张量积形式的三维延拓Kantorovich法求解弹性动力学问题

Three-dimensional Continuation Kantorovich Method in Form of Tensor Product to Solve Elastic Dynamics Problems

弹性动力学问题(空间二维,时间一维),如果采用简单形式的三维延拓Kantorovich法,会遇到迭代不收敛的数值困难。采用张量积形式的三维延拓Kantorovich法,取试函数逼近形式为,实现了迭代收敛,解决了这个数值困难。弹性薄膜强迫振动的数值算例显示了迭代过程的收敛性。

If the simple form of three-dimensional continuation Kantorovich method is adopted to solve elastic dynamics problem（one-dimensional time, two-dimensional space）, there may be numerical difficulties of iterative non-convergence. This paper uses three-dimensional continuation Kantorovich method in form of tensor product, takes the trial function approximation form as u（x,y,t）={X（x）}＇[T（t）]{Y（y）}, realizes the iterative convergence and solves the numerical difficulties. The numerical example of elastic membrane forced vibration shows that the convergence of the iterative process.