Topology Optimization Analysis For Framed Structures Based On The Improved Firefly Algorithm

Structure topology optimization is an effective way to realize the reasonable, natural and efficient of structures, which is conform to the theory of structural morphology of seeking the harmonious of elegant form and reasonable performance of structures. Therefore, it is of great significance that the topology optimization of framed structure is studied in this paper.Previous studies on topology optimization of framed structures are mainly in view of simple structures which made up of less number of bars such as 15 plane truss, 25 space truss, etc. On the contrary, the research of the complex structures which made up of larger number of bars is less or can only obtain less ideal results.On the above research background, this object has carried out some research works as follows:(1) Considering the highly nonlinear and multi peak of topology optimization of framed structural problem, this paper introduces the firefly algorithm which has the function of automatic population division, strong search ability and good at solving the higher dimension and higher nonlinear optimization problem. In order to apply the algorithm to topology optimization of framed structures, the Improved Firefly Algorithm(IFA) which suitable for solving large solution space optimization problems and has an excellent performance is proposed by embedding the random-weight and enhancing the attractiveness. And through the experiment of test function excellent performance of IFA is verified. In addition, the IFA is discretized to apply to topology optimization of framed structures.(2) An optimization method for topology optimization of framed structures based on the IFA is put forward in this paper. Firstly, the topology optimization problem of framed structures is formulated based on the ground structure approach. Then, a new topological coding is puts forward for large bar structure for large scale bar structures to reduce the probability of the presence of unstable systems. The essential techniques of variable property parameter of materials technology and geometric construction analysis are applied in structural analysis. And then, adaptive penalty function is applied to deal with the individual which violate the constraints which can determine punishment function value automatically according to the degree of constraints violation of individual. Subsequently, topology optimization of framed structures based on the IFA is put forward. Finally, the numerical examples are shown to verify the feasibility and efficiency of the proposed method by comparing with different deterministic methods.(3) The wide applicability of the method proposed in this paper is verified by several examples. At the same time, a variety of feasible solutions for structure design can be given by this method. Using this method, topology optimization problem of plane truss, spatial truss, plane frame and single-layer reticulated shell structure are solved under different optimization objective. In these examples, the influence of different optimization objective is analyzed and the relation of elegant form and reasonable performance of structures are explored.