Design of truss-structures for minimum weight using genetic algorithms

Optimization of truss-structures for finding optimal cross-sectional size, topology, and configuration of 2-D and 3-D trusses to achieve minimum weight is carried out using real-coded genetic algorithms (GAs). All the above three optimization techniques have been made possible by using a novel representation scheme. Although the proposed GA uses a fixed-length vector of design variables representing member areas and change in nodal coordinates, a simple member exclusion principle is introduced to obtain differing topologies. Moreover, practical considerations, such as inclusion of important nodes in the optimized structure is taken care of by using a concept of basic and non-basic nodes. Stress, deflection, and kinematic stability considerations are also handled using constraints. In a number of 2-D and 3-D trusses, the proposed technique finds intuitively optimal or near-optimal trusses, which are also found to have smaller weight than those that are reported in the literature

Designing Volumetric Truss Structures

We present the first algorithm for designing volumetric Michell Trusses. Our method uses a parametrization approach to generate trusses made of structural elements aligned with the primary direction of an object's stress field. Such trusses exhibit high strength-to-weight ratios. We demonstrate the structural robustness of our designs via a posteriori physical simulation. We believe our algorithm serves as an important complement to existing structural optimization tools and as a novel standalone design tool itself

Using nodal coordinates as variables for the dimensional synthesis of mechanisms

The method of the lower deformation energy has been successfully used for the synthesis of mechanisms for quite a while. It has shown to be a versatile, yet powerful method for assisting in the design of mechanisms. Until now, most of the implementations of this method used the dimensions of the mechanism as the synthesis variables, which has some advantages and some drawbacks. For example, the assembly configuration is not taken into account in the optimization process, and this means that the same initial configuration is used when computing the deformed positions in each synthesis point. This translates into a reduction of the total search space. A possible solution to this problem is the use of a set of initial coordinates as variables for the synthesis, which has been successfully applied to other methods. This also has some additional advantages, such as the fact that any generated mechanism can be assembled. Another advantage is that the fixed joint locations are also included in the optimization at no additional cost. But the change from dimensions to initial coordinates means a reformulation of the optimization problem when using derivatives if one wants them to be analytically derived. This paper tackles this reformulation, along with a proper comparison of the use of both alternatives using sequential quadratic programming methods. In order to do so, some examples are developed and studied.The authors wish to thank the Spanish Ministry of Economy and Competitiveness for its support through Grant DPI2013-46329-P and DPI2016-80372-R. Additionally the authors wish to thank the Education Department of the Basque Government for ist support through grant IT947-16

Conceptual design of long-span trusses using multi-stage heuristics

A hybrid method that addresses the design and optimization of long-span steel trusses is presented. By utilizing advancements in present day computing and biologically inspired analysis and design, an effort has been made to automate the process of evolving optimal trusses in an unstructured problem domain. Topology, geometry and sizing optimization of trusses are simultaneously addressed using a three stage methodology. Multi-objective genetic algorithms are used to optimize the member section sizes of truss topologies and geometries. Converting constraints into additional objectives provides a robust algorithm that results in improved convergence to the pareto-optimal set of solutions. In addition, the pareto-curve plotted based on how well the different objectives are satisfied helps in identifying the trade-offs that exist between these objectives, while also providing an efficient way to rank the population of solutions during the search process. A comparison study between multi-objective genetic algorithms, simulated annealing, and reactive taboo search is conducted to evaluate the efficiency of each method with relation to its overall performance, computational expense, sensitivity to initial parameter settings, and repeatability of finding near-global optimal designs. The benefit of using a three stage approach, and also implementing the entire model on parallel computers, is the high level of computational efficiency that is obtained for the entire process and the near-optimal solutions obtained. The overall efficiency and effectiveness of this method has been established by comparing the truss design results obtained using this method on bridge and roof truss benchmark problems with truss designs obtained by other researchers. One of the salient features of thisresearch is the large number of optimal trusses that are produced as the final result. The range of designs available provides the user with the flexibility to select the truss design that best matches their design requirements. By supporting human-computer interactions between these stages, the program also incorporates subjective aesthetic criteria, which assist in producing final designs in consonance with the user's requirements

Distributed multilevel optimization for complex structures

Optimization problems concerning complex structures with many design variables may entail an unacceptable computational cost. This problem can be reduced considerably with a multilevel approach: A structure consisting of several components is optimized as a whole (global) as well as on the component level. In this paper, an optimization method is discussed with applications in the assessment of the impact of new design considerations in the development of a structure. A strategy based on fully stressed design is applied for optimization problems in linear statics. A global model is used to calculate the interactions (e.g., loads) for each of the components. These components are then optimized using the prescribed interactions, followed by a new global calculation to update the interactions. Mixed discrete and continuous design variables as well as different design configurations are possible. An application of this strategy is presented in the form of the full optimization of a vertical tail plane center box of a generic large passenger aircraft. In linear dynamics, the parametrization of the component interactions is problematic due to the frequency dependence. Hence, a modified method is presented in which the speed of component mode synthesis is used to avoid this parametrization. This method is applied to a simple test case that originates from noise control. \u

