THE PRECISE SPACE-TIME FINITE ELEMENT METHOD FOR NONLINEAR DYNAMIC EQUATION

Based on the Hamilton variable action law, a space-time finite element is deduced. According to the principle of a transfer matrix and one-dimensionality of time, a space-time finite element matrix is transformed to a time-transfer matrix and initial value problems are converted to matrix multiplication problems so as to be solved more easily. In order to ensure the stability of the calculation, the precise space-time finite element method is established on the basis of the precise integration idea, and the calculation formula under the action of series loads is presented. The results of numerical analysis on a linear problem show that this method is very accurate and can be extended to nonlinear dynamic problems. Firstly, regarded a nonlinear solution as a superposition of an initial solution and an incremental solution, and then to calculate the incremental solution using a precise space-time finite element linear solution method, to modify solution gradually, the nonlinear solution can be achieved finally. The results of numerical experiments show that this method is a stable and efficient calculation method on solving nonlinear dynamic problems.