Theoretical Analysis And Experimental Study On Robustness Of Grid And Cable Supported Structures

The grid structures and the cable supported grid structures are major forms of space structure. They are often employed in the city landmarks. However, the structure performance under accidental interference is seldom considered during the design stage at present. It is valid to enhance the structural robustness for structural resistance capacity to the disproportionate destruction. In the existed research, the deference between the structural robustness in working state and in ultimate state is not distinguished. In the meanwhile, there is no quantitative evaluation method and robustness design method for these two different kinds of robustness respectively. What is worse, when a designer tries to arrange cables for the cable supported grid structures, adjustments around the positions chosen according to experience are usually required which can not widely fit to more complicated space structures. Therefore, it is necessary to study the robustness theory of the grid structures and the cable supported grid structures. In the meantime, the cable arrangement theory for the cable supported grid structures is also significant.This paper contains several researches, including the quantitative evaluation index based on the structural robustness, the robustness design for the grid structures in multiple conditions, the robustness design method for the cable supported grid structures, the cable arrangement theory for the cable supported grid structures and the structural experiment. The specific contents are as follows:For both linear and nonlinear structures, the quantitative evaluation index IR1 which is based on the structural robust capability in working state is defined using H2 norm of structural system transfer function. The quantitative evaluation index IR2 which is based on the structural robust stability in ultimate state is defined using H∞ norm of structural system transfer function. In order to provide tools for the optimization calculations below, the existed Big Bang-Big Crunch algorithm is improved to accelerate the convergence.The structural robustness evaluation method based on H2/H∞ theory is raised using the robust capability and robust stability quantitative evaluation index. The properties and the physical meanings of the robust capability and robust stability quantitative evaluation index are compared. The connection of the robust capability and robust stability with the strain energy and buckling is illustrated by an example. Moreover, the effect of the capability (the sections of elements, the constraint conditions and the stiffness distribution), the accidental damage and the critical elements on the robust capability and robust stability is analyzed.The robust capability is chosen as optimization objective, and, the robust stability is chosen as constraint. Then the topology optimization of continuum in multiple conditions is applied to search for the best distribution of structural stiffness and structural material which has the best robust capability. Finally, the robustness configuration is obtained which could provide a reference to the arrangement of the main elements. The robustness design for the grid structure in multiple conditions is realized. Several examples are calculated to verify the rationality of the robustness configurations.Introduce the initial prestress through the initial strain. Then the robustness design method is raised applying the robustness configuration and prestress combined optimization method to guide the design of structures which have better robust capability. The effect of the load distribution, the initial prestress and the trusses on the structural robustness configuration are discussed. The displacement vector diagrams and the properties of the structures with different material distributions are analyzed and compared to verify the rationality of the robustness configurations of the cable supported grid structures.For the cable supported grid structures with complicated upper surface, the robustness configuration of the upper shell is designed applying robustness design pattern first. Then the curves where the cables should be located are found out applying the Hough transfer method. The endpoints of the cables are optimized using the modified Big Bang-Big Crunch algorithm. The rational arrangement of cables is obtained by the cable arrangement theory finally. The cable arrangement theory is applied on the cable supported hyperbolic flat shell structure and the heart-shaped shell structure to provide a reference for engineering practice. The cable supported cylinder shell structure and the cable supported sphere shell structure are designed by the cable arrangement method and are compared with beam-string and suspended-dome structures to verify the rationality of the method.Two different cable supported hyperbolic flat shell structure models are made according to the robustness design and the conventional design respectively. They are tested in two different interference conditions as static overload and dynamic impact. In the test, the displacement responses are measured, the failure patterns are observed, in the meantime, the robust capability and robust stability quantitative evaluation indexes are calculated. It is verified that the structure designed applying the robustness configuration has better robustness.