Evolution Methods for Discrete Minimal Weight Design of Space Trusses with Stability Constraints

This paper provides a comparative study of evolution methods for minimal weight design of space trusses. Recently used genetic algorithms (GA), simulated annealing (SA) and tabu search (TS) methods are observed for metal structures where the truss member profiles are selected from available catalogue values. In this paper, global and local stability problems are considered using a path-following method for non-linear stability investigation. The results of the comparative study are presented for the commonly known numerical test problems. A twenty-four-member shallow dome structure was presented where structural instability constraints and member buckling are considered as well as using linear elastic material property. The effect of the nonlinear material law is compared in optimal design of the ten-bar truss structure and the twenty-five-bar transmission tower using an inverse Ramberg-Osgood material law

Truss topology optimization using an improved species-conserving genetic algorithm

YesThe aim of this article is to apply and improve the species-conserving genetic algorithm (SCGA) to search multiple solutions of truss topology optimization problems in a single run. A species is defined as a group of individuals with similar characteristics and is dominated by its species seed. The solutions of an optimization problem will be selected from the found species. To improve the accuracy of solutions, a species mutation technique is introduced to improve the fitness of the found species seeds and the combination of a neighbour mutation and a uniform mutation is applied to balance exploitation and exploration. A real vector is used to represent the corresponding cross-sectional areas and a member is thought to be existent if its area is bigger than a critical area. A finite element analysis model was developed to deal with more practical considerations in modelling, such as the existence of members, kinematic stability analysis, and computation of stresses and displacements. Cross-sectional areas and node connections are decision variables and optimized simultaneously to minimize the total weight of trusses. Numerical results demonstrate that some truss topology optimization examples have many global and local solutions, different topologies can be found using the proposed algorithm on a single run and some trusses have smaller weights than the solutions in the literature

Optimización de armaduras espaciales de acero utilizando algoritmos genéticos auto-adaptados : una primera aproximación.

En las últimas décadas, la optimización estructural mediante metaheurísticas ganó acogida en la comunidad científica; sin embargo, para garantizar buenos resultados se requiere una correcta selección de los parámetros de la metaheurísticas. En este trabajo se propone un algoritmo genético multi-cromosoma auto-adaptado para optimizar armaduras de acero tridimensionales. Las variables de diseño corresponden a las secciones asignadas a cada elemento en la armadura. El objetivo es la minimización del peso de la armadura, considerando desplazamientos y esfuerzos máximos como restricciones. El algoritmo propuesto se aplicó a la optimización de dos armaduras, produciendo diseños que pesan hasta un 35% menos que el mejor diseño inicial y son valores comparables al resultado obtenidos en otros trabajos. No obstante, la adaptación de los parámetros permite mayor robustez cuando se desea optimizar diferentes tipos de armadura y evita las ejecuciones del algoritmo de optimización que son necesarias para la calibración de sus parámetros

Effect of Variation in Geometrical Parameters on the Roof Trusses

The purpose of this project is to study the Effect of variation in geometrical parameters on the roof trusses in the design of plane truss by using angle section. The need of this study arises where sometimes it is difficult or taking much time to choose effective and economical truss geometry during the design period. In investigating the effectiveness of various truss geometry, a total of nine-truss geometry with simply pinned supports are chosen. The design loads are distributed to the joints so that there is no moment to be resisted by the members. A total of five span trusses with nine-truss geometry were analyzed and designed. Optimal trusses from each span of trusses are to be compared to determine whether the effective geometry is the same for different spans and heights. This study shows that there is no certainty in determining the most effective geometry neither with same span, height nor height over span ratio. The most effective truss geometry is actually specific for every truss span and height. For same span the among all the nine truss, Warren truss geometry seems to be the most optimum truss configuration with about 10% savings in weight when compared to its closest contenders Pratt truss or Howe truss. However, close results might be obtained where it does help to provide a good guideline in choosing a truss that does not waste much material. It has been observed from the results that warren truss is the most effective truss system in carrying the design loads. This feature has been attributed to the alignment of the compression chords and tension chords in a symmetric manner, which allows the truss to distribute the load in most effective way. Also it is noted that more the angle made by the compression and tension chords more effectively the load is distributed. Finally an optimality curve has been derived for understanding the relation between the span of the truss, optimum depth and least self-weight for the warren truss configuration. It is also observed that the optimum depth of any truss increases linearly with respect to its span