Optimization Theory And Reliability Analysis Of Prestressed Space Grid Structure

Prestressed space grid structure equipped with cable has a series of merits, such as beautiful modeling﹑reasonable force﹑good economic results and so on. This makes the new structure externalize powerful vitality, it's applied range is more and more extensive and it's construction scale is more and more ambitious. In order to promote the development of this kind of structure, on the basis of briefly introduction of basic overview and principle of prestressed space grid structure, the paper analyzes the optimization principle of prestressed space grid structure equipped with cable systematically from two aspects of continuous variables and mixed variables, and analyzes the system reliability of this structure deeply. At the meantime, the paper optimizes the system reliability of structure based on the stiffness and strength. The main contents of this article is summarized as follows:1. Based on the analysis and summary of relevant literatures at home and abroad, the paper sets forth the basic overview and principles of prestressed space grid structure, introduces the cable layout﹑prestressed loading﹑mechanism of force and other relevant contents, derives the element stiffness matrix of prestressed cable with"direct stiffness method"and lay the foundation of finite element analysis of the structure.2. The paper reviews the common algorithms of structural optimization designing, and introduces the relevant contents of the complex algorithm and genetic algorithm adopted in the paper in detail according to the characteristics of design variable of prestressed space grid structure. When the two algorithms are used in optimization analysis of prestressed space grid structure, the paper gives improvement measures according to the characteristics of slow convergence rate of complex algorithm in later period. Aimed at the long searching time﹑Easy to prematureness and poor local optimization ability in genetic algorithm, the paper gives the corresponding measures for improvement to make it applied to this structure more effectively.3. In the optimization analysis of prestressed space grid structure, we need to treat two design variables corresponding to cross-section of bar and prestressed. If dividing the two variables into different space, it will reduce optimization results and even make the most optimal solution can not be observed. In the paper we put the two variables in a same space and use appropriate optimization algorithm to optimize the prestressed space grid structure. First, we give optimization model and steps through regarding the cross-section of bar and prestressed as continuous variable and using multiple complex method to optimize. Second, in practical project, regardind the cross-section of bar as discrete variable in line with steel specifications and regarding the prestressed as continuous variable, using mixed-variable coding genetic algorithm to optimize the prestressed space grid structure, we give optimization model and steps too. The example shows that the two optimization methods of prestressed space grid structure are rational and effective.4.The high-order statical indeterminacy determines that the structural system reliability analysis is complex in prestressed space grid structures. Based on the summary of structural reliability analysis method, the paper introduces the relevant contents of branch-bound method and PNET method briefly, and analyzes the system reliability of prestressed space grid structure deeply. The paper gives the strength safety margin equation of structure system, derives the stiffness safety margin equation of system, analyzes the relevant problems between failures modes of systematic strength and stiffness, and derives the formula of Reliability Index of systematic strength and stiffness.5. On the basis of analysis of system reliability of prestressed space grid structure, the paper optimizes the reliability based on stiffness and strength of system, establish the optimization model with system reliability as constraints and structural weight as objective function . In the optimization analysis of prestressed space grid structure with improved genetic algorithm, the reliability constraints is considered into the fitness function of individual in the form of penalty function and the paper gives the specific processes of structural optimization combined with finite element theory﹑system reliability theory and genetic algorithm theory. The example shows that the structural optimization theory based on the structural system reliability is practicable in the paper.