Topology And Layout Optimization Of Framed Structures Based On Evolutionary Computation

According to different types of design variables, structural optimization can be classified into three levels: sizing, shape and topology optimization, from the easier to the more advanced. Moreover, the structural optimization which takes sizing, shape and topology variables into account is termed as structural layout optimization. Comparing with structural sizing and shape optimization, structural topology and layout optimization are perceived more efficient and challenging, to become a cutting edge issue in the region.The ultralight framed structures have a wide application prospect in the field of aerospace engineering, and the engineering references are relatively limited. Therefore, introducing topology variables into the optimization of these structures becomes particularly urgent. This paper focuses on topology and layout optimization of framed structures. The main contributions of this work are summarized as follows:As the standard evolutionary algorithms are generally proposed for uncons- trained optimization problems, adaptive penalty functions need to be introduced to reform the framed structures optimization problems. Two hybridized evolutionary algorithms(?-CMA-ES and FEPSO-AP) are proposed for framed structures optimization problem by combining state-of-the-art algorithms with adaptive penalty functions, which have been proved both efficient and effective with several benchmarks. Numerical results demonstrate that the proposed algorithms have desirable performance when comparing with other state-of-the-art algorithms.Topology optimization of framed structures with 0-1 programming is known as a difficult task, while the quantitative understanding of its difficulty is quite limited. In this paper, a graph model is established to study the distribution of framed structures topology in a typical design domain. And then, the topological evolution of framed structure is analyzed by using stochastic process, with the purpose to identify the lower bound of convergence rate of this problem. Analysis result finds that the search range of framed structures topology optimization with 0-1 topological variants is rather limited if not consider the coupling between different types of variables.A topology reconstruction method named evolutionary rods deletion determination(ERDD) is developed for solving singular optima of framed structures topology optimization. Different from the generalized sizing optimization employed by GSA, ERDD does not involve slim elements in structural analysis. With the guidance of evolutionary algorithms, ERDD amends the topology of ground structure in real time to handle the singularity of search domain. Numerical results demonstrate that the proposed method solves singular optima problem of framed structures in a simple and efficient manner.A topology reconstruction method named evolutionary nodes combination operator(ENCO) is proposed to extend the topological representation ability of GSA. It has for the first time set up a mapping relationship between the shape and topology variables by identifying and removing the length degenerated elements and the associated nodes. Thus, a bidirectional and non-bias truss topology amending can be realized. Several benchmarks demonstrate that ENCO improves the design quality of framed structure layout optimization remarkably.A structural modeling method named vectorized structure approach(VSA) is proposed for layout optimization of the topological-unknown framed structures. Differing from GSA, the proposed method kicks out the limitation of ground structure by embedding structural topology information into sizing and shape variables. In this way, the topological-unknown structures can be modeled and optimized by VSA-based evolutionary algorithms. The feasibility of VSA is demonstrated by two typical structural optimization cases. Finally, a representative aerospace engineering optimization problem is cited to verify the effectiveness of VSA.