Numerical inverse hanging method is a kind of efficient form-finding method which can generate shell structures free of bending moments under certain external loads. This paper proposes an improved numerical inverse hanging method based on the vector form intrinsic finite element (VFIFE), for improving the poor convergence performance of the existing method based on the nonlinear finite element method. By using VFIFE to find the equilibrium form of inverted structures and using the local linearization method to adjust the Young's modulus of cable elements, the form-control problem of inverted structures is solved. Moreover, a step rigidization method is proposed, which can realize the form-control of complex structures with multiple target points. Finally, the accuracy and efficiency of the numerical method is verified by observing one Isler's plaster model and comparing its physical shape with the numerical simulating result.@en

Firefly Algorithm (FA, for short) is inspired by the social behavior of fireflies and their phenomenon of bioluminescent communication. Based on the fundamentals of FA, two improved strategies are proposed to conduct size and topology optimization for trusses with discrete design variables. Firstly, development of structural topology optimization method and the basic principle of standard FA are introduced in detail. Then, in order to apply the algorithm to optimization problems with discrete variables, the initial positions of fireflies and the position updating formula are discretized. By embedding the random-weight and enhancing the attractiveness, the performance of this algorithm is improved, and thus an Improved Firefly Algorithm (IFA, for short) is proposed. Furthermore, using size variables which are capable of including topology variables and size and topology optimization for trusses with discrete variables is formulated based on the Ground Structure Approach. The essential techniques of variable elastic modulus technology and geometric construction analysis are applied in the structural analysis process. Subsequently, an optimization method for the size and topological design of trusses based on the IFA is introduced. Finally, two numerical examples are shown to verify the feasibility and efficiency of the proposed method by comparing with different deterministic methods.@en