Application And Research Of Precise Integration Algorithm About Space-time Finite Element

Dynamic problem is one of the important topics in the field of civil engineering. Many problems are required to accurately calculate dynamic response of the system, such as structural vibration control, structural analysis and optimization control etc, in order to provide good response data for structural design, testing and control. Rational, effective and high calculation accuracy, less time consuming and easy to program of numerical method is a hotspot in the dynamical field.Most of the existing numerical analysis method are based on the continuous time system, but the applied mechanics finite element, the control and signal processing, the transient field analysis needs discrete time systems, and need to consider different time of the displacement vector. So using the finite element on the time coordinates, combining time domain with space domain needs further research and development.Space-time FEM can greatly improve the calculation speed, smaller amount of calculation and easy programming. It will more advantage in large structural calculation. The method can solve the problem of moving load of structural vibration, fluctuation problem, contact problem, the geometric nonlinear problem, heat conduction problem, modern control problem, damage problem etc. In these fields, the space-time FEM is better than implicit algorithm and better than the explicit algorithm too, and can solve the nonlinear problem. In this paper, numerical example shows, compared with the traditional finite element method, the space-time FEM method has accuracy, convergence and stability advantages in solving time-dependent questions.In this paper, the main research contents are as follows:Based on the Hamilton law of varying action. Space-time FEM is deduced. And using one-dimension of time, the space-time transfer matrix is constructed. According to the precise integration method, precise space-time transfer matrix is given, so as to guarantee the stability of the solution and reduce the size of the solution. This paper further gives the substructure space-time finite element method, it can solve the problems of large calculation, simultaneously solve coupling problem of the traditional substructure internal nodes and external nodes.By space-time FEM method, this paper analyzes some strongly nonlinear problems such as structural damage analysis and hoisting in construction. It proves space-time FEM has a beneficial effect. Finally, this paper applies the space-time FEM combining with Open inventor to compile a set of 3d construction hoisting simulation software.At present, application of the spatial domain finite element is perfect, but there are wide developmental spaces in the study of space-time FEM, so this article will further explore.2) by the method of structural damage analysis, structure construction hoisting strongly nonlinear problems such as dynamic analysis, proved that the method has a good effect.At the end of the paper used the space-time finite element combining with Openinventor compiled a set of 3 d display is easy to control the construction hoisting simulation software.At home and abroad for application of finite element in the spatial domain research has quite perfect, and the study of space-time finite element method, has made great progress, but there are still a broad space for development, this article will further explore..