An earthquake-triggered fire domino scenario (E-FDS) is an example of a typical multi-hazard coupling event. The seismic damage can affect the fire resistance of engineering structures, leading to significant mutually amplified phenomena. In this work, a two-stage experimental program is designed to expound the earthquake-fire coupling failure mechanism of steel cylindrical tanks (SCTs). Quasi-static tests are adopted to simulate the damage characteristics of SCTs under seismic excitation (Stage I). Fire tests are adopted to investigate the fire-resistance performance of pre-damaged SCTs (Stage II). The influences of seismic damage on the fire resistance of SCTs are particularly of interest. Three potential seismic damage degrees are considered. The experimental results show that tank specimens exhibit typical diamond-shaped buckling after Stage I. The coupling failure analysis of SCTs is conducted through sequential thermodynamic coupling simulations. Due to factors such as geometric deformation, residual stress, and thermal radiation absorption capacity, the fire resistance of SCTs is significantly attenuated by seismic damage. For the three damage states, fire resistance time attenuation coefficients (0.868, 0.716, 0.511) and critical temperature attenuation coefficients (0.910, 0.779, 0.672) were obtained. This work provides pivotal insights into the mutually amplified phenomena in E-FDSs.@en

Hanging models play an important role in shaping a structure since a very early age, and were favored by A. Gaudi, H. Isler, F. Otto and other architects or engineers. Nowadays, with the development of numerical analysis theory and computer technique, it is more accurate and convenient to simulate these physical models via numerical means. Based on the background, this paper presents a numerical form-finding method of gridshell structures generated from hanging-chain models by using Dynamic Relaxation method and the NURBS technique, which aims to obtain more complex structural forms with multiple control points. This method uses global NURBS surface interpolation to describe the initial cable-net model passing through the given target points, which serve as the fitting points of the NURBS surface. The cable elements of the cable-net are not allowed to elongate after form-finding, and clearly, this kind of cable-nets belongs to geometrically unstable system, whose form-finding process of it has a very strong nonlinearity. To solve this problem, it uses the Dynamic Relaxation method, which can complete the form-finding of geometrically unstable systems but with some special sets, to get the equilibrium form of the hanging cable-net under the gravity. However, this structural form may no longer pass through the given target points, and then it introduces the inverse iteration method to adjust the coordinates of the fitting points of the NURBS, which actually means to find the initial structural form which after form-finding can just right meet the target requirements. At last, some numerical examples are presented to demonstrate the validity of the proposed method in this paper.@en

In current optimization methods for free-form shells, the shape and topology are usually optimized separately. These methods are based on the assumption that the shape and topology of a shell influence each other only slightly, but this is not always correct. Moreover, different parameterization models are used in the shape optimization and topology optimization of free-form shells, which brings difficulties to carry out the integrated optimization. To solve this problem, an integrated method is proposed for simultaneously optimizing shape and topology for free-form shells. A uniform parameterization model based on NURBS solids is established to parameterize the free-form shells. In this model, only a small number of variables are used to describe both the shape and topology of the shell. In this way, the integrated optimization problem can be simplified, thus decrease the computational complexity. The integrated optimization of shape and topology is a complicated and large-scale optimization problem. Solving this problem requires a suitable optimization method. In this paper, the Method of Moving Asymptotes (MMA) is adopted. Finally, numerical examples are presented to address the importance of the optimization sequences and show the effectiveness and application of the proposed method.@en

Discrete networks is a kind of form-active structural system which actively change its shape under varying load conditions. And for this kind of structural system, form-finding is the initial and essential part in their design process. Before the computer age, people complete the form-finding process using physical models, while with the advances in computational techniques, the research has focused on the numerical form-finding methods since the 1960s. A brief discussion on several numerical formfinding methods is presented in this paper. Firstly, two relatively mature numerical method, Dynamic Relaxation method and Force Density method, are introduced conceptually. And then, a newly developed numerical method, the Vector Form Intrinsic Finite Element method, is presented in more detail. At last, with a replacement of the calculation of the internal force of the element which obeys the Hooke's Law by the product of the force density and the length of the element, two derived methods based on the above three methods are proposed in this paper. Moreover, several numerical examples of hanging networks are shown to illustrate the validity and characteristic of the VFIFE method and the two newly proposed derived methods.@en

