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SUMMARYStructural robust optimization problems are often solved via the so-called Bi-level approach. This solution procedure often involves large computational efforts and sometimes its convergence properties are not so good because of the non-smooth nature of the Bi-level formulation. Another problem associated with the traditional Bi-level approach is that the confidence of the robustness of the obtained solutions cannot be fully assured at least theoretically. In the present paper, confidence single-level non-linear semidefinite programming (NLSDP) formulations for structural robust optimization problems under stiffness uncertainties are proposed. This is achieved by using some tools such as S-procedure and quadratic embedding for convex analysis. The resulted NLSDP problems are solved using the modified augmented Lagrange multiplier method which has sound mathematical properties. Numerical examples show that confidence robust optimal solutions can be obtained with the proposed approach effectively.

This article presents a study of airflow pattern inside a five-story wind-driven naturally ventilated atrium building. Firstly, field measurement conducted in the atrium building reveals the existence of reversed flows from the atrium to windows, which could cause air cross-contamination between floors during the period of an infectious disease outbreak. The computational fluid dynamics technique was then employed to further investigate the airflow pattern inside the building, under different wind directions and opening ratios. It is found that the airflow pattern inside a wind-driven naturally ventilated atrium building is very sensitive to the oncoming wind direction. Under parallel and perpendicular incident wind directions, the existence of adversely reversed flows in a certain floor and the re-entry of used air from an upper floor into its adjacent lower floors through the atrium results in the decrease of indoor air quality and the effective air exchange through windows. Nevertheless, the building has good natural ventilation performance under oblique incident wind direction, although the expected role of the atrium is still not fully achieved. In addition, the improvement of airflow pattern inside wind-driven naturally ventilated buildings cannot be achieved by simply modifying the opening ratios. Practical application: Considering the indoor airflow pattern could substantially influence the elimination efficiency of pollutants and overheated air, this study is expected to help designers and engineers who are considering the use of an atrium at the design stage to have a better understanding of the airflow pattern inside a wind-driven naturally ventilated atrium building.

Pre-tensioned cable net systems are being increasingly used in building fac xades. Due to the geometrical nonlinearities exhibited by the cables, people have to resort to the nonlinear response history analysis approach for analyzing the seismic responses of cable net structures. This article studies the effectiveness of linear response spectrum analysis method for nonlinear cable net systems. An energy-based parameter is used to describe the structural stiffness, based on which the equivalent single-degree-of-freedom systems for cable net structures with various irregularities could be established. By means of a pseudo-energy-equivalent approach, the nonlinear equivalent single-degree-of-freedom systems are transformed into linear ones, whose seismic responses are reasonable approximations of the accurate nonlinear results. It is revealed that the vibrating period of the equivalent linearized system is close to that of the nonlinear equivalent single-degree-of-freedom system, indicating that the nonlinear effects on seismic responses of cable net structures are not serious. Inspired by the theoretical analysis, large-scale numerical computations are carried out to check the accuracy of linear response spectrum analysis for nonlinear cable net structures. In the numerical computation, four cable net models are excited by 80 seismic records. Considering 19 different degrees of earthquake intensity, a total number of 6080 nonlinear response history analyses are executed, and the results are compared with those obtained from the linear response spectrum analysis. From the numerical results, the linear response spectrum analysis yields proper overestimations of seismic responses with errors within 35%, which may lead to slightly conservative yet acceptable designs in engineering practice. Given all the aforementioned discussions, it is concluded that the linear response spectrum analysis method is effective for seismic response analysis and aseismic design of nonlinear cable net structures.

The step-by-step modeling method considering nonlinear effects is an effective method for analyzing the mechanical behavior of steel structures during construction. However, two problems have limited the widespread application of the traditional step-by-step modeling method: the positioning of newly assembled members and the transformation of the stiffness matrix and the nodal load and displacement vectors between different stages of construction. In this article, a new concept of ''two moments of a construction stage'' (the initial and final moments of each construction stage) is proposed to improve the step-by-step modeling method. Based on this concept, an improved step-by-step modeling method, which considers the modified design configuration positioning principle for newly assembled members and provides a method for modifying the structural stiffness matrix at the initial moment of any construction stage, is proposed. A calculation program block based on the proposed method is compiled to analyze the mechanical behavior of a plane frame and a plane shallow arch during construction. The mechanical behavior of an engineering application, the connective corridor of Shanghai International Financial Centre, is also analyzed using the proposed method, and the calculated results are compared with the monitoring results. The numerical results show that the modified design configuration positioning principle is applicable for the positioning of newly assembled members and that the modification method for the structural stiffness matrix and the nodal load and displacement vectors at the initial moment of a construction stage efficiently solves the problem of their transformation between different stages of construction. The improved step-by-step modeling method proposed in this article is more valid and accurate than other methods for analyzing the mechanical behavior of steel structures during construction.