Structural optimization and dynamic analysis for double-layer spherical reticulated shell structures

Abstract

This paper is concerned with the geometrical optimum design and the aseismic analysis of double-layer reticulated shell structures. The characteristic of free vibration of reticulated shell structures, with respect to geometric parameter, is investigated. The variations of the eigenfrequency of shell structures, with respect to the ratio of height-to-span, span, grid division frequency and thickness of shell, are discussed. The Newmark method is used to calculate the stresses and displacements of the reticulated shell structure under earthquake action. The analysis results show that under a specified span, the eigenfrequency of the structure increases with the increase of the height-to-span ratio and then decreases afterwards. Therefore, there exists an optimum height-to-span ratio resulting in an optimum stiffness at the specified span. The optimum value of the ratio is found to be between 1/3 and 1/4 from the simulation study presented in this paper. At a specified height-to-span ratio, the increase of the value of structural span greatly reduces the eigenfrequency of the structure and then decreases the global stiffness of the structure. At the specified span and the specified height-to-span ratio, the eigenfrequency of the structure has a minor increase with the increase of the thickness and the grid division frequency of the reticulated shell structure. The partial double-layer reticulated shell structures have less stability compared with double-layer reticulated shell structures, but more stability in comparison with single-layer reticulated shell structures. The 1/6 partial double-layer reticulated shell structure has a best performance-to-price ratio. In other words, it has a higher buckling load, with smaller material consumption, compared with other partial double-layer reticulated shell structures. It is proposed to adopt the 1/6 partial double-layer reticulated shell structure in engineering if a double layer reticulated shell structure is required.