By using inflatable moulds and then spraying cellulose-water mixture, one ice dome and two ice towers were built in Harbin in December 2016. During the whole process, form-finding of the inflatable moulds as well as the construction of these ice composite shell structures are very important for the final results. The mould for the ice dome structure was a result of the manipulation of a synclastic membrane with a rope net. The mould for the ice tower structure consisted of some anticlastic surfaces. Form-finding of the inflatable moulds was conducted by the parametric tool “EasyForm” which is a self-programed plug-in in Grasshopper based on Vector Form Intrinsic Finite Element method. In a low-temperature work environment (-10 ℃ and below), the ice shell structures were constructed on the inflatable moulds. The cellulose-water mixture was sprayed in thin layers continuously and uniformly in order to make the surface of a shell of cellulose-reinforced ice. The construction process is introduced detailedly in this paper.@en

A greedy heuristic-based algorithm was put forward to obtain the approximate optimal solution for the DUDC(discrete unit disk cover) problem within polynomial time. Firstly, discrete cells were generated to represent the 2D plane. Then, alternative sets which can cover certain amount of target points were built. A greedy algorithm was articulated to find a minimal combination of the alternative sets, and full coverage of all target points was realized. The minimal covering circles were calculated considering the position of each point in the sets. The center of the minimal covering circles was selected as the location. Based on a case study, the effectiveness of the proposed algorithm was validated. The factors of influence the performance of the algorithm were also discussed and ratio of time complexity and approximation was analyzed.@en

A greedy heuristic-based algorithm was put forward to obtain the approximate optimal solution for the DUDC(discrete unit disk cover) problem within polynomial time. Firstly, discrete cells were generated to represent the 2D plane. Then, alternative sets which can cover certain amount of target points were built. A greedy algorithm was articulated to find a minimal combination of the alternative sets, and full coverage of all target points was realized. The minimal covering circles were calculated considering the position of each point in the sets. The center of the minimal covering circles was selected as the location. Based on a case study, the effectiveness of the proposed algorithm was validated. The factors of influence the performance of the algorithm were also discussed and ratio of time complexity and approximation was analyzed.@en

Shell structures generated from hanging models have structurally efficient forms. Form-control of these shells, which aims to obtain structural forms with single- and multiple target heights due to some architectural requirements, is discussed in this article. First, the vector form intrinsic finite element method is applied to generate the equilibrium form of hanging membranes and thus shell structures. Subsequently, the form-control problem is discussed, which aims to generate a structural form subject to given target height constrains. By introducing the Local Linearization Method to adjust Young’s modulus of the initial structural model, a form-control strategy to generate the equilibrium structural form with a single target height is proposed. By introducing the Inverse Iteration Method to adjust the geometry of the initial model, a form-control strategy to generate the equilibrium structural form with several target heights is proposed. Moreover, to verify the effectiveness of the vector form intrinsic finite element method and form-control strategies, structural analyses and shell behavior assessment of these shells are conducted. These strategies are effective and efficient, which can help architects or engineers to determine structurally efficient geometries in the design process much more easily.@en

Shell structures generated from hanging models have structurally efficient forms. Form-control of these shells, which aims to obtain structural forms with single- and multiple target heights due to some architectural requirements, is discussed in this article. First, the vector form intrinsic finite element method is applied to generate the equilibrium form of hanging membranes and thus shell structures. Subsequently, the form-control problem is discussed, which aims to generate a structural form subject to given target height constrains. By introducing the Local Linearization Method to adjust Young’s modulus of the initial structural model, a form-control strategy to generate the equilibrium structural form with a single target height is proposed. By introducing the Inverse Iteration Method to adjust the geometry of the initial model, a form-control strategy to generate the equilibrium structural form with several target heights is proposed. Moreover, to verify the effectiveness of the vector form intrinsic finite element method and form-control strategies, structural analyses and shell behavior assessment of these shells are conducted. These strategies are effective and efficient, which can help architects or engineers to determine structurally efficient geometries in the design process much more easily.@en

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