Algorithm And Applications Of Time-continuous Space-time Finite Element Method For Dynamics

Because of the calculation difficulty when solving the dynamic problems, development of the efficient algorithm for the dynamic differential equations is always an important research and the space-time finite element method can provide a feasible approach to it. Compare to the conventional finite element method and common-used time integration methods, the space-time finite element method has some advantages in precision and stability.In this paper, algorithm and applications of time-continuous space-time finite element method for dynamics are researched on the base of Hamilton law of varying action. First of all, with thrice Hermite interpolation to element displacement, the control equation of dynamics is derived in space-time domain. Two groups of space-time finite element formulae solving displacement and velocity are obtained. Secondly, in order to solve the difficulties on program-making, based on linear acceleration assumption, a group of space-time formulae are derived solving displacement, velocity and acceleration. Then the precision and stability of the above three groups of formulae are analyzed.The applications of space-time finite element method in large deformation and active vibration control are initially discussed. At last, programs are made and the analysis of numerical examples demonstrates that the space-time finite element method has excellent precision and stability and is an efficient method for dynamics.