弹塑性体中波传播问题的间断Galerkin有限元法

DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR WAVE PROPAGATION PROBLEMS IN ELASTO-PLASTIC CONTINUA

对结构动力学和波传播问题提出了一个时域间断的Galerkin有限元法 .其主要特点是对问题的半离散场方程的节点基本未知向量及其时间导数向量在时间域中分别采用三次多项式和线性 (P3 P1 )插值 ,节点基本未知 (位移 )向量在离散的时间段之间将自动保证连续 ,而仅仅是它的时间导数 (速度 )向量存在间断 .在非线性条件下 ,与现有的间断Galerkin有限元法相比 ,明显地节省了计算工作量 .对所提出的间断Galerkin有限元法发展了弹塑性非线性问题的隐式和显式算法 .数值计算结果表明了所提出方法的有效性 ,以及相对基于连续Galerkin有限元法的Newmark算法的计算结果的优越性 .

A time-discontinuous Galerkin finite element method (DGFEM) for structural dynamics and wave propagation problems is presented. The main distinct characteristic of the proposed DGFEM is that the specific P3-P1 interpolation approximation is adopted , which uses piecewise cubic (Hermite's polynomial) and linear interpolations for displacements and velocities, respectively. Consequently, continuity of the displacement vector at each discrete time instant is exactly ensured, whereas discontinuity of the velocity vector at the discrete time levels still remains. The computational cost is then obviously saved, particularly in the materially non-linear problems, as compared with that required to the existing DGFEM. Both the implicit and explicit algorithms to solve the derived formulations for the materially non-linear problems are developed. Numerical results illustrate good performance of the present method in eliminating spurious numerical oscillations and providing with much more accurate solutions over the traditional Galerkin finite element method using the Newmark algorithm in time domain.