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Theoretical and Experimental Study on Robustness of Spatial Latticed Structures

Author: ZhangCheng
Tutor: GaoBoQing
School: Zhejiang University
Course: Structural Engineering
Keywords: spatial latticed structures robustness robust H_∞control size optimization topologyoptimization Genetic Algorithm experimental study
CLC: TU31
Type: PhD thesis
Year: 2013
Downloads: 29
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Abstract

As the most widely used spatial structure form, spatial latticed structures have the features of large span, multi-components, and serious destruction consequences. But during the design procedure, little consideration is taken on the accidental interference. In recent years, spatial latticed structures increasingly suffer from man-made accidents and natural disasters, and collapse events have occurred sometimes. Enhancing the structural robustness can reduce its susceptibility to interference, and increase the resistance capacity to disproportionate destruction. Now the research of structural robustness is mainly focused on trusses and frame structures, while the study on spatial latticed structures is rare, and effective numerical expression and feasible design method are lack. The research of the robustness of spatial latticed structures is valuable for theory and engineering.This paper conducts research from several levels, including quantitative evaluations of structural robustness, the robustness of the typical spatial latticed structures, and optimization design methods based on robustness. The specific contents are as follows:Taking basis in robust H∞, control theory and the attributes of structures, a framework for quantitative assessing structural robustness is proposed according to the qualitative statement. Taking a SDOF system and truss structures as examples, properties and physical interpretation of the H∞, structural robustness index were clarified, and factors affecting structural robustness were studied. The results indicate that H∞structural robustness index can effectively and reasonably reflect structural robustness.For nonlinear systems, the uncertainties were expressed by convex model, and specific formula for elastic-plastic structural robustness was given, using L2norm as an evaluation of signal. Influence of elastic-plastic, redundancy and the uncertainties of loads and structural attributes were analyzed. The above two parts of research lay foubdation for structure analysis and design based on robustness.For the typical spherical latticed shells, including Kiewitt dome, Schwedler dome and ribbed type, and cylindrical latticed shells, including one-way orthogonal grid and three-way grid, influence of geometric parameters and grid configurations on the robustness of single-layer reticular shells were analyzed through parametric analysis. Then the components importance indices were calculated by component removal method. Furthermore the critical path for robustness was obtained. Finally, taking an engineering practice for example, the impact of different forms of supports to robustness was discussed.Based on large scale numerical calculations for different forms of spaec grid structures subjected to earthquake, dynamic failure modes and characteristics were analyzed, which showd fuzziness. Using fuzzy C-means method, the failure modes were classified into three categories: instability based progressive collapse, strength based overall collapse and strength based progressive collapse, and the numerical prototypes of failure modes were obtained. Finally the steps to analyze robustness of spatial latticed structures subjected to earthquake are proposed.Setting H∞, structural robustness indicators as the target, size level structural robustness optimization was investigated, using the genetic algorithm based on multi-elitist selection. The proposed method was verified by the examples of planar and three-dimensional truss structures, and the reasonable number of individuals in populations of genetic algorithm was explored either. Typical single-layer spherical and cylindrical latticed shell structures were optimization then, and reasonable cross-section arrangements were obtained. The results were verified by the robustness indicators based on bearing capacity and displacement.Using the SIMP material model to describe the stiffness of material, topology level structural robustness optimization was investigated. Robustness based design of spatial latticed structures is formulated as a continuum topology optimization problem, where the structural robustness is considered as the optimization objective. The feasibility and rationality of the method were verified by the plane stress model. As an example, robustness configurations of a single-layer spherical and a hyperboloid shell were obtained by robustness based structural design, which could provide an effective method for the topology optimization of spatial latticed structures.Two models of single-layer grid structures were designed by conventional and robustness based method respectively. Different interference scenarios were simulated by static and impact experiments, and robustness of the models were analyzed and compared. The results show that robustness based structural design improves structural robustness effectively.This paper systematically studied the robustness of spatial latticed structures. The research results can preliminarily provide theoretical basis and design methods to effectively prevent the disproportionate consequences.

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