SUMMARYIn this article size=topology optimization of trusses is performed using a genetic algorithm (GA), the force method and some concepts of graph theory. One of the main di culties with optimization with a GA is that the parameters involved are not completely known and the number of operations needed is often quite high. Application of some concepts of the force method, together with theory of graphs, make the generation of a suitable initial population well-matched with critical paths for the transformation of internal forces feasible. In the process of optimization generated topologically unstable trusses are identiÿed without any matrix manipulation and highly penalized. Identifying a suitable range for the cross-section of each member for the ground structure in the list of proÿles, the length of the substrings representing the cross-sectional design variables are reduced. Using a contraction algorithm, the length of the strings is further reduced and a GA is performed in a smaller domain of design space. The above process is accompanied by e cient methods for selection, and by using a suitable penalty function in order to reduce the number of numerical operations and to increase the speed of the optimization toward a global optimum. The e ciency of the present method is illustrated using some examples, and compared to those of previous studies.
SUMMARYIn the process of discrete-sizing optimal design of truss structures by Genetic Algorithm (GA), analysis should be performed several times. In this article, the force method is employed for the analysis. The advantage of using this method lies in the fact that the matrices corresponding to particular and complementary solutions are formed independently of the mechanical properties of members. These matrices are used several times in the process of the sequential analyses, increasing the speed of optimization. The second feature of the present method is the automatic nature of the prediction of the useful range of sections for a member from a list of proÿles with a large number of cross-sections. The third feature consists of a contraction process developed to increase the e ciency of the GA by which an optimal design for the ÿrst sub-string associated with member cross-sections is obtained. Improved designs are achieved in subsequent cycles by reducing the length of sub-strings.
In this article size/geometry optimization of trusses is performed using the force method and genetic algorithm. A large number of design variables consisting of cross‐sectional areas and nodal coordinates are involved in such an optimization, and due to a large number of constraints, the dimensions of the design space are often numerous and in the case of discrete values for cross sections usually discontinuous. In order to avoid local optima, modified genetic algorithms are developed. Furthermore, the force method is employed to improve the speed of the optimization. In the first phase of the described method, the initial geometry of the truss is fixed and near optimum ranges for the cross‐section areas are obtained using the relationships from the force method. In the second phase, the geometry of the structure is altered with the aim of designing lower‐weight structures. Within the Genetic Algorithm a new dynamic penalty function is defined and a modified process of reproduction is presented. A contraction process is also employed for the design space using shorter substrings for the design variables.
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