China's high-rise buildings are developing rapidly, and the number and height of buildings are increasing. For architecture, stability is the most important. With the height of the building getting higher and higher, the lateral displacement and internal force of the building will gradually increase, and when the lateral displacement and internal force exceed the bearing capacity of the building, they will deviate. Therefore, it is very important to calculate the bearing capacity of buildings in advance, and it is necessary to use the mechanical analysis method of high-rise buildings.
1 analytical methods of ordinary differential equation solver, finite strip method and spline function method
1. 1 Analysis method of ordinary differential equation solver
Ordinary differential equation solver is a mechanical analysis method of high-rise building structures that has been discovered and gradually put into use in recent years. With the increase of building height, the discretization method gradually exposes many problems, which seriously hinders the structural mechanical analysis of high-rise buildings. In the past, the building floor was not high, so the discretization method was very suitable, and the results of mechanical structure analysis could be obtained quickly. However, with the gradual increase of floors, the use of discretization method makes the calculation more complicated. With the increase and complexity of data, it becomes more and more difficult to solve the problem. In this context, ordinary differential equation solvers came into being. Its greatest advantage is that the solution process is greatly simplified, the operation process becomes concise, and the data can be analyzed quickly and the equation can be solved. Generally speaking, the ordinary differential equation solver has fewer equations for mechanical analysis of high-rise buildings, and can initially set the required error range, which means that the final analysis result can be more accurate and meet the initial requirements. Ordinary differential equation solvers have many advantages, but this does not mean that ordinary differential equation solvers are perfect. As far as the application of ordinary differential equation solver is concerned, the application scope of ordinary differential equation solver is still limited, and the analysis method of ordinary differential equation solver is not mature enough, which needs further improvement and experimental verification. In addition, the research on solving ordinary differential equations abroad is in-depth, and the research results and experimental results abroad are generally ideal. Therefore, domestic researchers can refer to foreign research results.
1.2 analysis methods of finite strip method and spline function method
The structural design of high-rise buildings in China is mostly regular, and there are many similar situations. Because the structural design of buildings is generally determined by local climatic conditions, geological conditions and hydrological conditions, different regions will have different architectural designs. For example, there are many castles in Europe and many platform buildings in China. The structural mechanics of high-rise buildings is also regular, and the structural design of high-rise buildings is generally simple. In this case, if the ordinary differential equation solver is used, the operation will become complicated and ill-conditioned equations will be generated, which makes the calculation process more difficult, so the finite strip method can be used. Finite strip method is a simple operation analysis method, which uses the simplest polynomial, so it can realize effective operation. In addition, based on the finite strip method, a method called spline function method is developed. Spline function is piecewise polynomial, which is more widely used than finite strip method. The similarity between finite strip method and spline function method is that they can both be applied to structural mechanics of high-rise buildings with certain regularity.
2. Structural analysis method based on zoning mixed finite element, elastic-plastic dynamics and structural optimization theory of high-rise buildings.
2. 1 partition mixed finite element analysis method
The zonal mixed finite element analysis method is based on the zonal generalized variational principle. If we study the block hybrid finite element analysis method, we must first have a basic understanding of the block generalized variational principle. The partition generalized variational principle is put forward for the growing finite element, because with the development of finite element, many types and characteristics have appeared. Some of these features have * * * characteristics. In order to solve these finite elements effectively, a block generalized variational principle is proposed. Its essence is classified analysis, which classifies different finite elements and analyzes and solves them on the basis of classification. The zonal mixed finite element method is developed from the zonal generalized variational principle. The zonal mixed finite element method divides the elastic body into two regions, and different elements and unknown quantities are used in different regions. Through this partition calculation and analysis method, the conditions and quantity of the equation can be guaranteed to meet the requirements. The advantages of zonal hybrid finite element method are obvious. First of all, it is very practical, because zoning is very flexible and can effectively cover many types of high-rise buildings. Secondly, the accuracy is very high, because the calculation method of block mixed finite element is the simultaneous solution of target block and target unknown, so the final result is comparable to the actual result. Therefore, the zonal mixed finite element method will be more widely used.
2.2 Elasto-plastic dynamic analysis method of high-rise building structure
The elastic-plastic dynamic analysis method of high-rise building structure has been applied in China for a long time. With the continuous development of related scientific research, the elastic-plastic dynamic analysis method of high-rise building structure has become one of the most widely used and effective methods. The biggest difference between this method and the first two methods is that the data obtained are different. The elastic-plastic dynamic analysis method of high-rise building structure collects relevant data information through seismic waves, and the obtained seismic wave information can be directly used without secondary processing. The data are embedded in the structure, and the related equations are calculated and analyzed by mathematical and physical methods, so as to obtain the relevant structural mechanics information of high-rise buildings. Under different earthquake levels, the elastic and inelastic changes of the structure, structural component changes and structural deformation changes are simulated. Through this information, the mechanical analysis of high-rise buildings can be effectively carried out, so as to realize the earthquake resistance and stability of high-rise buildings and ensure the safety of buildings. But this method also has a very big drawback, that is, it is too idealistic. Because the seismic wave obtained by this method is simulated, not real seismic wave, the analysis data obtained by virtual seismic wave will be deviated from the real seismic wave, and accurate data can not be obtained for elastic-plastic dynamic analysis of high-rise buildings. At present, there are different opinions about this method in the industry. Many researches on artificial random input seismic waves at home and abroad are relatively accurate, and the simulation data based on it are also close to the actual situation. Therefore, as long as we consider the related errors and improve the technology and related equipment, the elastic-plastic dynamic analysis method of high-rise buildings in the future will be recognized by most people.
2.3 structural analysis method of optimization theory
The previous analysis method was passive analysis and research, while the structural analysis method of optimization theory was active design and simulation. This method is based on the optimization theory of mathematics. In short, the structural analysis method of optimization theory is to find the most suitable structural analysis method among many structural design schemes to optimize the effect. It is carried out with the help of computer technology. Through the polarization design of a space building structure, on this basis, relevant analysis is carried out, such as the optimal number analysis and optimal layout of shear walls in frame-shear wall structure, so that the designed structure has the strongest adaptability. The biggest advantage of this method is that it can grasp the essence of the problem and establish the mathematical model of the optimal stiffness of shear wall, which is very convincing to some extent. The structural analysis method of optimization theory is still being further explored and improved, and its future development is worth looking forward to.
3 Conclusion
At present, the structural mechanics analysis methods of high-rise buildings show an obvious classification trend. For example, finite strip method and spline function method are all aimed at regular structural mechanics of high-rise buildings. The methods listed by the author are currently the mechanical analysis methods of high-rise building structures with high attention, but from the development direction, the mechanical analysis methods of high-rise building structures are developing in the direction of subdivision, pertinence, simplification and high efficiency. With the continuous development of scientific research, there may be better mechanical analysis methods for high-rise buildings in the future.
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