Research On Precise Element Method For Analysis Of Frame Structure

Along with the rapid development of the high-rise building, the frame structures are more and more popular in China. The precise analysis on the mechanical properties of the frame structure is significant. Structural analysis is the key to the design of engineering structures. Either the precise analytical method or traditional approximate methods is of defective more or less. Therefore, based on the homogenization high precision direct integration technology and matrix theory,this paper has proposed a precise element method of the analysis on frame structure. The precise element method is a new structure analysis method. It overcomes the deficiencies of the finite element method, whose accuracy depends on elements'orders. The precise element method also breaks through the limitation of the transfer matrix method in the application of multi-storey frame structures. Because the control equation of each element is solved by the homogenization of precise integration, the computation accuracy can achieve the full accuracy of the computer. Thus its accuracy is extremely high. The variables of algebra equations are only the state variables at every node. Compared to the finite element method, the numbers of unknown variables are greatly reduced, so that the computation efficiency is improved effectively. The precise element method can be used to analyze any form of continuous structures. Comparing to the traditional transfer matrix method, it has the advantage of wide application range. Furthermore, as it doesn't require to equivalent the pressures loaded on the structure, the more complex external pressures are, contrasting to other structural analysis methods, the more significant the advantages of the precise element method are.Firstly, this paper has described the existing structural analysis methods, including the traditional structural mechanics method, transfer matrix method and finite element method. They have their own advantages, but they also have some deficiencies. Traditional methods, especially the analytical method has the advantage of high accuracy. However, their application range is limited. The finite element method is used widely. Because it's an approximate method, its accuracy is affected by many factors. The accuracy of the transfer matrix method is high, but it can't analyze multi-layer structures. It is limited in the analysis of beam structures and single-layer structures. By the comparison with the advantages and shortcomings of the above methods, a precise element method of the analysis on the frame structure is proposed in the paper.Secondly, on the basis of the homogenization high precision direct integration technology and matrix theory, taking the plane and space frame structure as an example, we develop the precise element method of static and dynamic analysis. The details of the analysis processes are also described in this paper. The emphasis is on the derivation of the structural element analysis, including the static and free vibration analysis of the direct beam and curved beam. The deformation compatibility relations and equilibrium equations of the nodes are the key to the whole structural analysis. The way to deal with these relationships is given in this paper. At the same time, we also give the solutions for the case that structures have external loads or special connections. Examples showed that the method is correct and effective.Finally, the paper has summarized this research, and has looked into the directions and areas of the further research of precise element method.