry optimisation of plane trusses designed for supporting distributed loads. The objective of the optimisation is to minimise the weight of the truss subject to a constraint on the number and locations of the load bearing nodes. The origin of this constraint is in the distributed load domain rather than the truss domain. The proposed GA uses a variable-length vector of design variables representing the number of nodes and nodal coordinates. Hence, in contrary to other GA-based truss geometry design and optimisation methods, it neither needs to have all nodes prelocated (or to use a grid of potential nodes) nor does it require that the truss topology to be fixed. The mutation operator used is dynamic arithmetic, while a geometric cross-over generates trusses of the next generation. A new concept of partial fitness has been used in mating process to perform an educated cross-over, aimed at enhancing the convergence rate of the algorithm. Case studies have been carried out to show the practicality and efficiency of the algorithm.

IRJET, 2020

Weight optimization of trusses is very important due to economic considerations. This paper presents optimum design of plane and space trusses using genetic algorithm. The objective function of the optimization problem is the total weight of the truss with displacement constraint. In this study rank based selection is used to minimize the number of iterations to reach the optimum solution. Algorithm for weight minimization of steel trusses has been developed in SCILAB using Genetic Algorithm. Genetic algorithm is a natural selection search method intended to combine good solutions to a problem from many generations to get best results. First generation is selected randomly and then crossover and mutation is applied. All the chromosomes are represented individually by a binary string and hence it is termed as Genetic programming. The algorithm was applied on a reference book problem and result in more optimized results with lesser mathematical effort.